diff --git a/GPy/FAQ.txt b/GPy/FAQ.txt deleted file mode 100644 index 66ba4834..00000000 --- a/GPy/FAQ.txt +++ /dev/null @@ -1,8 +0,0 @@ -Frequently Asked Questions --------------------------- - -Unit tests are run through Travis-Ci. They can be run locally through entering the GPy route diretory and writing - -nosetests testing/ - -Documentation is handled by Sphinx. To build the documentation: diff --git a/GPy/__init__.py b/GPy/__init__.py index 47232eb8..5e091170 100644 --- a/GPy/__init__.py +++ b/GPy/__init__.py @@ -2,15 +2,10 @@ # Licensed under the BSD 3-clause license (see LICENSE.txt) import warnings warnings.filterwarnings("ignore", category=DeprecationWarning) -import os - - -def read(fname): - with open(os.path.join(os.path.dirname(__file__), fname)) as f: - return f.read() -__version__ = read('version') import core +from core.parameterization import transformations, priors +constraints = transformations import models import mappings import inference @@ -19,27 +14,36 @@ import examples import likelihoods import testing from numpy.testing import Tester -from nose.tools import nottest import kern -from core import priors +import plotting -@nottest -def tests(): - Tester(testing).test(verbose=10) +# Direct imports for convenience: +from core import Model +from core.parameterization import Param, Parameterized, ObsAr -if os.name == 'nt': +#@nottest +try: + #Get rid of nose dependency by only ignoring if you have nose installed + from nose.tools import nottest + @nottest + def tests(): + Tester(testing).test(verbose=10) +except: + def tests(): + Tester(testing).test(verbose=10) + +def load(file_path): """ - Fortran seems to like to intercept keyboard interrupts on windows. - This means that when a model is optimizing and the user presses Ctrl-C, - the program will crash. Since it's kind of nice to be able to stop - the optimization at any time, we define our own handler below. + Load a previously pickled model, using `m.pickle('path/to/file.pickle)' + :param file_name: path/to/file.pickle """ - import win32api - import thread - - def handler(sig, hook=thread.interrupt_main): - hook() - return 1 - - win32api.SetConsoleCtrlHandler(handler, 1) + import cPickle as pickle + try: + with open(file_path, 'rb') as f: + m = pickle.load(f) + except: + import pickle as pickle + with open(file_path, 'rb') as f: + m = pickle.load(f) + return m diff --git a/GPy/coding_style_guide.txt b/GPy/coding_style_guide.txt deleted file mode 100644 index 0cc732e4..00000000 --- a/GPy/coding_style_guide.txt +++ /dev/null @@ -1,10 +0,0 @@ -In this text document we will describe coding conventions to be used in GPy to keep things consistent. - -All arrays containing data are two dimensional. The first dimension is the number of data, the second dimension is number of features. This keeps things consistent with the idea of a design matrix. - -Input matrices are either X or t, output matrices are Y. - -Input dimensionality is input_dim, output dimensionality is output_dim, number of data is num_data. - -Data sets are preprocessed in the datasets.py file. This file also records where the data set was obtained from in the dictionary stored in the file. Long term we should move this dictionary to sqlite or similar. - diff --git a/GPy/core/__init__.py b/GPy/core/__init__.py index 9813d5ae..a0ee51da 100644 --- a/GPy/core/__init__.py +++ b/GPy/core/__init__.py @@ -1,11 +1,11 @@ -# Copyright (c) 2012, GPy authors (see AUTHORS.txt). +# Copyright (c) 2012-2014, GPy authors (see AUTHORS.txt). # Licensed under the BSD 3-clause license (see LICENSE.txt) from model import * -from parameterized import * -import priors +from parameterization.parameterized import adjust_name_for_printing, Parameterizable +from parameterization.param import Param, ParamConcatenation +from parameterization.observable_array import ObsAr + from gp import GP from sparse_gp import SparseGP -from fitc import FITC -from svigp import SVIGP from mapping import * diff --git a/GPy/core/domains.py b/GPy/core/domains.py deleted file mode 100644 index cefac6c2..00000000 --- a/GPy/core/domains.py +++ /dev/null @@ -1,26 +0,0 @@ -''' -Created on 4 Jun 2013 - -@author: maxz - -(Hyper-)Parameter domains defined for :py:mod:`~GPy.core.priors` and :py:mod:`~GPy.kern`. -These domains specify the legitimate realm of the parameters to live in. - -:const:`~GPy.core.domains.REAL` : - real domain, all values in the real numbers are allowed - -:const:`~GPy.core.domains.POSITIVE`: - positive domain, only positive real values are allowed - -:const:`~GPy.core.domains.NEGATIVE`: - same as :const:`~GPy.core.domains.POSITIVE`, but only negative values are allowed - -:const:`~GPy.core.domains.BOUNDED`: - only values within the bounded range are allowed, - the bounds are specified withing the object with the bounded range -''' - -REAL = 'real' -POSITIVE = "positive" -NEGATIVE = 'negative' -BOUNDED = 'bounded' diff --git a/GPy/core/fitc.py b/GPy/core/fitc.py deleted file mode 100644 index 97b4fb1d..00000000 --- a/GPy/core/fitc.py +++ /dev/null @@ -1,248 +0,0 @@ -# Copyright (c) 2012, GPy authors (see AUTHORS.txt). -# Licensed under the BSD 3-clause license (see LICENSE.txt) - -import numpy as np -import pylab as pb -from ..util.linalg import mdot, jitchol, chol_inv, tdot, symmetrify, pdinv, dtrtrs -from ..util.plot import gpplot -from .. import kern -from scipy import stats -from sparse_gp import SparseGP - -class FITC(SparseGP): - """ - - Sparse FITC approximation - - :param X: inputs - :type X: np.ndarray (num_data x Q) - :param likelihood: a likelihood instance, containing the observed data - :type likelihood: GPy.likelihood.(Gaussian | EP) - :param kernel: the kernel (covariance function). See link kernels - :type kernel: a GPy.kern.kern instance - :param Z: inducing inputs (optional, see note) - :type Z: np.ndarray (M x Q) | None - :param normalize_(X|Y): whether to normalize the data before computing (predictions will be in original scales) - :type normalize_(X|Y): bool - - """ - - def __init__(self, X, likelihood, kernel, Z, normalize_X=False): - SparseGP.__init__(self, X, likelihood, kernel, Z, X_variance=None, normalize_X=False) - assert self.output_dim == 1, "FITC model is not defined for handling multiple outputs" - - def update_likelihood_approximation(self, **kwargs): - """ - Approximates a non-Gaussian likelihood using Expectation Propagation - - For a Gaussian likelihood, no iteration is required: - this function does nothing - """ - self.likelihood.restart() - self.likelihood.fit_FITC(self.Kmm,self.psi1,self.psi0, **kwargs) - self._set_params(self._get_params()) - - def _compute_kernel_matrices(self): - # kernel computations, using BGPLVM notation - self.Kmm = self.kern.K(self.Z) - self.psi0 = self.kern.Kdiag(self.X) - self.psi1 = self.kern.K(self.Z, self.X) - self.psi2 = None - - def _computations(self): - #factor Kmm - self.Lm = jitchol(self.Kmm) - self.Lmi,info = dtrtrs(self.Lm,np.eye(self.num_inducing),lower=1) - Lmipsi1 = np.dot(self.Lmi,self.psi1) - self.Qnn = np.dot(Lmipsi1.T,Lmipsi1).copy() - self.Diag0 = self.psi0 - np.diag(self.Qnn) - self.beta_star = self.likelihood.precision/(1. + self.likelihood.precision*self.Diag0[:,None]) #NOTE: beta_star contains Diag0 and the precision - self.V_star = self.beta_star * self.likelihood.Y - - # The rather complex computations of self.A - tmp = self.psi1 * (np.sqrt(self.beta_star.flatten().reshape(1, self.num_data))) - tmp, _ = dtrtrs(self.Lm, np.asfortranarray(tmp), lower=1) - self.A = tdot(tmp) - - # factor B - self.B = np.eye(self.num_inducing) + self.A - self.LB = jitchol(self.B) - self.LBi = chol_inv(self.LB) - self.psi1V = np.dot(self.psi1, self.V_star) - - Lmi_psi1V, info = dtrtrs(self.Lm, np.asfortranarray(self.psi1V), lower=1, trans=0) - self._LBi_Lmi_psi1V, _ = dtrtrs(self.LB, np.asfortranarray(Lmi_psi1V), lower=1, trans=0) - - Kmmipsi1 = np.dot(self.Lmi.T,Lmipsi1) - b_psi1_Ki = self.beta_star * Kmmipsi1.T - Ki_pbp_Ki = np.dot(Kmmipsi1,b_psi1_Ki) - Kmmi = np.dot(self.Lmi.T,self.Lmi) - LBiLmi = np.dot(self.LBi,self.Lmi) - LBL_inv = np.dot(LBiLmi.T,LBiLmi) - VVT = np.outer(self.V_star,self.V_star) - VV_p_Ki = np.dot(VVT,Kmmipsi1.T) - Ki_pVVp_Ki = np.dot(Kmmipsi1,VV_p_Ki) - psi1beta = self.psi1*self.beta_star.T - H = self.Kmm + mdot(self.psi1,psi1beta.T) - LH = jitchol(H) - LHi = chol_inv(LH) - Hi = np.dot(LHi.T,LHi) - - betapsi1TLmiLBi = np.dot(psi1beta.T,LBiLmi.T) - alpha = np.array([np.dot(a.T,a) for a in betapsi1TLmiLBi])[:,None] - gamma_1 = mdot(VVT,self.psi1.T,Hi) - pHip = mdot(self.psi1.T,Hi,self.psi1) - gamma_2 = mdot(self.beta_star*pHip,self.V_star) - gamma_3 = self.V_star * gamma_2 - - self._dL_dpsi0 = -0.5 * self.beta_star#dA_dpsi0: logdet(self.beta_star) - self._dL_dpsi0 += .5 * self.V_star**2 #dA_psi0: yT*beta_star*y - self._dL_dpsi0 += .5 *alpha #dC_dpsi0 - self._dL_dpsi0 += 0.5*mdot(self.beta_star*pHip,self.V_star)**2 - self.V_star * mdot(self.V_star.T,pHip*self.beta_star).T #dD_dpsi0 - - self._dL_dpsi1 = b_psi1_Ki.copy() #dA_dpsi1: logdet(self.beta_star) - self._dL_dpsi1 += -np.dot(psi1beta.T,LBL_inv) #dC_dpsi1 - self._dL_dpsi1 += gamma_1 - mdot(psi1beta.T,Hi,self.psi1,gamma_1) #dD_dpsi1 - - self._dL_dKmm = -0.5 * np.dot(Kmmipsi1,b_psi1_Ki) #dA_dKmm: logdet(self.beta_star) - self._dL_dKmm += .5*(LBL_inv - Kmmi) + mdot(LBL_inv,psi1beta,Kmmipsi1.T) #dC_dKmm - self._dL_dKmm += -.5 * mdot(Hi,self.psi1,gamma_1) #dD_dKmm - - self._dpsi1_dtheta = 0 - self._dpsi1_dX = 0 - self._dKmm_dtheta = 0 - self._dKmm_dX = 0 - - self._dpsi1_dX_jkj = 0 - self._dpsi1_dtheta_jkj = 0 - - for i,V_n,alpha_n,gamma_n,gamma_k in zip(range(self.num_data),self.V_star,alpha,gamma_2,gamma_3): - K_pp_K = np.dot(Kmmipsi1[:,i:(i+1)],Kmmipsi1[:,i:(i+1)].T) - _dpsi1 = (-V_n**2 - alpha_n + 2.*gamma_k - gamma_n**2) * Kmmipsi1.T[i:(i+1),:] - _dKmm = .5*(V_n**2 + alpha_n + gamma_n**2 - 2.*gamma_k) * K_pp_K #Diag_dD_dKmm - self._dpsi1_dtheta += self.kern.dK_dtheta(_dpsi1,self.X[i:i+1,:],self.Z) - self._dKmm_dtheta += self.kern.dK_dtheta(_dKmm,self.Z) - self._dKmm_dX += self.kern.dK_dX(_dKmm ,self.Z) - self._dpsi1_dX += self.kern.dK_dX(_dpsi1.T,self.Z,self.X[i:i+1,:]) - - # the partial derivative vector for the likelihood - if self.likelihood.num_params == 0: - # save computation here. - self.partial_for_likelihood = None - elif self.likelihood.is_heteroscedastic: - raise NotImplementedError, "heteroscedatic derivates not implemented." - else: - # likelihood is not heterscedatic - dbstar_dnoise = self.likelihood.precision * (self.beta_star**2 * self.Diag0[:,None] - self.beta_star) - Lmi_psi1 = mdot(self.Lmi,self.psi1) - LBiLmipsi1 = np.dot(self.LBi,Lmi_psi1) - aux_0 = np.dot(self._LBi_Lmi_psi1V.T,LBiLmipsi1) - aux_1 = self.likelihood.Y.T * np.dot(self._LBi_Lmi_psi1V.T,LBiLmipsi1) - aux_2 = np.dot(LBiLmipsi1.T,self._LBi_Lmi_psi1V) - - dA_dnoise = 0.5 * self.input_dim * (dbstar_dnoise/self.beta_star).sum() - 0.5 * self.input_dim * np.sum(self.likelihood.Y**2 * dbstar_dnoise) - dC_dnoise = -0.5 * np.sum(mdot(self.LBi.T,self.LBi,Lmi_psi1) * Lmi_psi1 * dbstar_dnoise.T) - - dD_dnoise_1 = mdot(self.V_star*LBiLmipsi1.T,LBiLmipsi1*dbstar_dnoise.T*self.likelihood.Y.T) - alpha = mdot(LBiLmipsi1,self.V_star) - alpha_ = mdot(LBiLmipsi1.T,alpha) - dD_dnoise_2 = -0.5 * self.input_dim * np.sum(alpha_**2 * dbstar_dnoise ) - - dD_dnoise_1 = mdot(self.V_star.T,self.psi1.T,self.Lmi.T,self.LBi.T,self.LBi,self.Lmi,self.psi1,dbstar_dnoise*self.likelihood.Y) - dD_dnoise_2 = 0.5*mdot(self.V_star.T,self.psi1.T,Hi,self.psi1,dbstar_dnoise*self.psi1.T,Hi,self.psi1,self.V_star) - dD_dnoise = dD_dnoise_1 + dD_dnoise_2 - - self.partial_for_likelihood = dA_dnoise + dC_dnoise + dD_dnoise - - def log_likelihood(self): - """ Compute the (lower bound on the) log marginal likelihood """ - A = -0.5 * self.num_data * self.output_dim * np.log(2.*np.pi) + 0.5 * np.sum(np.log(self.beta_star)) - 0.5 * np.sum(self.V_star * self.likelihood.Y) - C = -self.output_dim * (np.sum(np.log(np.diag(self.LB)))) - D = 0.5 * np.sum(np.square(self._LBi_Lmi_psi1V)) - return A + C + D + self.likelihood.Z - - def _log_likelihood_gradients(self): - pass - return np.hstack((self.dL_dZ().flatten(), self.dL_dtheta(), self.likelihood._gradients(partial=self.partial_for_likelihood))) - - def dL_dtheta(self): - dL_dtheta = self.kern.dKdiag_dtheta(self._dL_dpsi0,self.X) - dL_dtheta += self.kern.dK_dtheta(self._dL_dpsi1,self.X,self.Z) - dL_dtheta += self.kern.dK_dtheta(self._dL_dKmm,X=self.Z) - dL_dtheta += self._dKmm_dtheta - dL_dtheta += self._dpsi1_dtheta - return dL_dtheta - - def dL_dZ(self): - dL_dZ = self.kern.dK_dX(self._dL_dpsi1.T,self.Z,self.X) - dL_dZ += self.kern.dK_dX(self._dL_dKmm,X=self.Z) - dL_dZ += self._dpsi1_dX - dL_dZ += self._dKmm_dX - return dL_dZ - - def _raw_predict(self, Xnew, X_variance_new=None, which_parts='all', full_cov=False): - assert X_variance_new is None, "FITC model is not defined for handling uncertain inputs." - - if self.likelihood.is_heteroscedastic: - Iplus_Dprod_i = 1./(1.+ self.Diag0 * self.likelihood.precision.flatten()) - self.Diag = self.Diag0 * Iplus_Dprod_i - self.P = Iplus_Dprod_i[:,None] * self.psi1.T - self.RPT0 = np.dot(self.Lmi,self.psi1) - self.L = np.linalg.cholesky(np.eye(self.num_inducing) + np.dot(self.RPT0,((1. - Iplus_Dprod_i)/self.Diag0)[:,None]*self.RPT0.T)) - self.R,info = dtrtrs(self.L,self.Lmi,lower=1) - self.RPT = np.dot(self.R,self.P.T) - self.Sigma = np.diag(self.Diag) + np.dot(self.RPT.T,self.RPT) - self.w = self.Diag * self.likelihood.v_tilde - self.Gamma = np.dot(self.R.T, np.dot(self.RPT,self.likelihood.v_tilde)) - self.mu = self.w + np.dot(self.P,self.Gamma) - - """ - Make a prediction for the generalized FITC model - - Arguments - --------- - X : Input prediction data - Nx1 numpy array (floats) - """ - # q(u|f) = N(u| R0i*mu_u*f, R0i*C*R0i.T) - - # Ci = I + (RPT0)Di(RPT0).T - # C = I - [RPT0] * (input_dim+[RPT0].T*[RPT0])^-1*[RPT0].T - # = I - [RPT0] * (input_dim + self.Qnn)^-1 * [RPT0].T - # = I - [RPT0] * (U*U.T)^-1 * [RPT0].T - # = I - V.T * V - U = np.linalg.cholesky(np.diag(self.Diag0) + self.Qnn) - V,info = dtrtrs(U,self.RPT0.T,lower=1) - C = np.eye(self.num_inducing) - np.dot(V.T,V) - mu_u = np.dot(C,self.RPT0)*(1./self.Diag0[None,:]) - #self.C = C - #self.RPT0 = np.dot(self.R0,self.Knm.T) P0.T - #self.mu_u = mu_u - #self.U = U - # q(u|y) = N(u| R0i*mu_H,R0i*Sigma_H*R0i.T) - mu_H = np.dot(mu_u,self.mu) - self.mu_H = mu_H - Sigma_H = C + np.dot(mu_u,np.dot(self.Sigma,mu_u.T)) - # q(f_star|y) = N(f_star|mu_star,sigma2_star) - Kx = self.kern.K(self.Z, Xnew, which_parts=which_parts) - KR0T = np.dot(Kx.T,self.Lmi.T) - mu_star = np.dot(KR0T,mu_H) - if full_cov: - Kxx = self.kern.K(Xnew,which_parts=which_parts) - var = Kxx + np.dot(KR0T,np.dot(Sigma_H - np.eye(self.num_inducing),KR0T.T)) - else: - Kxx = self.kern.Kdiag(Xnew,which_parts=which_parts) - var = (Kxx + np.sum(KR0T.T*np.dot(Sigma_H - np.eye(self.num_inducing),KR0T.T),0))[:,None] - return mu_star[:,None],var - else: - raise NotImplementedError, "Heteroscedastic case not implemented." - """ - Kx = self.kern.K(self.Z, Xnew) - mu = mdot(Kx.T, self.C/self.scale_factor, self.psi1V) - if full_cov: - Kxx = self.kern.K(Xnew) - var = Kxx - mdot(Kx.T, (self.Kmmi - self.C/self.scale_factor**2), Kx) #NOTE this won't work for plotting - else: - Kxx = self.kern.Kdiag(Xnew) - var = Kxx - np.sum(Kx*np.dot(self.Kmmi - self.C/self.scale_factor**2, Kx),0) - return mu,var[:,None] - """ diff --git a/GPy/core/gp.py b/GPy/core/gp.py index 0d1b69a0..25066381 100644 --- a/GPy/core/gp.py +++ b/GPy/core/gp.py @@ -1,204 +1,459 @@ -# Copyright (c) 2012, GPy authors (see AUTHORS.txt). +# Copyright (c) 2012-2014, GPy authors (see AUTHORS.txt). # Licensed under the BSD 3-clause license (see LICENSE.txt) - import numpy as np -import pylab as pb +import sys from .. import kern -from ..util.linalg import pdinv, mdot, tdot, dpotrs, dtrtrs -from ..likelihoods import EP, Laplace -from gp_base import GPBase +from model import Model +from parameterization import ObsAr +from .. import likelihoods +from ..inference.latent_function_inference import exact_gaussian_inference, expectation_propagation +from parameterization.variational import VariationalPosterior -class GP(GPBase): +import logging +from GPy.util.normalizer import MeanNorm +logger = logging.getLogger("GP") + +class GP(Model): """ - Gaussian Process model for regression and EP + General purpose Gaussian process model :param X: input observations + :param Y: output observations :param kernel: a GPy kernel, defaults to rbf+white :param likelihood: a GPy likelihood - :param normalize_X: whether to normalize the input data before computing (predictions will be in original scales) - :type normalize_X: False|True + :param inference_method: The :class:`~GPy.inference.latent_function_inference.LatentFunctionInference` inference method to use for this GP :rtype: model object + :param Norm normalizer: + normalize the outputs Y. + Prediction will be un-normalized using this normalizer. + If normalizer is None, we will normalize using MeanNorm. + If normalizer is False, no normalization will be done. .. Note:: Multiple independent outputs are allowed using columns of Y + """ - def __init__(self, X, likelihood, kernel, normalize_X=False): - GPBase.__init__(self, X, likelihood, kernel, normalize_X=normalize_X) - self.update_likelihood_approximation() + def __init__(self, X, Y, kernel, likelihood, inference_method=None, name='gp', Y_metadata=None, normalizer=False): + super(GP, self).__init__(name) + assert X.ndim == 2 + if isinstance(X, (ObsAr, VariationalPosterior)): + self.X = X.copy() + else: self.X = ObsAr(X) - def _set_params(self, p): - new_kern_params = p[:self.kern.num_params_transformed()] - new_likelihood_params = p[self.kern.num_params_transformed():] - old_likelihood_params = self.likelihood._get_params() + self.num_data, self.input_dim = self.X.shape - self.kern._set_params_transformed(new_kern_params) - self.likelihood._set_params_transformed(new_likelihood_params) + assert Y.ndim == 2 + logger.info("initializing Y") - self.K = self.kern.K(self.X) - - #Re fit likelihood approximation (if it is an approx), as parameters have changed - if isinstance(self.likelihood, Laplace): - self.likelihood.fit_full(self.K) - - self.K += self.likelihood.covariance_matrix - - self.Ki, self.L, self.Li, self.K_logdet = pdinv(self.K) - - # the gradient of the likelihood wrt the covariance matrix - if self.likelihood.YYT is None: - # alpha = np.dot(self.Ki, self.likelihood.Y) - alpha, _ = dpotrs(self.L, self.likelihood.Y, lower=1) - - self.dL_dK = 0.5 * (tdot(alpha) - self.output_dim * self.Ki) + if normalizer is True: + self.normalizer = MeanNorm() + elif normalizer is False: + self.normalizer = None else: - # tmp = mdot(self.Ki, self.likelihood.YYT, self.Ki) - tmp, _ = dpotrs(self.L, np.asfortranarray(self.likelihood.YYT), lower=1) - tmp, _ = dpotrs(self.L, np.asfortranarray(tmp.T), lower=1) - self.dL_dK = 0.5 * (tmp - self.output_dim * self.Ki) + self.normalizer = normalizer - #Adding dZ_dK (0 for a non-approximate likelihood, compensates for - #additional gradients of K when log-likelihood has non-zero Z term) - self.dL_dK += self.likelihood.dZ_dK - - def _get_params(self): - return np.hstack((self.kern._get_params_transformed(), self.likelihood._get_params())) - - def _get_param_names(self): - return self.kern._get_param_names_transformed() + self.likelihood._get_param_names() - - def update_likelihood_approximation(self, **kwargs): - """ - Approximates a non-gaussian likelihood using Expectation Propagation - - For a Gaussian likelihood, no iteration is required: - this function does nothing - """ - self.likelihood.restart() - self.likelihood.fit_full(self.kern.K(self.X), **kwargs) - self._set_params(self._get_params()) # update the GP - - def _model_fit_term(self): - """ - Computes the model fit using YYT if it's available - """ - if self.likelihood.YYT is None: - tmp, _ = dtrtrs(self.L, np.asfortranarray(self.likelihood.Y), lower=1) - return -0.5 * np.sum(np.square(tmp)) - # return -0.5 * np.sum(np.square(np.dot(self.Li, self.likelihood.Y))) + if self.normalizer is not None: + self.normalizer.scale_by(Y) + self.Y_normalized = ObsAr(self.normalizer.normalize(Y)) + self.Y = Y else: - return -0.5 * np.sum(np.multiply(self.Ki, self.likelihood.YYT)) + self.Y = ObsAr(Y) + self.Y_normalized = self.Y + + assert Y.shape[0] == self.num_data + _, self.output_dim = self.Y.shape + + #TODO: check the type of this is okay? + self.Y_metadata = Y_metadata + + assert isinstance(kernel, kern.Kern) + #assert self.input_dim == kernel.input_dim + self.kern = kernel + + assert isinstance(likelihood, likelihoods.Likelihood) + self.likelihood = likelihood + + #find a sensible inference method + logger.info("initializing inference method") + if inference_method is None: + if isinstance(likelihood, likelihoods.Gaussian) or isinstance(likelihood, likelihoods.MixedNoise): + inference_method = exact_gaussian_inference.ExactGaussianInference() + else: + inference_method = expectation_propagation.EP() + print "defaulting to ", inference_method, "for latent function inference" + self.inference_method = inference_method + + logger.info("adding kernel and likelihood as parameters") + self.link_parameter(self.kern) + self.link_parameter(self.likelihood) + + def set_XY(self, X=None, Y=None): + """ + Set the input / output data of the model + This is useful if we wish to change our existing data but maintain the same model + + :param X: input observations + :type X: np.ndarray + :param Y: output observations + :type Y: np.ndarray + """ + self.update_model(False) + if Y is not None: + if self.normalizer is not None: + self.normalizer.scale_by(Y) + self.Y_normalized = ObsAr(self.normalizer.normalize(Y)) + self.Y = Y + else: + self.Y = ObsAr(Y) + self.Y_normalized = self.Y + if X is not None: + if self.X in self.parameters: + # LVM models + if isinstance(self.X, VariationalPosterior): + assert isinstance(X, type(self.X)), "The given X must have the same type as the X in the model!" + self.unlink_parameter(self.X) + self.X = X + self.link_parameters(self.X) + else: + self.unlink_parameter(self.X) + from ..core import Param + self.X = Param('latent mean',X) + self.link_parameters(self.X) + else: + self.X = ObsAr(X) + self.update_model(True) + + def set_X(self,X): + """ + Set the input data of the model + + :param X: input observations + :type X: np.ndarray + """ + self.set_XY(X=X) + + def set_Y(self,Y): + """ + Set the output data of the model + + :param X: output observations + :type X: np.ndarray + """ + self.set_XY(Y=Y) + + def parameters_changed(self): + """ + Method that is called upon any changes to :class:`~GPy.core.parameterization.param.Param` variables within the model. + In particular in the GP class this method reperforms inference, recalculating the posterior and log marginal likelihood and gradients of the model + + .. warning:: + This method is not designed to be called manually, the framework is set up to automatically call this method upon changes to parameters, if you call + this method yourself, there may be unexpected consequences. + """ + self.posterior, self._log_marginal_likelihood, self.grad_dict = self.inference_method.inference(self.kern, self.X, self.likelihood, self.Y_normalized, self.Y_metadata) + self.likelihood.update_gradients(self.grad_dict['dL_dthetaL']) + self.kern.update_gradients_full(self.grad_dict['dL_dK'], self.X) def log_likelihood(self): """ - The log marginal likelihood of the GP. + The log marginal likelihood of the model, :math:`p(\mathbf{y})`, this is the objective function of the model being optimised + """ + return self._log_marginal_likelihood - For an EP model, can be written as the log likelihood of a regression - model for a new variable Y* = v_tilde/tau_tilde, with a covariance - matrix K* = K + diag(1./tau_tilde) plus a normalization term. + def _raw_predict(self, _Xnew, full_cov=False, kern=None): """ - return (-0.5 * self.num_data * self.output_dim * np.log(2.*np.pi) - - 0.5 * self.output_dim * self.K_logdet + self._model_fit_term() + self.likelihood.Z) + For making predictions, does not account for normalization or likelihood - def _log_likelihood_gradients(self): - """ - The gradient of all parameters. + full_cov is a boolean which defines whether the full covariance matrix + of the prediction is computed. If full_cov is False (default), only the + diagonal of the covariance is returned. - Note, we use the chain rule: dL_dtheta = dL_dK * d_K_dtheta + .. math:: + p(f*|X*, X, Y) = \int^{\inf}_{\inf} p(f*|f,X*)p(f|X,Y) df + = N(f*| K_{x*x}(K_{xx} + \Sigma)^{-1}Y, K_{x*x*} - K_{xx*}(K_{xx} + \Sigma)^{-1}K_{xx*} + \Sigma := \texttt{Likelihood.variance / Approximate likelihood covariance} """ - return np.hstack((self.kern.dK_dtheta(dL_dK=self.dL_dK, X=self.X), self.likelihood._gradients(partial=np.diag(self.dL_dK)))) + if kern is None: + kern = self.kern - def _raw_predict(self, _Xnew, which_parts='all', full_cov=False, stop=False): - """ - Internal helper function for making predictions, does not account - for normalization or likelihood - """ - Kx = self.kern.K(_Xnew, self.X, which_parts=which_parts).T - # KiKx = np.dot(self.Ki, Kx) - KiKx, _ = dpotrs(self.L, np.asfortranarray(Kx), lower=1) - mu = np.dot(KiKx.T, self.likelihood.Y) + Kx = kern.K(_Xnew, self.X).T + WiKx = np.dot(self.posterior.woodbury_inv, Kx) + mu = np.dot(Kx.T, self.posterior.woodbury_vector) if full_cov: - Kxx = self.kern.K(_Xnew, which_parts=which_parts) - var = Kxx - np.dot(KiKx.T, Kx) + Kxx = kern.K(_Xnew) + var = Kxx - np.dot(Kx.T, WiKx) else: - Kxx = self.kern.Kdiag(_Xnew, which_parts=which_parts) - var = Kxx - np.sum(np.multiply(KiKx, Kx), 0) - var = var[:, None] - if stop: - debug_this # @UndefinedVariable + Kxx = kern.Kdiag(_Xnew) + var = Kxx - np.sum(WiKx*Kx, 0) + var = var.reshape(-1, 1) + + #force mu to be a column vector + if len(mu.shape)==1: mu = mu[:,None] return mu, var - def predict(self, Xnew, which_parts='all', full_cov=False, **likelihood_args): + def predict(self, Xnew, full_cov=False, Y_metadata=None, kern=None): """ Predict the function(s) at the new point(s) Xnew. :param Xnew: The points at which to make a prediction - :type Xnew: np.ndarray, Nnew x self.input_dim - :param which_parts: specifies which outputs kernel(s) to use in prediction - :type which_parts: ('all', list of bools) - :param full_cov: whether to return the full covariance matrix, or just the diagonal + :type Xnew: np.ndarray (Nnew x self.input_dim) + :param full_cov: whether to return the full covariance matrix, or just + the diagonal :type full_cov: bool - :returns: mean: posterior mean, a Numpy array, Nnew x self.input_dim - :returns: var: posterior variance, a Numpy array, Nnew x 1 if full_cov=False, Nnew x Nnew otherwise - :returns: lower and upper boundaries of the 95% confidence intervals, Numpy arrays, Nnew x self.input_dim - + :param Y_metadata: metadata about the predicting point to pass to the likelihood + :param kern: The kernel to use for prediction (defaults to the model + kern). this is useful for examining e.g. subprocesses. + :returns: (mean, var, lower_upper): + mean: posterior mean, a Numpy array, Nnew x self.input_dim + var: posterior variance, a Numpy array, Nnew x 1 if full_cov=False, Nnew x Nnew otherwise + lower_upper: lower and upper boundaries of the 95% confidence intervals, Numpy arrays, Nnew x self.input_dim If full_cov and self.input_dim > 1, the return shape of var is Nnew x Nnew x self.input_dim. If self.input_dim == 1, the return shape is Nnew x Nnew. This is to allow for different normalizations of the output dimensions. - """ - # normalize X values - Xnew = (Xnew.copy() - self._Xoffset) / self._Xscale - mu, var = self._raw_predict(Xnew, full_cov=full_cov, which_parts=which_parts) + #predict the latent function values + mu, var = self._raw_predict(Xnew, full_cov=full_cov, kern=kern) + if self.normalizer is not None: + mu, var = self.normalizer.inverse_mean(mu), self.normalizer.inverse_variance(var) # now push through likelihood - mean, var, _025pm, _975pm = self.likelihood.predictive_values(mu, var, full_cov, **likelihood_args) - return mean, var, _025pm, _975pm + mean, var = self.likelihood.predictive_values(mu, var, full_cov, Y_metadata) + return mean, var - def _raw_predict_single_output(self, _Xnew, output, which_parts='all', full_cov=False,stop=False): + def predict_quantiles(self, X, quantiles=(2.5, 97.5), Y_metadata=None): """ - For a specific output, calls _raw_predict() at the new point(s) _Xnew. - This functions calls _add_output_index(), so _Xnew should not have an index column specifying the output. - --------- + Get the predictive quantiles around the prediction at X - :param Xnew: The points at which to make a prediction - :type Xnew: np.ndarray, Nnew x self.input_dim - :param output: output to predict - :type output: integer in {0,..., output_dim-1} - :param which_parts: specifies which outputs kernel(s) to use in prediction - :type which_parts: ('all', list of bools) - :param full_cov: whether to return the full covariance matrix, or just the diagonal - - .. Note:: For multiple non-independent outputs models only. + :param X: The points at which to make a prediction + :type X: np.ndarray (Xnew x self.input_dim) + :param quantiles: tuple of quantiles, default is (2.5, 97.5) which is the 95% interval + :type quantiles: tuple + :returns: list of quantiles for each X and predictive quantiles for interval combination + :rtype: [np.ndarray (Xnew x self.input_dim), np.ndarray (Xnew x self.input_dim)] """ - _Xnew = self._add_output_index(_Xnew, output) - return self._raw_predict(_Xnew, which_parts=which_parts,full_cov=full_cov, stop=stop) + m, v = self._raw_predict(X, full_cov=False) + if self.normalizer is not None: + m, v = self.normalizer.inverse_mean(m), self.normalizer.inverse_variance(v) + return self.likelihood.predictive_quantiles(m, v, quantiles, Y_metadata) - def predict_single_output(self, Xnew,output=0, which_parts='all', full_cov=False, likelihood_args=dict()): + def predictive_gradients(self, Xnew): """ - For a specific output, calls predict() at the new point(s) Xnew. - This functions calls _add_output_index(), so Xnew should not have an index column specifying the output. + Compute the derivatives of the latent function with respect to X* - :param Xnew: The points at which to make a prediction - :type Xnew: np.ndarray, Nnew x self.input_dim - :param which_parts: specifies which outputs kernel(s) to use in prediction - :type which_parts: ('all', list of bools) - :param full_cov: whether to return the full covariance matrix, or just the diagonal - :type full_cov: bool - :returns: mean: posterior mean, a Numpy array, Nnew x self.input_dim - :returns: var: posterior variance, a Numpy array, Nnew x 1 if full_cov=False, Nnew x Nnew otherwise - :returns: lower and upper boundaries of the 95% confidence intervals, Numpy arrays, Nnew x self.input_dim + Given a set of points at which to predict X* (size [N*,Q]), compute the + derivatives of the mean and variance. Resulting arrays are sized: + dmu_dX* -- [N*, Q ,D], where D is the number of output in this GP (usually one). + + dv_dX* -- [N*, Q], (since all outputs have the same variance) + :param X: The points at which to get the predictive gradients + :type X: np.ndarray (Xnew x self.input_dim) + :returns: dmu_dX, dv_dX + :rtype: [np.ndarray (N*, Q ,D), np.ndarray (N*,Q) ] - .. Note:: For multiple non-independent outputs models only. """ - Xnew = self._add_output_index(Xnew, output) - return self.predict(Xnew, which_parts=which_parts, full_cov=full_cov, likelihood_args=likelihood_args) + dmu_dX = np.empty((Xnew.shape[0],Xnew.shape[1],self.output_dim)) + for i in range(self.output_dim): + dmu_dX[:,:,i] = self.kern.gradients_X(self.posterior.woodbury_vector[:,i:i+1].T, Xnew, self.X) - def getstate(self): - return GPBase.getstate(self) + # gradients wrt the diagonal part k_{xx} + dv_dX = self.kern.gradients_X(np.eye(Xnew.shape[0]), Xnew) + #grads wrt 'Schur' part K_{xf}K_{ff}^{-1}K_{fx} + alpha = -2.*np.dot(self.kern.K(Xnew, self.X),self.posterior.woodbury_inv) + dv_dX += self.kern.gradients_X(alpha, Xnew, self.X) + return dmu_dX, dv_dX - def setstate(self, state): - GPBase.setstate(self, state) - self._set_params(self._get_params()) + def posterior_samples_f(self,X,size=10, full_cov=True): + """ + Samples the posterior GP at the points X. + + :param X: The points at which to take the samples. + :type X: np.ndarray (Nnew x self.input_dim) + :param size: the number of a posteriori samples. + :type size: int. + :param full_cov: whether to return the full covariance matrix, or just the diagonal. + :type full_cov: bool. + :returns: Ysim: set of simulations + :rtype: np.ndarray (N x samples) + """ + m, v = self._raw_predict(X, full_cov=full_cov) + if self.normalizer is not None: + m, v = self.normalizer.inverse_mean(m), self.normalizer.inverse_variance(v) + v = v.reshape(m.size,-1) if len(v.shape)==3 else v + if not full_cov: + Ysim = np.random.multivariate_normal(m.flatten(), np.diag(v.flatten()), size).T + else: + Ysim = np.random.multivariate_normal(m.flatten(), v, size).T + + return Ysim + + def posterior_samples(self, X, size=10, full_cov=False, Y_metadata=None): + """ + Samples the posterior GP at the points X. + + :param X: the points at which to take the samples. + :type X: np.ndarray (Nnew x self.input_dim.) + :param size: the number of a posteriori samples. + :type size: int. + :param full_cov: whether to return the full covariance matrix, or just the diagonal. + :type full_cov: bool. + :param noise_model: for mixed noise likelihood, the noise model to use in the samples. + :type noise_model: integer. + :returns: Ysim: set of simulations, a Numpy array (N x samples). + """ + Ysim = self.posterior_samples_f(X, size, full_cov=full_cov) + Ysim = self.likelihood.samples(Ysim, Y_metadata) + + return Ysim + + def plot_f(self, plot_limits=None, which_data_rows='all', + which_data_ycols='all', fixed_inputs=[], + levels=20, samples=0, fignum=None, ax=None, resolution=None, + plot_raw=True, + linecol=None,fillcol=None, Y_metadata=None, data_symbol='kx'): + """ + Plot the GP's view of the world, where the data is normalized and before applying a likelihood. + This is a call to plot with plot_raw=True. + Data will not be plotted in this, as the GP's view of the world + may live in another space, or units then the data. + + Can plot only part of the data and part of the posterior functions + using which_data_rowsm which_data_ycols. + + :param plot_limits: The limits of the plot. If 1D [xmin,xmax], if 2D [[xmin,ymin],[xmax,ymax]]. Defaluts to data limits + :type plot_limits: np.array + :param which_data_rows: which of the training data to plot (default all) + :type which_data_rows: 'all' or a slice object to slice model.X, model.Y + :param which_data_ycols: when the data has several columns (independant outputs), only plot these + :type which_data_ycols: 'all' or a list of integers + :param fixed_inputs: a list of tuple [(i,v), (i,v)...], specifying that input index i should be set to value v. + :type fixed_inputs: a list of tuples + :param resolution: the number of intervals to sample the GP on. Defaults to 200 in 1D and 50 (a 50x50 grid) in 2D + :type resolution: int + :param levels: number of levels to plot in a contour plot. + :param levels: for 2D plotting, the number of contour levels to use is ax is None, create a new figure + :type levels: int + :param samples: the number of a posteriori samples to plot + :type samples: int + :param fignum: figure to plot on. + :type fignum: figure number + :param ax: axes to plot on. + :type ax: axes handle + :param linecol: color of line to plot [Tango.colorsHex['darkBlue']] + :type linecol: color either as Tango.colorsHex object or character ('r' is red, 'g' is green) as is standard in matplotlib + :param fillcol: color of fill [Tango.colorsHex['lightBlue']] + :type fillcol: color either as Tango.colorsHex object or character ('r' is red, 'g' is green) as is standard in matplotlib + :param Y_metadata: additional data associated with Y which may be needed + :type Y_metadata: dict + :param data_symbol: symbol as used matplotlib, by default this is a black cross ('kx') + :type data_symbol: color either as Tango.colorsHex object or character ('r' is red, 'g' is green) alongside marker type, as is standard in matplotlib. + """ + assert "matplotlib" in sys.modules, "matplotlib package has not been imported." + from ..plotting.matplot_dep import models_plots + kw = {} + if linecol is not None: + kw['linecol'] = linecol + if fillcol is not None: + kw['fillcol'] = fillcol + return models_plots.plot_fit(self, plot_limits, which_data_rows, + which_data_ycols, fixed_inputs, + levels, samples, fignum, ax, resolution, + plot_raw=plot_raw, Y_metadata=Y_metadata, + data_symbol=data_symbol, **kw) + + def plot(self, plot_limits=None, which_data_rows='all', + which_data_ycols='all', fixed_inputs=[], + levels=20, samples=0, fignum=None, ax=None, resolution=None, + plot_raw=False, + linecol=None,fillcol=None, Y_metadata=None, data_symbol='kx'): + """ + Plot the posterior of the GP. + - In one dimension, the function is plotted with a shaded region identifying two standard deviations. + - In two dimsensions, a contour-plot shows the mean predicted function + - In higher dimensions, use fixed_inputs to plot the GP with some of the inputs fixed. + + Can plot only part of the data and part of the posterior functions + using which_data_rowsm which_data_ycols. + + :param plot_limits: The limits of the plot. If 1D [xmin,xmax], if 2D [[xmin,ymin],[xmax,ymax]]. Defaluts to data limits + :type plot_limits: np.array + :param which_data_rows: which of the training data to plot (default all) + :type which_data_rows: 'all' or a slice object to slice model.X, model.Y + :param which_data_ycols: when the data has several columns (independant outputs), only plot these + :type which_data_ycols: 'all' or a list of integers + :param fixed_inputs: a list of tuple [(i,v), (i,v)...], specifying that input index i should be set to value v. + :type fixed_inputs: a list of tuples + :param resolution: the number of intervals to sample the GP on. Defaults to 200 in 1D and 50 (a 50x50 grid) in 2D + :type resolution: int + :param levels: number of levels to plot in a contour plot. + :param levels: for 2D plotting, the number of contour levels to use is ax is None, create a new figure + :type levels: int + :param samples: the number of a posteriori samples to plot + :type samples: int + :param fignum: figure to plot on. + :type fignum: figure number + :param ax: axes to plot on. + :type ax: axes handle + :param linecol: color of line to plot [Tango.colorsHex['darkBlue']] + :type linecol: color either as Tango.colorsHex object or character ('r' is red, 'g' is green) as is standard in matplotlib + :param fillcol: color of fill [Tango.colorsHex['lightBlue']] + :type fillcol: color either as Tango.colorsHex object or character ('r' is red, 'g' is green) as is standard in matplotlib + :param Y_metadata: additional data associated with Y which may be needed + :type Y_metadata: dict + :param data_symbol: symbol as used matplotlib, by default this is a black cross ('kx') + :type data_symbol: color either as Tango.colorsHex object or character ('r' is red, 'g' is green) alongside marker type, as is standard in matplotlib. + """ + assert "matplotlib" in sys.modules, "matplotlib package has not been imported." + from ..plotting.matplot_dep import models_plots + kw = {} + if linecol is not None: + kw['linecol'] = linecol + if fillcol is not None: + kw['fillcol'] = fillcol + return models_plots.plot_fit(self, plot_limits, which_data_rows, + which_data_ycols, fixed_inputs, + levels, samples, fignum, ax, resolution, + plot_raw=plot_raw, Y_metadata=Y_metadata, + data_symbol=data_symbol, **kw) + + def input_sensitivity(self, summarize=True): + """ + Returns the sensitivity for each dimension of this model + """ + return self.kern.input_sensitivity(summarize=summarize) + + def optimize(self, optimizer=None, start=None, **kwargs): + """ + Optimize the model using self.log_likelihood and self.log_likelihood_gradient, as well as self.priors. + kwargs are passed to the optimizer. They can be: + + :param max_f_eval: maximum number of function evaluations + :type max_f_eval: int + :messages: whether to display during optimisation + :type messages: bool + :param optimizer: which optimizer to use (defaults to self.preferred optimizer), a range of optimisers can be found in :module:`~GPy.inference.optimization`, they include 'scg', 'lbfgs', 'tnc'. + :type optimizer: string + """ + self.inference_method.on_optimization_start() + try: + super(GP, self).optimize(optimizer, start, **kwargs) + except KeyboardInterrupt: + print "KeyboardInterrupt caught, calling on_optimization_end() to round things up" + self.inference_method.on_optimization_end() + raise + + def infer_newX(self, Y_new, optimize=True, ): + """ + Infer the distribution of X for the new observed data *Y_new*. + + :param Y_new: the new observed data for inference + :type Y_new: numpy.ndarray + :param optimize: whether to optimize the location of new X (True by default) + :type optimize: boolean + :return: a tuple containing the posterior estimation of X and the model that optimize X + :rtype: (:class:`~GPy.core.parameterization.variational.VariationalPosterior` or numpy.ndarray, :class:`~GPy.core.model.Model`) + """ + from ..inference.latent_function_inference.inferenceX import infer_newX + return infer_newX(self, Y_new, optimize=optimize) diff --git a/GPy/core/gp_base.py b/GPy/core/gp_base.py deleted file mode 100644 index 7d58c82c..00000000 --- a/GPy/core/gp_base.py +++ /dev/null @@ -1,275 +0,0 @@ -import numpy as np -from .. import kern -from ..util.plot import gpplot, Tango, x_frame1D, x_frame2D -import pylab as pb -from GPy.core.model import Model -import warnings -from ..likelihoods import Gaussian, Gaussian_Mixed_Noise - -class GPBase(Model): - """ - Gaussian process base model for holding shared behaviour between - sparse_GP and GP models, and potentially other models in the future. - - Here we define some functions that are use - """ - def __init__(self, X, likelihood, kernel, normalize_X=False): - if len(X.shape)==1: - X = X.reshape(-1,1) - warnings.warn("One dimension output (N,) being reshaped to (N,1)") - self.X = X - assert len(self.X.shape) == 2, "too many dimensions for X input" - self.num_data, self.input_dim = self.X.shape - assert isinstance(kernel, kern.kern) - self.kern = kernel - self.likelihood = likelihood - assert self.X.shape[0] == self.likelihood.data.shape[0] - self.num_data, self.output_dim = self.likelihood.data.shape - - if normalize_X: - self._Xoffset = X.mean(0)[None, :] - self._Xscale = X.std(0)[None, :] - self.X = (X.copy() - self._Xoffset) / self._Xscale - else: - self._Xoffset = np.zeros((1, self.input_dim)) - self._Xscale = np.ones((1, self.input_dim)) - - super(GPBase, self).__init__() - # Model.__init__(self) - # All leaf nodes should call self._set_params(self._get_params()) at - # the end - - - def posterior_samples_f(self,X,size=10,which_parts='all'): - """ - Samples the posterior GP at the points X. - - :param X: The points at which to take the samples. - :type X: np.ndarray, Nnew x self.input_dim. - :param size: the number of a posteriori samples to plot. - :type size: int. - :param which_parts: which of the kernel functions to plot (additively). - :type which_parts: 'all', or list of bools. - :param full_cov: whether to return the full covariance matrix, or just the diagonal. - :type full_cov: bool. - :returns: Ysim: set of simulations, a Numpy array (N x samples). - """ - m, v = self._raw_predict(X, which_parts=which_parts, full_cov=True) - v = v.reshape(m.size,-1) if len(v.shape)==3 else v - Ysim = np.random.multivariate_normal(m.flatten(), v, size).T - - return Ysim - - def posterior_samples(self,X,size=10,which_parts='all',noise_model=None): - """ - Samples the posterior GP at the points X. - - :param X: the points at which to take the samples. - :type X: np.ndarray, Nnew x self.input_dim. - :param size: the number of a posteriori samples to plot. - :type size: int. - :param which_parts: which of the kernel functions to plot (additively). - :type which_parts: 'all', or list of bools. - :param full_cov: whether to return the full covariance matrix, or just the diagonal. - :type full_cov: bool. - :param noise_model: for mixed noise likelihood, the noise model to use in the samples. - :type noise_model: integer. - :returns: Ysim: set of simulations, a Numpy array (N x samples). - """ - Ysim = self.posterior_samples_f(X, size, which_parts=which_parts) - if isinstance(self.likelihood,Gaussian): - noise_std = np.sqrt(self.likelihood._get_params()) - Ysim += np.random.normal(0,noise_std,Ysim.shape) - elif isinstance(self.likelihood,Gaussian_Mixed_Noise): - assert noise_model is not None, "A noise model must be specified." - noise_std = np.sqrt(self.likelihood._get_params()[noise_model]) - Ysim += np.random.normal(0,noise_std,Ysim.shape) - else: - Ysim = self.likelihood.noise_model.samples(Ysim) - - return Ysim - - def plot_f(self, *args, **kwargs): - """ - Plot the GP's view of the world, where the data is normalized and before applying a likelihood. - - This is a convenience function: we simply call self.plot with the - argument use_raw_predict set True. All args and kwargs are passed on to - plot. - - see also: gp_base.plot - """ - kwargs['plot_raw'] = True - self.plot(*args, **kwargs) - - def plot(self, plot_limits=None, which_data_rows='all', - which_data_ycols='all', which_parts='all', fixed_inputs=[], - levels=20, samples=0, fignum=None, ax=None, resolution=None, - plot_raw=False, - linecol=Tango.colorsHex['darkBlue'],fillcol=Tango.colorsHex['lightBlue']): - """ - Plot the posterior of the GP. - - In one dimension, the function is plotted with a shaded region identifying two standard deviations. - - In two dimsensions, a contour-plot shows the mean predicted function - - In higher dimensions, use fixed_inputs to plot the GP with some of the inputs fixed. - - Can plot only part of the data and part of the posterior functions - using which_data_rowsm which_data_ycols and which_parts - - :param plot_limits: The limits of the plot. If 1D [xmin,xmax], if 2D [[xmin,ymin],[xmax,ymax]]. Defaluts to data limits - :type plot_limits: np.array - :param which_data_rows: which of the training data to plot (default all) - :type which_data_rows: 'all' or a slice object to slice self.X, self.Y - :param which_data_ycols: when the data has several columns (independant outputs), only plot these - :type which_data_rows: 'all' or a list of integers - :param which_parts: which of the kernel functions to plot (additively) - :type which_parts: 'all', or list of bools - :param fixed_inputs: a list of tuple [(i,v), (i,v)...], specifying that input index i should be set to value v. - :type fixed_inputs: a list of tuples - :param resolution: the number of intervals to sample the GP on. Defaults to 200 in 1D and 50 (a 50x50 grid) in 2D - :type resolution: int - :param levels: number of levels to plot in a contour plot. - :type levels: int - :param samples: the number of a posteriori samples to plot - :type samples: int - :param fignum: figure to plot on. - :type fignum: figure number - :param ax: axes to plot on. - :type ax: axes handle - :type output: integer (first output is 0) - :param linecol: color of line to plot. - :type linecol: - :param fillcol: color of fill - :param levels: for 2D plotting, the number of contour levels to use is ax is None, create a new figure - """ - #deal with optional arguments - if which_data_rows == 'all': - which_data_rows = slice(None) - if which_data_ycols == 'all': - which_data_ycols = np.arange(self.output_dim) - if len(which_data_ycols)==0: - raise ValueError('No data selected for plotting') - if ax is None: - fig = pb.figure(num=fignum) - ax = fig.add_subplot(111) - - #work out what the inputs are for plotting (1D or 2D) - fixed_dims = np.array([i for i,v in fixed_inputs]) - free_dims = np.setdiff1d(np.arange(self.input_dim),fixed_dims) - - #one dimensional plotting - if len(free_dims) == 1: - - #define the frame on which to plot - resolution = resolution or 200 - Xu = self.X * self._Xscale + self._Xoffset #NOTE self.X are the normalized values now - Xnew, xmin, xmax = x_frame1D(Xu[:,free_dims], plot_limits=plot_limits) - Xgrid = np.empty((Xnew.shape[0],self.input_dim)) - Xgrid[:,free_dims] = Xnew - for i,v in fixed_inputs: - Xgrid[:,i] = v - - #make a prediction on the frame and plot it - if plot_raw: - m, v = self._raw_predict(Xgrid, which_parts=which_parts) - lower = m - 2*np.sqrt(v) - upper = m + 2*np.sqrt(v) - Y = self.likelihood.Y - else: - m, v, lower, upper = self.predict(Xgrid, which_parts=which_parts, sampling=False) #Compute the exact mean - m_, v_, lower, upper = self.predict(Xgrid, which_parts=which_parts, sampling=True, num_samples=15000) #Apporximate the percentiles - Y = self.likelihood.data - for d in which_data_ycols: - gpplot(Xnew, m[:, d], lower[:, d], upper[:, d], axes=ax, edgecol=linecol, fillcol=fillcol) - ax.plot(Xu[which_data_rows,free_dims], Y[which_data_rows, d], 'kx', mew=1.5) - - #optionally plot some samples - if samples: #NOTE not tested with fixed_inputs - Ysim = self.posterior_samples(Xgrid, samples, which_parts=which_parts) - for yi in Ysim.T: - ax.plot(Xnew, yi[:,None], Tango.colorsHex['darkBlue'], linewidth=0.25) - #ax.plot(Xnew, yi[:,None], marker='x', linestyle='--',color=Tango.colorsHex['darkBlue']) #TODO apply this line for discrete outputs. - - #set the limits of the plot to some sensible values - ymin, ymax = min(np.append(Y[which_data_rows, which_data_ycols].flatten(), lower)), max(np.append(Y[which_data_rows, which_data_ycols].flatten(), upper)) - ymin, ymax = ymin - 0.1 * (ymax - ymin), ymax + 0.1 * (ymax - ymin) - ax.set_xlim(xmin, xmax) - ax.set_ylim(ymin, ymax) - - #2D plotting - elif len(free_dims) == 2: - - #define the frame for plotting on - resolution = resolution or 50 - Xu = self.X * self._Xscale + self._Xoffset #NOTE self.X are the normalized values now - Xnew, _, _, xmin, xmax = x_frame2D(Xu[:,free_dims], plot_limits, resolution) - Xgrid = np.empty((Xnew.shape[0],self.input_dim)) - Xgrid[:,free_dims] = Xnew - for i,v in fixed_inputs: - Xgrid[:,i] = v - x, y = np.linspace(xmin[0], xmax[0], resolution), np.linspace(xmin[1], xmax[1], resolution) - - #predict on the frame and plot - if plot_raw: - m, _ = self._raw_predict(Xgrid, which_parts=which_parts) - Y = self.likelihood.Y - else: - m, _, _, _ = self.predict(Xgrid, which_parts=which_parts,sampling=False) - Y = self.likelihood.data - for d in which_data_ycols: - m_d = m[:,d].reshape(resolution, resolution).T - contour = ax.contour(x, y, m_d, levels, vmin=m.min(), vmax=m.max(), cmap=pb.cm.jet) - scatter = ax.scatter(self.X[which_data_rows, free_dims[0]], self.X[which_data_rows, free_dims[1]], 40, Y[which_data_rows, d], cmap=pb.cm.jet, vmin=m.min(), vmax=m.max(), linewidth=0.) - - #set the limits of the plot to some sensible values - ax.set_xlim(xmin[0], xmax[0]) - ax.set_ylim(xmin[1], xmax[1]) - - if samples: - warnings.warn("Samples are rather difficult to plot for 2D inputs...") - return contour, scatter - else: - raise NotImplementedError, "Cannot define a frame with more than two input dimensions" - - def getstate(self): - """ - Get the curent state of the class. This is only used to efficiently - pickle the model. See also self.setstate - """ - return Model.getstate(self) + [self.X, - self.num_data, - self.input_dim, - self.kern, - self.likelihood, - self.output_dim, - self._Xoffset, - self._Xscale] - - def setstate(self, state): - """ - Set the state of the model. Used for efficient pickling - """ - self._Xscale = state.pop() - self._Xoffset = state.pop() - self.output_dim = state.pop() - self.likelihood = state.pop() - self.kern = state.pop() - self.input_dim = state.pop() - self.num_data = state.pop() - self.X = state.pop() - Model.setstate(self, state) - - def log_predictive_density(self, x_test, y_test): - """ - Calculation of the log predictive density - - .. math: - p(y_{*}|D) = p(y_{*}|f_{*})p(f_{*}|\mu_{*}\\sigma^{2}_{*}) - - :param x_test: test observations (x_{*}) - :type x_test: (Nx1) array - :param y_test: test observations (y_{*}) - :type y_test: (Nx1) array - """ - mu_star, var_star = self._raw_predict(x_test) - return self.likelihood.log_predictive_density(y_test, mu_star, var_star) diff --git a/GPy/core/mapping.py b/GPy/core/mapping.py index 7b2c89b9..111fec6f 100644 --- a/GPy/core/mapping.py +++ b/GPy/core/mapping.py @@ -1,24 +1,19 @@ -# Copyright (c) 2013, GPy authors (see AUTHORS.txt). +# Copyright (c) 2013,2014, GPy authors (see AUTHORS.txt). # Licensed under the BSD 3-clause license (see LICENSE.txt) -from ..util.plot import Tango, x_frame1D, x_frame2D -from parameterized import Parameterized +import sys +from parameterization import Parameterized import numpy as np -import pylab as pb class Mapping(Parameterized): """ - Base model for shared behavior between models that can act like a mapping. + Base model for shared behavior between models that can act like a mapping. """ - def __init__(self, input_dim, output_dim): + def __init__(self, input_dim, output_dim, name='mapping'): self.input_dim = input_dim self.output_dim = output_dim - - super(Mapping, self).__init__() - # Model.__init__(self) - # All leaf nodes should call self._set_params(self._get_params()) at - # the end + super(Mapping, self).__init__(name=name) def f(self, X): raise NotImplementedError @@ -35,7 +30,8 @@ class Mapping(Parameterized): raise NotImplementedError def df_dtheta(self, dL_df, X): - """The gradient of the outputs of the multi-layer perceptron with respect to each of the parameters. + """The gradient of the outputs of the mapping with respect to each of the parameters. + :param dL_df: gradient of the objective with respect to the function. :type dL_df: ndarray (num_data x output_dim) :param X: input locations where the function is evaluated. @@ -43,85 +39,42 @@ class Mapping(Parameterized): :returns: Matrix containing gradients with respect to parameters of each output for each input data. :rtype: ndarray (num_params length) """ + raise NotImplementedError - def plot(self, plot_limits=None, which_data='all', which_parts='all', resolution=None, levels=20, samples=0, fignum=None, ax=None, fixed_inputs=[], linecol=Tango.colorsHex['darkBlue']): + def plot(self, *args): """ - - Plot the mapping. - Plots the mapping associated with the model. - In one dimension, the function is plotted. - - In two dimsensions, a contour-plot shows the function + - In two dimensions, a contour-plot shows the function - In higher dimensions, we've not implemented this yet !TODO! Can plot only part of the data and part of the posterior functions using which_data and which_functions - :param plot_limits: The limits of the plot. If 1D [xmin,xmax], if 2D [[xmin,ymin],[xmax,ymax]]. Defaluts to data limits - :type plot_limits: np.array - :param which_data: which if the training data to plot (default all) - :type which_data: 'all' or a slice object to slice self.X, self.Y - :param which_parts: which of the kernel functions to plot (additively) - :type which_parts: 'all', or list of bools - :param resolution: the number of intervals to sample the GP on. Defaults to 200 in 1D and 50 (a 50x50 grid) in 2D - :type resolution: int - :param levels: number of levels to plot in a contour plot. - :type levels: int - :param samples: the number of a posteriori samples to plot - :type samples: int - :param fignum: figure to plot on. - :type fignum: figure number - :param ax: axes to plot on. - :type ax: axes handle - :param fixed_inputs: a list of tuple [(i,v), (i,v)...], specifying that input index i should be set to value v. - :type fixed_inputs: a list of tuples - :param linecol: color of line to plot. - :type linecol: - :param levels: for 2D plotting, the number of contour levels to use is ax is None, create a new figure - + This is a convenience function: arguments are passed to + GPy.plotting.matplot_dep.models_plots.plot_mapping """ - # TODO include samples - if which_data == 'all': - which_data = slice(None) - - if ax is None: - fig = pb.figure(num=fignum) - ax = fig.add_subplot(111) - - plotdims = self.input_dim - len(fixed_inputs) - - if plotdims == 1: - - Xu = self.X * self._Xscale + self._Xoffset # NOTE self.X are the normalized values now - - fixed_dims = np.array([i for i,v in fixed_inputs]) - freedim = np.setdiff1d(np.arange(self.input_dim),fixed_dims) - - Xnew, xmin, xmax = x_frame1D(Xu[:,freedim], plot_limits=plot_limits) - Xgrid = np.empty((Xnew.shape[0],self.input_dim)) - Xgrid[:,freedim] = Xnew - for i,v in fixed_inputs: - Xgrid[:,i] = v - - f = self.predict(Xgrid, which_parts=which_parts) - for d in range(y.shape[1]): - ax.plot(Xnew, f[:, d], edgecol=linecol) - - elif self.X.shape[1] == 2: - resolution = resolution or 50 - Xnew, _, _, xmin, xmax = x_frame2D(self.X, plot_limits, resolution) - x, y = np.linspace(xmin[0], xmax[0], resolution), np.linspace(xmin[1], xmax[1], resolution) - f = self.predict(Xnew, which_parts=which_parts) - m = m.reshape(resolution, resolution).T - ax.contour(x, y, f, levels, vmin=m.min(), vmax=m.max(), cmap=pb.cm.jet) # @UndefinedVariable - ax.set_xlim(xmin[0], xmax[0]) - ax.set_ylim(xmin[1], xmax[1]) + if "matplotlib" in sys.modules: + from ..plotting.matplot_dep import models_plots + mapping_plots.plot_mapping(self,*args) else: - raise NotImplementedError, "Cannot define a frame with more than two input dimensions" + raise NameError, "matplotlib package has not been imported." -from GPy.core.model import Model +class Bijective_mapping(Mapping): + """ + This is a mapping that is bijective, i.e. you can go from X to f and + also back from f to X. The inverse mapping is called g(). + """ + def __init__(self, input_dim, output_dim, name='bijective_mapping'): + super(Bijective_apping, self).__init__(name=name) + + def g(self, f): + """Inverse mapping from output domain of the function to the inputs.""" + raise NotImplementedError + +from model import Model class Mapping_check_model(Model): """ diff --git a/GPy/core/model.py b/GPy/core/model.py index 6fbc9623..2cdecdf9 100644 --- a/GPy/core/model.py +++ b/GPy/core/model.py @@ -1,182 +1,35 @@ -# Copyright (c) 2012, 2013, GPy authors (see AUTHORS.txt). +# Copyright (c) 2012-2014, GPy authors (see AUTHORS.txt). # Licensed under the BSD 3-clause license (see LICENSE.txt) from .. import likelihoods from ..inference import optimization -from ..util.linalg import jitchol -from GPy.util.misc import opt_wrapper -from parameterized import Parameterized +from ..util.misc import opt_wrapper +from parameterization import Parameterized import multiprocessing as mp import numpy as np -from GPy.core.domains import POSITIVE, REAL from numpy.linalg.linalg import LinAlgError +import itertools # import numdifftools as ndt class Model(Parameterized): - _fail_count = 0 # Count of failed optimization steps (see objective) - _allowed_failures = 10 # number of allowed failures - def __init__(self): - Parameterized.__init__(self) - self.priors = None + _fail_count = 0 # Count of failed optimization steps (see objective) + _allowed_failures = 10 # number of allowed failures + + def __init__(self, name): + super(Model, self).__init__(name) # Parameterized.__init__(self) self.optimization_runs = [] self.sampling_runs = [] - self.preferred_optimizer = 'scg' - # self._set_params(self._get_params()) has been taken out as it should only be called on leaf nodes + self.preferred_optimizer = 'bfgs' + from .parameterization.ties_and_remappings import Tie + self.tie = Tie() + self.link_parameter(self.tie, -1) + self.add_observer(self.tie, self.tie._parameters_changed_notification, priority=-500) + def log_likelihood(self): raise NotImplementedError, "this needs to be implemented to use the model class" def _log_likelihood_gradients(self): - raise NotImplementedError, "this needs to be implemented to use the model class" - - def getstate(self): - """ - Get the current state of the class. - Inherited from Parameterized, so add those parameters to the state - - :return: list of states from the model. - - """ - return Parameterized.getstate(self) + \ - [self.priors, self.optimization_runs, - self.sampling_runs, self.preferred_optimizer] - - def setstate(self, state): - """ - set state from previous call to getstate - call Parameterized with the rest of the state - - :param state: the state of the model. - :type state: list as returned from getstate. - - """ - self.preferred_optimizer = state.pop() - self.sampling_runs = state.pop() - self.optimization_runs = state.pop() - self.priors = state.pop() - Parameterized.setstate(self, state) - - def set_prior(self, regexp, what): - """ - - Sets priors on the model parameters. - - **Notes** - - Asserts that the prior is suitable for the constraint. If the - wrong constraint is in place, an error is raised. If no - constraint is in place, one is added (warning printed). - - For tied parameters, the prior will only be "counted" once, thus - a prior object is only inserted on the first tied index - - :param regexp: regular expression of parameters on which priors need to be set. - :type param: string, regexp, or integer array - :param what: prior to set on parameter. - :type what: GPy.core.Prior type - - """ - if self.priors is None: - self.priors = [None for i in range(self._get_params().size)] - - which = self.grep_param_names(regexp) - - # check tied situation - tie_partial_matches = [tie for tie in self.tied_indices if (not set(tie).isdisjoint(set(which))) & (not set(tie) == set(which))] - if len(tie_partial_matches): - raise ValueError, "cannot place prior across partial ties" - tie_matches = [tie for tie in self.tied_indices if set(which) == set(tie) ] - if len(tie_matches) > 1: - raise ValueError, "cannot place prior across multiple ties" - elif len(tie_matches) == 1: - which = which[:1] # just place a prior object on the first parameter - - - # check constraints are okay - - if what.domain is POSITIVE: - constrained_positive_indices = [i for i, t in zip(self.constrained_indices, self.constraints) if t.domain is POSITIVE] - if len(constrained_positive_indices): - constrained_positive_indices = np.hstack(constrained_positive_indices) - else: - constrained_positive_indices = np.zeros(shape=(0,)) - bad_constraints = np.setdiff1d(self.all_constrained_indices(), constrained_positive_indices) - assert not np.any(which[:, None] == bad_constraints), "constraint and prior incompatible" - unconst = np.setdiff1d(which, constrained_positive_indices) - if len(unconst): - print "Warning: constraining parameters to be positive:" - print '\n'.join([n for i, n in enumerate(self._get_param_names()) if i in unconst]) - print '\n' - self.constrain_positive(unconst) - elif what.domain is REAL: - assert not np.any(which[:, None] == self.all_constrained_indices()), "constraint and prior incompatible" - else: - raise ValueError, "prior not recognised" - - # store the prior in a local list - for w in which: - self.priors[w] = what - - def get_gradient(self, name, return_names=False): - """ - Get model gradient(s) by name. The name is applied as a regular expression and all parameters that match that regular expression are returned. - - :param name: the name of parameters required (as a regular expression). - :type name: regular expression - :param return_names: whether or not to return the names matched (default False) - :type return_names: bool - """ - matches = self.grep_param_names(name) - if len(matches): - if return_names: - return self._log_likelihood_gradients()[matches], np.asarray(self._get_param_names())[matches].tolist() - else: - return self._log_likelihood_gradients()[matches] - else: - raise AttributeError, "no parameter matches %s" % name - - def log_prior(self): - """evaluate the prior""" - if self.priors is not None: - return np.sum([p.lnpdf(x) for p, x in zip(self.priors, self._get_params()) if p is not None]) - else: - return 0. - - def _log_prior_gradients(self): - """evaluate the gradients of the priors""" - if self.priors is None: - return 0. - x = self._get_params() - ret = np.zeros(x.size) - [np.put(ret, i, p.lnpdf_grad(xx)) for i, (p, xx) in enumerate(zip(self.priors, x)) if not p is None] - return ret - - def _transform_gradients(self, g): - x = self._get_params() - for index, constraint in zip(self.constrained_indices, self.constraints): - g[index] = g[index] * constraint.gradfactor(x[index]) - [np.put(g, i, v) for i, v in [(t[0], np.sum(g[t])) for t in self.tied_indices]] - if len(self.tied_indices) or len(self.fixed_indices): - to_remove = np.hstack((self.fixed_indices + [t[1:] for t in self.tied_indices])) - return np.delete(g, to_remove) - else: - return g - - def randomize(self): - """ - Randomize the model. - Make this draw from the prior if one exists, else draw from N(0,1) - """ - # first take care of all parameters (from N(0,1)) - x = self._get_params_transformed() - x = np.random.randn(x.size) - self._set_params_transformed(x) - # now draw from prior where possible - x = self._get_params() - if self.priors is not None: - [np.put(x, i, p.rvs(1)) for i, p in enumerate(self.priors) if not p is None] - self._set_params(x) - self._set_params_transformed(self._get_params_transformed()) # makes sure all of the tied parameters get the same init (since there's only one prior object...) - + return self.gradient def optimize_restarts(self, num_restarts=10, robust=False, verbose=True, parallel=False, num_processes=None, **kwargs): """ @@ -207,10 +60,12 @@ class Model(Parameterized): :param messages: whether to display during optimisation :type messages: bool - .. note:: If num_processes is None, the number of workes in the multiprocessing pool is automatically set to the number of processors on the current machine. + .. note:: If num_processes is None, the number of workes in the + multiprocessing pool is automatically set to the number of processors + on the current machine. """ - initial_parameters = self._get_params_transformed() + initial_parameters = self.optimizer_array.copy() if parallel: try: @@ -221,8 +76,8 @@ class Model(Parameterized): job = pool.apply_async(opt_wrapper, args=(self,), kwds=kwargs) jobs.append(job) - pool.close() # signal that no more data coming in - pool.join() # wait for all the tasks to complete + pool.close() # signal that no more data coming in + pool.join() # wait for all the tasks to complete except KeyboardInterrupt: print "Ctrl+c received, terminating and joining pool." pool.terminate() @@ -246,11 +101,11 @@ class Model(Parameterized): if len(self.optimization_runs): i = np.argmin([o.f_opt for o in self.optimization_runs]) - self._set_params_transformed(self.optimization_runs[i].x_opt) + self.optimizer_array = self.optimization_runs[i].x_opt else: - self._set_params_transformed(initial_parameters) + self.optimizer_array = initial_parameters - def ensure_default_constraints(self): + def ensure_default_constraints(self, warning=True): """ Ensure that any variables which should clearly be positive have been constrained somehow. The method performs a regular @@ -258,183 +113,164 @@ class Model(Parameterized): 'variance', 'lengthscale', 'precision' and 'kappa'. If any of these terms are present in the name the parameter is constrained positive. - """ - positive_strings = ['variance', 'lengthscale', 'precision', 'decay', 'kappa'] - # param_names = self._get_param_names() - currently_constrained = self.all_constrained_indices() - to_make_positive = [] - for s in positive_strings: - for i in self.grep_param_names(".*" + s): - if not (i in currently_constrained): - to_make_positive.append(i) - if len(to_make_positive): - self.constrain_positive(np.asarray(to_make_positive)) - def objective_function(self, x): + DEPRECATED. + """ + raise DeprecationWarning, 'parameters now have default constraints' + + def objective_function(self): + """ + The objective function for the given algorithm. + + This function is the true objective, which wants to be minimized. + Note that all parameters are already set and in place, so you just need + to return the objective function here. + + For probabilistic models this is the negative log_likelihood + (including the MAP prior), so we return it here. If your model is not + probabilistic, just return your objective to minimize here! + """ + return -float(self.log_likelihood()) - self.log_prior() + + def objective_function_gradients(self): + """ + The gradients for the objective function for the given algorithm. + The gradients are w.r.t. the *negative* objective function, as + this framework works with *negative* log-likelihoods as a default. + + You can find the gradient for the parameters in self.gradient at all times. + This is the place, where gradients get stored for parameters. + + This function is the true objective, which wants to be minimized. + Note that all parameters are already set and in place, so you just need + to return the gradient here. + + For probabilistic models this is the gradient of the negative log_likelihood + (including the MAP prior), so we return it here. If your model is not + probabilistic, just return your *negative* gradient here! + """ + return -(self._log_likelihood_gradients() + self._log_prior_gradients()) + + def _grads(self, x): + """ + Gets the gradients from the likelihood and the priors. + + Failures are handled robustly. The algorithm will try several times to + return the gradients, and will raise the original exception if + the objective cannot be computed. + + :param x: the parameters of the model. + :type x: np.array + """ + try: + # self._set_params_transformed(x) + self.optimizer_array = x + obj_grads = self._transform_gradients(self.objective_function_gradients()) + self._fail_count = 0 + except (LinAlgError, ZeroDivisionError, ValueError): + if self._fail_count >= self._allowed_failures: + raise + self._fail_count += 1 + obj_grads = np.clip(self._transform_gradients(self.objective_function_gradients()), -1e100, 1e100) + return obj_grads + + def _objective(self, x): """ The objective function passed to the optimizer. It combines the likelihood and the priors. Failures are handled robustly. The algorithm will try several times to - return the objective, and will raise the original exception if it + return the objective, and will raise the original exception if the objective cannot be computed. :param x: the parameters of the model. :parameter type: np.array """ try: - self._set_params_transformed(x) + self.optimizer_array = x + obj = self.objective_function() self._fail_count = 0 - except (LinAlgError, ZeroDivisionError, ValueError) as e: + except (LinAlgError, ZeroDivisionError, ValueError): if self._fail_count >= self._allowed_failures: - raise e + raise self._fail_count += 1 return np.inf - return -self.log_likelihood() - self.log_prior() + return obj - def objective_function_gradients(self, x): - """ - Gets the gradients from the likelihood and the priors. - - Failures are handled robustly. The algorithm will try several times to - return the gradients, and will raise the original exception if it - the objective cannot be computed. - - :param x: the parameters of the model. - :parameter type: np.array - """ + def _objective_grads(self, x): try: - self._set_params_transformed(x) - obj_grads = -self._transform_gradients(self._log_likelihood_gradients() + self._log_prior_gradients()) + self.optimizer_array = x + obj_f, obj_grads = self.objective_function(), self._transform_gradients(self.objective_function_gradients()) self._fail_count = 0 - except (LinAlgError, ZeroDivisionError, ValueError) as e: + except (LinAlgError, ZeroDivisionError, ValueError): if self._fail_count >= self._allowed_failures: - raise e - self._fail_count += 1 - obj_grads = np.clip(-self._transform_gradients(self._log_likelihood_gradients() + self._log_prior_gradients()), -1e100, 1e100) - return obj_grads - - def objective_and_gradients(self, x): - """ - Compute the objective function of the model and the gradient of the model at the point given by x. - - :param x: the point at which gradients are to be computed. - :type np.array: - """ - - try: - self._set_params_transformed(x) - obj_f = -self.log_likelihood() - self.log_prior() - self._fail_count = 0 - obj_grads = -self._transform_gradients(self._log_likelihood_gradients() + self._log_prior_gradients()) - except (LinAlgError, ZeroDivisionError, ValueError) as e: - if self._fail_count >= self._allowed_failures: - raise e + raise self._fail_count += 1 obj_f = np.inf - obj_grads = np.clip(-self._transform_gradients(self._log_likelihood_gradients() + self._log_prior_gradients()), -1e100, 1e100) + obj_grads = np.clip(self._transform_gradients(self.objective_function_gradients()), -1e100, 1e100) return obj_f, obj_grads def optimize(self, optimizer=None, start=None, **kwargs): """ Optimize the model using self.log_likelihood and self.log_likelihood_gradient, as well as self.priors. + kwargs are passed to the optimizer. They can be: :param max_f_eval: maximum number of function evaluations :type max_f_eval: int :messages: whether to display during optimisation :type messages: bool - :param optimzer: which optimizer to use (defaults to self.preferred optimizer) - :type optimzer: string TODO: valid strings? + :param optimizer: which optimizer to use (defaults to self.preferred optimizer) + :type optimizer: string + + Valid optimizers are: + - 'scg': scaled conjugate gradient method, recommended for stability. + See also GPy.inference.optimization.scg + - 'fmin_tnc': truncated Newton method (see scipy.optimize.fmin_tnc) + - 'simplex': the Nelder-Mead simplex method (see scipy.optimize.fmin), + - 'lbfgsb': the l-bfgs-b method (see scipy.optimize.fmin_l_bfgs_b), + - 'sgd': stochastic gradient decsent (see scipy.optimize.sgd). For experts only! + + """ + if self.is_fixed: + print 'nothing to optimize' + if self.size == 0: + print 'nothing to optimize' + + if not self.update_model(): + print "setting updates on again" + self.update_model(True) + + if start == None: + start = self.optimizer_array + if optimizer is None: optimizer = self.preferred_optimizer - if start == None: - start = self._get_params_transformed() + if isinstance(optimizer, optimization.Optimizer): + opt = optimizer + opt.model = self + else: + optimizer = optimization.get_optimizer(optimizer) + opt = optimizer(start, model=self, **kwargs) - optimizer = optimization.get_optimizer(optimizer) - opt = optimizer(start, model=self, **kwargs) - - opt.run(f_fp=self.objective_and_gradients, f=self.objective_function, fp=self.objective_function_gradients) + opt.run(f_fp=self._objective_grads, f=self._objective, fp=self._grads) self.optimization_runs.append(opt) - self._set_params_transformed(opt.x_opt) + self.optimizer_array = opt.x_opt def optimize_SGD(self, momentum=0.1, learning_rate=0.01, iterations=20, **kwargs): # assert self.Y.shape[1] > 1, "SGD only works with D > 1" - sgd = SGD.StochasticGD(self, iterations, learning_rate, momentum, **kwargs) # @UndefinedVariable + sgd = SGD.StochasticGD(self, iterations, learning_rate, momentum, **kwargs) # @UndefinedVariable sgd.run() self.optimization_runs.append(sgd) - def Laplace_covariance(self): - """return the covariance matrix of a Laplace approximation at the current (stationary) point.""" - # TODO add in the prior contributions for MAP estimation - # TODO fix the hessian for tied, constrained and fixed components - if hasattr(self, 'log_likelihood_hessian'): - A = -self.log_likelihood_hessian() - - else: - print "numerically calculating Hessian. please be patient!" - x = self._get_params() - def f(x): - self._set_params(x) - return self.log_likelihood() - h = ndt.Hessian(f) # @UndefinedVariable - A = -h(x) - self._set_params(x) - # check for almost zero components on the diagonal which screw up the cholesky - aa = np.nonzero((np.diag(A) < 1e-6) & (np.diag(A) > 0.))[0] - A[aa, aa] = 0. - return A - - def Laplace_evidence(self): - """Returns an estiamte of the model evidence based on the Laplace approximation. - Uses a numerical estimate of the Hessian if none is available analytically.""" - A = self.Laplace_covariance() - try: - hld = np.sum(np.log(np.diag(jitchol(A)[0]))) - except: - return np.nan - return 0.5 * self._get_params().size * np.log(2 * np.pi) + self.log_likelihood() - hld - - def __str__(self): - s = Parameterized.__str__(self).split('\n') - #def __str__(self, names=None): - # if names is None: - # names = self._get_print_names() - #s = Parameterized.__str__(self, names=names).split('\n') - # add priors to the string - if self.priors is not None: - strs = [str(p) if p is not None else '' for p in self.priors] - else: - strs = [''] * len(self._get_params()) - # strs = [''] * len(self._get_param_names()) - # name_indices = self.grep_param_names("|".join(names)) - # strs = np.array(strs)[name_indices] - width = np.array(max([len(p) for p in strs] + [5])) + 4 - - log_like = self.log_likelihood() - log_prior = self.log_prior() - obj_funct = '\nLog-likelihood: {0:.3e}'.format(log_like) - if len(''.join(strs)) != 0: - obj_funct += ', Log prior: {0:.3e}, LL+prior = {0:.3e}'.format(log_prior, log_like + log_prior) - obj_funct += '\n\n' - s[0] = obj_funct + s[0] - s[0] += "|{h:^{col}}".format(h='prior', col=width) - s[1] += '-' * (width + 1) - - for p in range(2, len(strs) + 2): - s[p] += '|{prior:^{width}}'.format(prior=strs[p - 2], width=width) - - return '\n'.join(s) - - - def checkgrad(self, target_param=None, verbose=False, step=1e-6, tolerance=1e-3): + def _checkgrad(self, target_param=None, verbose=False, step=1e-6, tolerance=1e-3, df_tolerance=1e-12): """ Check the gradient of the ,odel by comparing to a numerical - estimate. If the verbose flag is passed, invividual + estimate. If the verbose flag is passed, individual components are tested (and printed) :param verbose: If True, print a "full" checking of each parameter @@ -447,37 +283,54 @@ class Model(Parameterized): Note:- The gradient is considered correct if the ratio of the analytical and numerical gradients is within of unity. - """ - x = self._get_params_transformed().copy() + The *dF_ratio* indicates the limit of numerical accuracy of numerical gradients. + If it is too small, e.g., smaller than 1e-12, the numerical gradients are usually + not accurate enough for the tests (shown with blue). + """ + x = self.optimizer_array.copy() if not verbose: - # just check the global ratio - - #choose a random direction to find the linear approximation in - if x.size==2: - dx = step * np.ones(2) # random direction for 2 parameters can fail dure to symmetry + # make sure only to test the selected parameters + if target_param is None: + transformed_index = range(len(x)) else: - dx = step * np.sign(np.random.uniform(-1, 1, x.size)) + transformed_index = self._raveled_index_for(target_param) + if self._has_fixes(): + indices = np.r_[:self.size] + which = (transformed_index[:, None] == indices[self._fixes_][None, :]).nonzero() + transformed_index = (indices - (~self._fixes_).cumsum())[transformed_index[which[0]]] + + if transformed_index.size == 0: + print "No free parameters to check" + return + + # just check the global ratio + dx = np.zeros(x.shape) + dx[transformed_index] = step * (np.sign(np.random.uniform(-1, 1, transformed_index.size)) if transformed_index.size != 2 else 1.) # evaulate around the point x - f1, g1 = self.objective_and_gradients(x + dx) - f2, g2 = self.objective_and_gradients(x - dx) - gradient = self.objective_function_gradients(x) + f1 = self._objective(x + dx) + f2 = self._objective(x - dx) + gradient = self._grads(x) - numerical_gradient = (f1 - f2) / (2 * dx) - global_ratio = (f1 - f2) / (2 * np.dot(dx, np.where(gradient==0, 1e-32, gradient))) + dx = dx[transformed_index] + gradient = gradient[transformed_index] - return (np.abs(1. - global_ratio) < tolerance) or (np.abs(gradient - numerical_gradient).mean() < tolerance) + denominator = (2 * np.dot(dx, gradient)) + global_ratio = (f1 - f2) / np.where(denominator == 0., 1e-32, denominator) + global_diff = np.abs(f1 - f2) < tolerance and np.allclose(gradient, 0, atol=tolerance) + if global_ratio is np.nan: + global_ratio = 0 + return np.abs(1. - global_ratio) < tolerance or global_diff else: # check the gradient of each parameter individually, and do some pretty printing try: - names = self._get_param_names_transformed() + names = self._get_param_names() except NotImplementedError: names = ['Variable %i' % i for i in range(len(x))] - # Prepare for pretty-printing - header = ['Name', 'Ratio', 'Difference', 'Analytical', 'Numerical'] + header = ['Name', 'Ratio', 'Difference', 'Analytical', 'Numerical', 'dF_ratio'] max_names = max([len(names[i]) for i in range(len(names))] + [len(header[0])]) float_len = 10 cols = [max_names] @@ -487,115 +340,77 @@ class Model(Parameterized): header_string = map(lambda x: '|'.join(x), [header_string]) separator = '-' * len(header_string[0]) print '\n'.join([header_string[0], separator]) - if target_param is None: - param_list = range(len(x)) + param_index = range(len(x)) + transformed_index = param_index else: - param_list = self.grep_param_names(target_param, transformed=True, search=True) - if not np.any(param_list): + param_index = self._raveled_index_for(target_param) + if self._has_fixes(): + indices = np.r_[:self.size] + which = (param_index[:, None] == indices[self._fixes_][None, :]).nonzero() + param_index = param_index[which[0]] + transformed_index = (indices - (~self._fixes_).cumsum())[param_index] + # print param_index, transformed_index + else: + transformed_index = param_index + + if param_index.size == 0: print "No free parameters to check" return - - for i in param_list: + gradient = self._grads(x).copy() + np.where(gradient == 0, 1e-312, gradient) + ret = True + for nind, xind in itertools.izip(param_index, transformed_index): xx = x.copy() - xx[i] += step - f1, g1 = self.objective_and_gradients(xx) - xx[i] -= 2.*step - f2, g2 = self.objective_and_gradients(xx) - gradient = self.objective_function_gradients(x)[i] - + xx[xind] += step + f1 = self._objective(xx) + xx[xind] -= 2.*step + f2 = self._objective(xx) + df_ratio = np.abs((f1-f2)/min(f1,f2)) + df_unstable = df_ratioModel', self.name + '
'], + ['Log-likelihood', '{}
'.format(float(self.log_likelihood()))], + ["Number of Parameters", '{}
'.format(self.size)]] + from operator import itemgetter + to_print = [""] + ["{}: {}".format(name, detail) for name, detail in model_details] + ["
Parameters:"] + to_print.append(super(Model, self)._repr_html_()) + return "\n".join(to_print) - if not hasattr(self, 'kern'): - raise ValueError, "this model has no kernel" + def __str__(self): + model_details = [['Name', self.name], + ['Log-likelihood', '{}'.format(float(self.log_likelihood()))], + ["Number of Parameters", '{}'.format(self.size)]] + from operator import itemgetter + max_len = reduce(lambda a, b: max(len(b[0]), a), model_details, 0) + to_print = [""] + ["{0:{l}} : {1}".format(name, detail, l=max_len) for name, detail in model_details] + ["Parameters:"] + to_print.append(super(Model, self).__str__()) + return "\n".join(to_print) - k = [p for p in self.kern.parts if p.name in ['rbf', 'linear', 'rbf_inv']] - if (not len(k) == 1) or (not k[0].ARD): - raise ValueError, "cannot determine sensitivity for this kernel" - k = k[0] - - if k.name == 'rbf': - return 1. / k.lengthscale - elif k.name == 'rbf_inv': - return k.inv_lengthscale - elif k.name == 'linear': - return k.variances - - - def pseudo_EM(self, stop_crit=.1, **kwargs): - """ - EM - like algorithm for Expectation Propagation and Laplace approximation - - :param stop_crit: convergence criterion - :type stop_crit: float - - .. Note: kwargs are passed to update_likelihood and optimize functions. - """ - assert isinstance(self.likelihood, (likelihoods.EP, likelihoods.EP_Mixed_Noise, likelihoods.Laplace)), "pseudo_EM is only available for approximate likelihoods" - ll_change = stop_crit + 1. - iteration = 0 - last_ll = -np.inf - - convergence = False - alpha = 0 - stop = False - - #Handle **kwargs - ep_args = {} - for arg in kwargs.keys(): - if arg in ('epsilon','power_ep'): - ep_args[arg] = kwargs[arg] - del kwargs[arg] - - while not stop: - last_approximation = self.likelihood.copy() - last_params = self._get_params() - if len(ep_args) == 2: - self.update_likelihood_approximation(epsilon=ep_args['epsilon'],power_ep=ep_args['power_ep']) - elif len(ep_args) == 1: - if ep_args.keys()[0] == 'epsilon': - self.update_likelihood_approximation(epsilon=ep_args['epsilon']) - elif ep_args.keys()[0] == 'power_ep': - self.update_likelihood_approximation(power_ep=ep_args['power_ep']) - else: - self.update_likelihood_approximation() - new_ll = self.log_likelihood() - ll_change = new_ll - last_ll - - if ll_change < 0: - self.likelihood = last_approximation # restore previous likelihood approximation - self._set_params(last_params) # restore model parameters - print "Log-likelihood decrement: %s \nLast likelihood update discarded." % ll_change - stop = True - else: - self.optimize(**kwargs) - last_ll = self.log_likelihood() - if ll_change < stop_crit: - stop = True - iteration += 1 - if stop: - print "%s iterations." % iteration - self.update_likelihood_approximation() diff --git a/GPy/core/parameterization/__init__.py b/GPy/core/parameterization/__init__.py new file mode 100644 index 00000000..8e9aa094 --- /dev/null +++ b/GPy/core/parameterization/__init__.py @@ -0,0 +1,5 @@ +# Copyright (c) 2012, GPy authors (see AUTHORS.txt). +# Licensed under the BSD 3-clause license (see LICENSE.txt) + +from param import Param, ObsAr +from parameterized import Parameterized diff --git a/GPy/core/parameterization/domains.py b/GPy/core/parameterization/domains.py new file mode 100644 index 00000000..c04b414f --- /dev/null +++ b/GPy/core/parameterization/domains.py @@ -0,0 +1,25 @@ +# Copyright (c) 2012, GPy authors (see AUTHORS.txt). +# Licensed under the BSD 3-clause license (see LICENSE.txt) + +""" +(Hyper-)Parameter domains defined for :py:mod:`~GPy.core.priors` and :py:mod:`~GPy.kern`. +These domains specify the legitimate realm of the parameters to live in. + +:const:`~GPy.core.domains._REAL` : + real domain, all values in the real numbers are allowed + +:const:`~GPy.core.domains._POSITIVE`: + positive domain, only positive real values are allowed + +:const:`~GPy.core.domains._NEGATIVE`: + same as :const:`~GPy.core.domains._POSITIVE`, but only negative values are allowed + +:const:`~GPy.core.domains._BOUNDED`: + only values within the bounded range are allowed, + the bounds are specified withing the object with the bounded range +""" + +_REAL = 'real' +_POSITIVE = "positive" +_NEGATIVE = 'negative' +_BOUNDED = 'bounded' diff --git a/GPy/core/parameterization/index_operations.py b/GPy/core/parameterization/index_operations.py new file mode 100644 index 00000000..61c82da1 --- /dev/null +++ b/GPy/core/parameterization/index_operations.py @@ -0,0 +1,302 @@ +# Copyright (c) 2014, Max Zwiessele +# Licensed under the BSD 3-clause license (see LICENSE.txt) + +import numpy +from numpy.lib.function_base import vectorize +from lists_and_dicts import IntArrayDict + +def extract_properties_to_index(index, props): + prop_index = dict() + for i, cl in enumerate(props): + for c in cl: + ind = prop_index.get(c, list()) + ind.append(index[i]) + prop_index[c] = ind + + for c, i in prop_index.items(): + prop_index[c] = numpy.array(i, dtype=int) + + return prop_index + + +class ParameterIndexOperations(object): + """ + This object wraps a dictionary, whos keys are _operations_ that we'd like + to apply to a parameter array, and whose values are np integer arrays which + index the parameter array appropriately. + + A model instance will contain one instance of this class for each thing + that needs indexing (i.e. constraints, ties and priors). Parameters within + the model constain instances of the ParameterIndexOperationsView class, + which can map from a 'local' index (starting 0) to this global index. + + Here's an illustration: + + #======================================================================= + model : 0 1 2 3 4 5 6 7 8 9 + key1: 4 5 + key2: 7 8 + + param1: 0 1 2 3 4 5 + key1: 2 3 + key2: 5 + + param2: 0 1 2 3 4 + key1: 0 + key2: 2 3 + #======================================================================= + + The views of this global index have a subset of the keys in this global + (model) index. + + Adding a new key (e.g. a constraint) to a view will cause the view to pass + the new key to the global index, along with the local index and an offset. + This global index then stores the key and the appropriate global index + (which can be seen by the view). + + See also: + ParameterIndexOperationsView + + """ + _offset = 0 + def __init__(self, constraints=None): + self._properties = IntArrayDict() + if constraints is not None: + for t, i in constraints.iteritems(): + self.add(t, i) + + def iteritems(self): + return self._properties.iteritems() + + def items(self): + return self._properties.items() + + def properties(self): + return self._properties.keys() + + def iterproperties(self): + return self._properties.iterkeys() + + def shift_right(self, start, size): + for ind in self.iterindices(): + toshift = ind>=start + ind[toshift] += size + + def shift_left(self, start, size): + for v, ind in self.items(): + todelete = (ind>=start) * (ind=start + if toshift.size != 0: + ind[toshift] -= size + if ind.size != 0: self._properties[v] = ind + else: del self._properties[v] + + def clear(self): + self._properties.clear() + + @property + def size(self): + return reduce(lambda a,b: a+b.size, self.iterindices(), 0) + + def iterindices(self): + return self._properties.itervalues() + + def indices(self): + return self._properties.values() + + def properties_for(self, index): + """ + Returns a list of properties, such that each entry in the list corresponds + to the element of the index given. + + Example: + let properties: 'one':[1,2,3,4], 'two':[3,5,6] + + >>> properties_for([2,3,5]) + [['one'], ['one', 'two'], ['two']] + """ + return vectorize(lambda i: [prop for prop in self.iterproperties() if i in self[prop]], otypes=[list])(index) + + def properties_to_index_dict(self, index): + """ + Return a dictionary, containing properties as keys and indices as index + Thus, the indices for each constraint, which is contained will be collected as + one dictionary + + Example: + let properties: 'one':[1,2,3,4], 'two':[3,5,6] + + >>> properties_to_index_dict([2,3,5]) + {'one':[2,3], 'two':[3,5]} + """ + props = self.properties_for(index) + prop_index = extract_properties_to_index(index, props) + return prop_index + + def add(self, prop, indices): + self._properties[prop] = combine_indices(self._properties[prop], indices) + + def remove(self, prop, indices): + if prop in self._properties: + diff = remove_indices(self[prop], indices) + removed = numpy.intersect1d(self[prop], indices, True) + if not index_empty(diff): + self._properties[prop] = diff + else: + del self._properties[prop] + return removed.astype(int) + return numpy.array([]).astype(int) + + def update(self, parameter_index_view, offset=0): + for i, v in parameter_index_view.iteritems(): + self.add(i, v+offset) + + def copy(self): + return self.__deepcopy__(None) + + def __deepcopy__(self, memo): + return ParameterIndexOperations(dict(self.iteritems())) + + def __getitem__(self, prop): + return self._properties[prop] + + def __delitem__(self, prop): + del self._properties[prop] + + def __str__(self, *args, **kwargs): + import pprint + return pprint.pformat(dict(self._properties)) + +def combine_indices(arr1, arr2): + return numpy.union1d(arr1, arr2) + +def remove_indices(arr, to_remove): + return numpy.setdiff1d(arr, to_remove, True) + +def index_empty(index): + return numpy.size(index) == 0 + +class ParameterIndexOperationsView(object): + def __init__(self, param_index_operations, offset, size): + self._param_index_ops = param_index_operations + self._offset = offset + self._size = size + + def __getstate__(self): + return [self._param_index_ops, self._offset, self._size] + + def __setstate__(self, state): + self._param_index_ops = state[0] + self._offset = state[1] + self._size = state[2] + + def _filter_index(self, ind): + return ind[(ind >= self._offset) * (ind < (self._offset + self._size))] - self._offset + + + def iteritems(self): + for i, ind in self._param_index_ops.iteritems(): + ind2 = self._filter_index(ind) + if ind2.size > 0: + yield i, ind2 + + def items(self): + return [[i,v] for i,v in self.iteritems()] + + def properties(self): + return [i for i in self.iterproperties()] + + + def iterproperties(self): + for i, _ in self.iteritems(): + yield i + + + def shift_right(self, start, size): + self._param_index_ops.shift_right(start+self._offset, size) + + def shift_left(self, start, size): + self._param_index_ops.shift_left(start+self._offset, size) + + def clear(self): + for i, ind in self.items(): + self._param_index_ops.remove(i, ind+self._offset) + + @property + def size(self): + return reduce(lambda a,b: a+b.size, self.iterindices(), 0) + + + def iterindices(self): + for _, ind in self.iteritems(): + yield ind + + + def indices(self): + return [ind for ind in self.iterindices()] + + + def properties_for(self, index): + """ + Returns a list of properties, such that each entry in the list corresponds + to the element of the index given. + + Example: + let properties: 'one':[1,2,3,4], 'two':[3,5,6] + + >>> properties_for([2,3,5]) + [['one'], ['one', 'two'], ['two']] + """ + return vectorize(lambda i: [prop for prop in self.iterproperties() if i in self[prop]], otypes=[list])(index) + + def properties_to_index_dict(self, index): + """ + Return a dictionary, containing properties as keys and indices as index + Thus, the indices for each constraint, which is contained will be collected as + one dictionary + + Example: + let properties: 'one':[1,2,3,4], 'two':[3,5,6] + + >>> properties_to_index_dict([2,3,5]) + {'one':[2,3], 'two':[3,5]} + """ + return extract_properties_to_index(index, self.properties_for(index)) + + + def add(self, prop, indices): + self._param_index_ops.add(prop, indices+self._offset) + + + def remove(self, prop, indices): + removed = self._param_index_ops.remove(prop, numpy.array(indices)+self._offset) + if removed.size > 0: + return removed-self._offset + return removed + + + def __getitem__(self, prop): + ind = self._filter_index(self._param_index_ops[prop]) + return ind + + def __delitem__(self, prop): + self.remove(prop, self[prop]) + + def __str__(self, *args, **kwargs): + import pprint + return pprint.pformat(dict(self.iteritems())) + + def update(self, parameter_index_view, offset=0): + for i, v in parameter_index_view.iteritems(): + self.add(i, v+offset) + + + def copy(self): + return self.__deepcopy__(None) + + def __deepcopy__(self, memo): + return ParameterIndexOperations(dict(self.iteritems())) + pass + diff --git a/GPy/core/parameterization/lists_and_dicts.py b/GPy/core/parameterization/lists_and_dicts.py new file mode 100644 index 00000000..5afbb8ed --- /dev/null +++ b/GPy/core/parameterization/lists_and_dicts.py @@ -0,0 +1,139 @@ +# Copyright (c) 2014, Max Zwiessele +# Licensed under the BSD 3-clause license (see LICENSE.txt) + +from collections import defaultdict +import weakref + +def intarray_default_factory(): + import numpy as np + return np.int_([]) + +class IntArrayDict(defaultdict): + def __init__(self, default_factory=None): + """ + Default will be self._default, if not set otherwise + """ + defaultdict.__init__(self, intarray_default_factory) + +class ArrayList(list): + """ + List to store ndarray-likes in. + It will look for 'is' instead of calling __eq__ on each element. + """ + def __contains__(self, other): + for el in self: + if el is other: + return True + return False + + def index(self, item): + index = 0 + for el in self: + if el is item: + return index + index += 1 + raise ValueError, "{} is not in list".format(item) + pass + +class ObserverList(object): + """ + A list which containts the observables. + It only holds weak references to observers, such that unbound + observers dont dangle in memory. + """ + def __init__(self): + self._poc = [] + + def __getitem__(self, ind): + p,o,c = self._poc[ind] + return p, o(), c + + def remove(self, priority, observer, callble): + """ + Remove one observer, which had priority and callble. + """ + self.flush() + for i in range(len(self) - 1, -1, -1): + p,o,c = self[i] + if priority==p and observer==o and callble==c: + del self._poc[i] + + def __repr__(self): + return self._poc.__repr__() + + def add(self, priority, observer, callble): + """ + Add an observer with priority and callble + """ + if observer is not None: + ins = 0 + for pr, _, _ in self: + if priority > pr: + break + ins += 1 + self._poc.insert(ins, (priority, weakref.ref(observer), callble)) + + def __str__(self): + from . import ObsAr, Param + from parameter_core import Parameterizable + ret = [] + curr_p = None + + def frmt(o): + if isinstance(o, ObsAr): + return 'ObsArr <{}>'.format(hex(id(o))) + elif isinstance(o, (Param,Parameterizable)): + return '{}'.format(o.hierarchy_name()) + else: + return repr(o) + for p, o, c in self: + curr = '' + if curr_p != p: + pre = "{!s}: ".format(p) + curr_pre = pre + else: curr_pre = " "*len(pre) + curr_p = p + curr += curr_pre + + ret.append(curr + ", ".join([frmt(o), str(c)])) + return '\n'.join(ret) + + def flush(self): + """ + Make sure all weak references, which point to nothing are flushed (deleted) + """ + self._poc = [(p,o,c) for p,o,c in self._poc if o() is not None] + + def __iter__(self): + self.flush() + for p, o, c in self._poc: + yield p, o(), c + + def __len__(self): + self.flush() + return self._poc.__len__() + + def __deepcopy__(self, memo): + s = ObserverList() + for p,o,c in self: + import copy + s.add(p, copy.deepcopy(o, memo), copy.deepcopy(c, memo)) + s.flush() + return s + + def __getstate__(self): + self.flush() + from ...util.caching import Cacher + obs = [] + for p, o, c in self: + if (getattr(o, c.__name__, None) is not None + and not isinstance(o, Cacher)): + obs.append((p,o,c.__name__)) + return obs + + def __setstate__(self, state): + self._poc = [] + for p, o, c in state: + self.add(p,o,getattr(o, c)) + + pass diff --git a/GPy/core/parameterization/observable.py b/GPy/core/parameterization/observable.py new file mode 100644 index 00000000..4782d2ea --- /dev/null +++ b/GPy/core/parameterization/observable.py @@ -0,0 +1,66 @@ +# Copyright (c) 2014, Max Zwiessele +# Licensed under the BSD 3-clause license (see LICENSE.txt) + + +class Observable(object): + """ + Observable pattern for parameterization. + + This Object allows for observers to register with self and a (bound!) function + as an observer. Every time the observable changes, it sends a notification with + self as only argument to all its observers. + """ + def __init__(self, *args, **kwargs): + super(Observable, self).__init__() + from lists_and_dicts import ObserverList + self.observers = ObserverList() + + def add_observer(self, observer, callble, priority=0): + """ + Add an observer `observer` with the callback `callble` + and priority `priority` to this observers list. + """ + self.observers.add(priority, observer, callble) + + def remove_observer(self, observer, callble=None): + """ + Either (if callble is None) remove all callables, + which were added alongside observer, + or remove callable `callble` which was added alongside + the observer `observer`. + """ + to_remove = [] + for poc in self.observers: + _, obs, clble = poc + if callble is not None: + if (obs is observer) and (callble == clble): + to_remove.append(poc) + else: + if obs is observer: + to_remove.append(poc) + for r in to_remove: + self.observers.remove(*r) + + def notify_observers(self, which=None, min_priority=None): + """ + Notifies all observers. Which is the element, which kicked off this + notification loop. The first argument will be self, the second `which`. + + NOTE: notifies only observers with priority p > min_priority! + ^^^^^^^^^^^^^^^^ + :param min_priority: only notify observers with priority > min_priority + if min_priority is None, notify all observers in order + """ + if which is None: + which = self + if min_priority is None: + [callble(self, which=which) for _, _, callble in self.observers] + else: + for p, _, callble in self.observers: + if p <= min_priority: + break + callble(self, which=which) + + def change_priority(self, observer, callble, priority): + self.remove_observer(observer, callble) + self.add_observer(observer, callble, priority) diff --git a/GPy/core/parameterization/observable_array.py b/GPy/core/parameterization/observable_array.py new file mode 100644 index 00000000..271fe7b9 --- /dev/null +++ b/GPy/core/parameterization/observable_array.py @@ -0,0 +1,147 @@ +# Copyright (c) 2014, Max Zwiessele +# Licensed under the BSD 3-clause license (see LICENSE.txt) + + +import numpy as np +from parameter_core import Pickleable +from observable import Observable + +class ObsAr(np.ndarray, Pickleable, Observable): + """ + An ndarray which reports changes to its observers. + The observers can add themselves with a callable, which + will be called every time this array changes. The callable + takes exactly one argument, which is this array itself. + """ + __array_priority__ = -1 # Never give back ObsAr + def __new__(cls, input_array, *a, **kw): + # allways make a copy of input paramters, as we need it to be in C order: + if not isinstance(input_array, ObsAr): + obj = np.atleast_1d(np.require(input_array, dtype=np.float64, requirements=['W', 'C'])).view(cls) + else: obj = input_array + super(ObsAr, obj).__init__(*a, **kw) + return obj + + def __array_finalize__(self, obj): + # see InfoArray.__array_finalize__ for comments + if obj is None: return + self.observers = getattr(obj, 'observers', None) + + def __array_wrap__(self, out_arr, context=None): + return out_arr.view(np.ndarray) + + def _setup_observers(self): + # do not setup anything, as observable arrays do not have default observers + pass + + @property + def values(self): + return self.view(np.ndarray) + + def copy(self): + from lists_and_dicts import ObserverList + memo = {} + memo[id(self)] = self + memo[id(self.observers)] = ObserverList() + return self.__deepcopy__(memo) + + def __deepcopy__(self, memo): + s = self.__new__(self.__class__, input_array=self.view(np.ndarray).copy()) + memo[id(self)] = s + import copy + Pickleable.__setstate__(s, copy.deepcopy(self.__getstate__(), memo)) + return s + + def __reduce__(self): + func, args, state = super(ObsAr, self).__reduce__() + return func, args, (state, Pickleable.__getstate__(self)) + + def __setstate__(self, state): + np.ndarray.__setstate__(self, state[0]) + Pickleable.__setstate__(self, state[1]) + + def __setitem__(self, s, val): + super(ObsAr, self).__setitem__(s, val) + self.notify_observers() + + def __getslice__(self, start, stop): + return self.__getitem__(slice(start, stop)) + + def __setslice__(self, start, stop, val): + return self.__setitem__(slice(start, stop), val) + + def __ilshift__(self, *args, **kwargs): + r = np.ndarray.__ilshift__(self, *args, **kwargs) + self.notify_observers() + return r + + def __irshift__(self, *args, **kwargs): + r = np.ndarray.__irshift__(self, *args, **kwargs) + self.notify_observers() + return r + + + def __ixor__(self, *args, **kwargs): + r = np.ndarray.__ixor__(self, *args, **kwargs) + self.notify_observers() + return r + + + def __ipow__(self, *args, **kwargs): + r = np.ndarray.__ipow__(self, *args, **kwargs) + self.notify_observers() + return r + + + def __ifloordiv__(self, *args, **kwargs): + r = np.ndarray.__ifloordiv__(self, *args, **kwargs) + self.notify_observers() + return r + + + def __isub__(self, *args, **kwargs): + r = np.ndarray.__isub__(self, *args, **kwargs) + self.notify_observers() + return r + + + def __ior__(self, *args, **kwargs): + r = np.ndarray.__ior__(self, *args, **kwargs) + self.notify_observers() + return r + + + def __itruediv__(self, *args, **kwargs): + r = np.ndarray.__itruediv__(self, *args, **kwargs) + self.notify_observers() + return r + + + def __idiv__(self, *args, **kwargs): + r = np.ndarray.__idiv__(self, *args, **kwargs) + self.notify_observers() + return r + + + def __iand__(self, *args, **kwargs): + r = np.ndarray.__iand__(self, *args, **kwargs) + self.notify_observers() + return r + + + def __imod__(self, *args, **kwargs): + r = np.ndarray.__imod__(self, *args, **kwargs) + self.notify_observers() + return r + + + def __iadd__(self, *args, **kwargs): + r = np.ndarray.__iadd__(self, *args, **kwargs) + self.notify_observers() + return r + + + def __imul__(self, *args, **kwargs): + r = np.ndarray.__imul__(self, *args, **kwargs) + self.notify_observers() + return r diff --git a/GPy/core/parameterization/param.py b/GPy/core/parameterization/param.py new file mode 100644 index 00000000..c7d6be5d --- /dev/null +++ b/GPy/core/parameterization/param.py @@ -0,0 +1,476 @@ +# Copyright (c) 2014, Max Zwiessele +# Licensed under the BSD 3-clause license (see LICENSE.txt) + +import itertools +import numpy +np = numpy +from parameter_core import Parameterizable, adjust_name_for_printing, Pickleable +from observable_array import ObsAr + +###### printing +__constraints_name__ = "Constraint" +__index_name__ = "Index" +__tie_name__ = "Tied to" +__priors_name__ = "Prior" +__precision__ = numpy.get_printoptions()['precision'] # numpy printing precision used, sublassing numpy ndarray after all +__print_threshold__ = 5 +###### + +class Param(Parameterizable, ObsAr): + """ + Parameter object for GPy models. + + :param str name: name of the parameter to be printed + :param input_array: array which this parameter handles + :type input_array: numpy.ndarray + :param default_constraint: The default constraint for this parameter + :type default_constraint: + + You can add/remove constraints by calling constrain on the parameter itself, e.g: + + - self[:,1].constrain_positive() + - self[0].tie_to(other) + - self.untie() + - self[:3,:].unconstrain() + - self[1].fix() + + Fixing parameters will fix them to the value they are right now. If you change + the fixed value, it will be fixed to the new value! + + See :py:class:`GPy.core.parameterized.Parameterized` for more details on constraining etc. + + """ + __array_priority__ = -1 # Never give back Param + _fixes_ = None + parameters = [] + def __new__(cls, name, input_array, default_constraint=None): + obj = numpy.atleast_1d(super(Param, cls).__new__(cls, input_array=input_array)) + obj._current_slice_ = (slice(obj.shape[0]),) + obj._realshape_ = obj.shape + obj._realsize_ = obj.size + obj._realndim_ = obj.ndim + obj._original_ = obj + return obj + + def __init__(self, name, input_array, default_constraint=None, *a, **kw): + self._in_init_ = True + super(Param, self).__init__(name=name, default_constraint=default_constraint, *a, **kw) + self._in_init_ = False + + def build_pydot(self,G): + import pydot + node = pydot.Node(id(self), shape='trapezium', label=self.name)#, fontcolor='white', color='white') + G.add_node(node) + for _, o, _ in self.observers: + label = o.name if hasattr(o, 'name') else str(o) + observed_node = pydot.Node(id(o), label=label) + G.add_node(observed_node) + edge = pydot.Edge(str(id(self)), str(id(o)), color='darkorange2', arrowhead='vee') + G.add_edge(edge) + + return node + + def __array_finalize__(self, obj): + # see InfoArray.__array_finalize__ for comments + if obj is None: return + super(Param, self).__array_finalize__(obj) + self._parent_ = getattr(obj, '_parent_', None) + self._parent_index_ = getattr(obj, '_parent_index_', None) + self._default_constraint_ = getattr(obj, '_default_constraint_', None) + self._current_slice_ = getattr(obj, '_current_slice_', None) + self._realshape_ = getattr(obj, '_realshape_', None) + self._realsize_ = getattr(obj, '_realsize_', None) + self._realndim_ = getattr(obj, '_realndim_', None) + self._original_ = getattr(obj, '_original_', None) + self._name = getattr(obj, '_name', None) + self._gradient_array_ = getattr(obj, '_gradient_array_', None) + self.constraints = getattr(obj, 'constraints', None) + self.priors = getattr(obj, 'priors', None) + + @property + def param_array(self): + """ + As we are a leaf, this just returns self + """ + return self + + @property + def values(self): + """ + Return self as numpy array view + """ + return self.view(np.ndarray) + + @property + def gradient(self): + """ + Return a view on the gradient, which is in the same shape as this parameter is. + Note: this is not the real gradient array, it is just a view on it. + + To work on the real gradient array use: self.full_gradient + """ + if getattr(self, '_gradient_array_', None) is None: + self._gradient_array_ = numpy.empty(self._realshape_, dtype=numpy.float64) + return self._gradient_array_#[self._current_slice_] + + @gradient.setter + def gradient(self, val): + self._gradient_array_[:] = val + + #=========================================================================== + # Array operations -> done + #=========================================================================== + def __getitem__(self, s, *args, **kwargs): + if not isinstance(s, tuple): + s = (s,) + #if not reduce(lambda a, b: a or numpy.any(b is Ellipsis), s, False) and len(s) <= self.ndim: + # s += (Ellipsis,) + new_arr = super(Param, self).__getitem__(s, *args, **kwargs) + try: + new_arr._current_slice_ = s + new_arr._gradient_array_ = self.gradient[s] + new_arr._original_ = self._original_ + except AttributeError: pass # returning 0d array or float, double etc + return new_arr + + def _raveled_index(self, slice_index=None): + # return an index array on the raveled array, which is formed by the current_slice + # of this object + extended_realshape = numpy.cumprod((1,) + self._realshape_[:0:-1])[::-1] + ind = self._indices(slice_index) + if ind.ndim < 2: ind = ind[:, None] + return numpy.asarray(numpy.apply_along_axis(lambda x: numpy.sum(extended_realshape * x), 1, ind), dtype=int) + + def _raveled_index_for(self, obj): + return self._raveled_index() + + #=========================================================================== + # Constrainable + #=========================================================================== + def _ensure_fixes(self): + if not self._has_fixes(): self._fixes_ = numpy.ones(self._realsize_, dtype=bool) + + #=========================================================================== + # Convenience + #=========================================================================== + @property + def is_fixed(self): + from transformations import __fixed__ + return self.constraints[__fixed__].size == self.size + + def _get_original(self, param): + return self._original_ + + #=========================================================================== + # Pickling and copying + #=========================================================================== + def copy(self): + return Parameterizable.copy(self, which=self) + + def __deepcopy__(self, memo): + s = self.__new__(self.__class__, name=self.name, input_array=self.view(numpy.ndarray).copy()) + memo[id(self)] = s + import copy + Pickleable.__setstate__(s, copy.deepcopy(self.__getstate__(), memo)) + return s + def _setup_observers(self): + """ + Setup the default observers + + 1: pass through to parent, if present + """ + if self.has_parent(): + self.add_observer(self._parent_, self._parent_._pass_through_notify_observers, -np.inf) + + #=========================================================================== + # Printing -> done + #=========================================================================== + @property + def _description_str(self): + if self.size <= 1: + return [str(self.view(numpy.ndarray)[0])] + else: return [str(self.shape)] + def parameter_names(self, add_self=False, adjust_for_printing=False, recursive=True): + # this is just overwrighting the parameterized calls to parameter names, in order to maintain OOP + if adjust_for_printing: + return [adjust_name_for_printing(self.name)] + return [self.name] + @property + def flattened_parameters(self): + return [self] + @property + def parameter_shapes(self): + return [self.shape] + @property + def num_params(self): + return 0 + @property + def _constraints_str(self): + return [' '.join(map(lambda c: str(c[0]) if c[1].size == self._realsize_ else "{" + str(c[0]) + "}", self.constraints.iteritems()))] + @property + def _priors_str(self): + return [' '.join(map(lambda c: str(c[0]) if c[1].size == self._realsize_ else "{" + str(c[0]) + "}", self.priors.iteritems()))] + @property + def _ties_str(self): + return [''] + def _ties_for(self, ravi): + return [['N/A']]*ravi.size + def __repr__(self, *args, **kwargs): + name = "\033[1m{x:s}\033[0;0m:\n".format( + x=self.hierarchy_name()) + return name + super(Param, self).__repr__(*args, **kwargs) + def _indices(self, slice_index=None): + # get a int-array containing all indices in the first axis. + if slice_index is None: + slice_index = self._current_slice_ + try: + indices = np.indices(self._realshape_, dtype=int) + indices = indices[(slice(None),)+slice_index] + indices = np.rollaxis(indices, 0, indices.ndim).reshape(-1,self._realndim_) + #print indices_ + #if not np.all(indices==indices__): + # import ipdb; ipdb.set_trace() + except: + indices = np.indices(self._realshape_, dtype=int) + indices = indices[(slice(None),)+slice_index] + indices = np.rollaxis(indices, 0, indices.ndim) + return indices + def _max_len_names(self, gen, header): + gen = map(lambda x: " ".join(map(str, x)), gen) + return reduce(lambda a, b:max(a, len(b)), gen, len(header)) + def _max_len_values(self): + return reduce(lambda a, b:max(a, len("{x:=.{0}g}".format(__precision__, x=b))), self.flat, len(self.hierarchy_name())) + def _max_len_index(self, ind): + return reduce(lambda a, b:max(a, len(str(b))), ind, len(__index_name__)) + def _short(self): + # short string to print + name = self.hierarchy_name() + if self._realsize_ < 2: + return name + ind = self._indices() + if ind.size > 4: indstr = ','.join(map(str, ind[:2])) + "..." + ','.join(map(str, ind[-2:])) + else: indstr = ','.join(map(str, ind)) + return name + '[' + indstr + ']' + + def _repr_html_(self, constr_matrix=None, indices=None, prirs=None, ties=None): + """Representation of the parameter in html for notebook display.""" + filter_ = self._current_slice_ + vals = self.flat + if indices is None: indices = self._indices(filter_) + ravi = self._raveled_index(filter_) + if constr_matrix is None: constr_matrix = self.constraints.properties_for(ravi) + if prirs is None: prirs = self.priors.properties_for(ravi) + if ties is None: ties = self._ties_for(ravi) + ties = [' '.join(map(lambda x: x, t)) for t in ties] + header_format = """ + + {i} + {x} + {c} + {p} + {t} +""" + header = header_format.format(x=self.hierarchy_name(), c=__constraints_name__, i=__index_name__, t=__tie_name__, p=__priors_name__) # nice header for printing + if not ties: ties = itertools.cycle(['']) + return "\n".join([''] + [header] + ["".format(x=x, c=" ".join(map(str, c)), p=" ".join(map(str, p)), t=(t or ''), i=i) for i, x, c, t, p in itertools.izip(indices, vals, constr_matrix, ties, prirs)] + ["
{i}{x}{c}{p}{t}
"]) + + def __str__(self, constr_matrix=None, indices=None, prirs=None, ties=None, lc=None, lx=None, li=None, lp=None, lt=None, only_name=False): + filter_ = self._current_slice_ + vals = self.flat + if indices is None: indices = self._indices(filter_) + ravi = self._raveled_index(filter_) + if constr_matrix is None: constr_matrix = self.constraints.properties_for(ravi) + if prirs is None: prirs = self.priors.properties_for(ravi) + if ties is None: ties = self._ties_for(ravi) + ties = [' '.join(map(lambda x: x, t)) for t in ties] + if lc is None: lc = self._max_len_names(constr_matrix, __constraints_name__) + if lx is None: lx = self._max_len_values() + if li is None: li = self._max_len_index(indices) + if lt is None: lt = self._max_len_names(ties, __tie_name__) + if lp is None: lp = self._max_len_names(prirs, __tie_name__) + sep = '-' + header_format = " {i:{5}^{2}s} | \033[1m{x:{5}^{1}s}\033[0;0m | {c:{5}^{0}s} | {p:{5}^{4}s} | {t:{5}^{3}s}" + if only_name: header = header_format.format(lc, lx, li, lt, lp, ' ', x=self.hierarchy_name(), c=sep*lc, i=sep*li, t=sep*lt, p=sep*lp) # nice header for printing + else: header = header_format.format(lc, lx, li, lt, lp, ' ', x=self.hierarchy_name(), c=__constraints_name__, i=__index_name__, t=__tie_name__, p=__priors_name__) # nice header for printing + if not ties: ties = itertools.cycle(['']) + return "\n".join([header] + [" {i!s:^{3}s} | {x: >{1}.{2}g} | {c:^{0}s} | {p:^{5}s} | {t:^{4}s} ".format(lc, lx, __precision__, li, lt, lp, x=x, c=" ".join(map(str, c)), p=" ".join(map(str, p)), t=(t or ''), i=i) for i, x, c, t, p in itertools.izip(indices, vals, constr_matrix, ties, prirs)]) # return all the constraints with right indices + # except: return super(Param, self).__str__() + +class ParamConcatenation(object): + def __init__(self, params): + """ + Parameter concatenation for convenience of printing regular expression matched arrays + you can index this concatenation as if it was the flattened concatenation + of all the parameters it contains, same for setting parameters (Broadcasting enabled). + + See :py:class:`GPy.core.parameter.Param` for more details on constraining. + """ + # self.params = params + from lists_and_dicts import ArrayList + self.params = ArrayList([]) + for p in params: + for p in p.flattened_parameters: + if p not in self.params: + self.params.append(p) + self._param_sizes = [p.size for p in self.params] + startstops = numpy.cumsum([0] + self._param_sizes) + self._param_slices_ = [slice(start, stop) for start,stop in zip(startstops, startstops[1:])] + + parents = dict() + for p in self.params: + if p.has_parent(): + parent = p._parent_ + level = 0 + while parent is not None: + if parent in parents: + parents[parent] = max(level, parents[parent]) + else: + parents[parent] = level + level += 1 + parent = parent._parent_ + import operator + self.parents = map(lambda x: x[0], sorted(parents.iteritems(), key=operator.itemgetter(1))) + #=========================================================================== + # Get/set items, enable broadcasting + #=========================================================================== + def __getitem__(self, s): + ind = numpy.zeros(sum(self._param_sizes), dtype=bool); ind[s] = True; + params = [p.param_array.flat[ind[ps]] for p,ps in zip(self.params, self._param_slices_) if numpy.any(p.param_array.flat[ind[ps]])] + if len(params)==1: return params[0] + return ParamConcatenation(params) + def __setitem__(self, s, val, update=True): + if isinstance(val, ParamConcatenation): + val = val.values() + ind = numpy.zeros(sum(self._param_sizes), dtype=bool); ind[s] = True; + vals = self.values(); vals[s] = val + for p, ps in zip(self.params, self._param_slices_): + p.flat[ind[ps]] = vals[ps] + if update: + self.update_all_params() + def values(self): + return numpy.hstack([p.param_array.flat for p in self.params]) + #=========================================================================== + # parameter operations: + #=========================================================================== + def update_all_params(self): + for par in self.parents: + par.notify_observers() + + def constrain(self, constraint, warning=True): + [param.constrain(constraint, trigger_parent=False) for param in self.params] + self.update_all_params() + constrain.__doc__ = Param.constrain.__doc__ + + def constrain_positive(self, warning=True): + [param.constrain_positive(warning, trigger_parent=False) for param in self.params] + self.update_all_params() + constrain_positive.__doc__ = Param.constrain_positive.__doc__ + + def constrain_fixed(self, value=None, warning=True, trigger_parent=True): + [param.constrain_fixed(value, warning, trigger_parent) for param in self.params] + constrain_fixed.__doc__ = Param.constrain_fixed.__doc__ + fix = constrain_fixed + + def constrain_negative(self, warning=True): + [param.constrain_negative(warning, trigger_parent=False) for param in self.params] + self.update_all_params() + constrain_negative.__doc__ = Param.constrain_negative.__doc__ + + def constrain_bounded(self, lower, upper, warning=True): + [param.constrain_bounded(lower, upper, warning, trigger_parent=False) for param in self.params] + self.update_all_params() + constrain_bounded.__doc__ = Param.constrain_bounded.__doc__ + + def unconstrain(self, *constraints): + [param.unconstrain(*constraints) for param in self.params] + unconstrain.__doc__ = Param.unconstrain.__doc__ + + def unconstrain_negative(self): + [param.unconstrain_negative() for param in self.params] + unconstrain_negative.__doc__ = Param.unconstrain_negative.__doc__ + + def unconstrain_positive(self): + [param.unconstrain_positive() for param in self.params] + unconstrain_positive.__doc__ = Param.unconstrain_positive.__doc__ + + def unconstrain_fixed(self): + [param.unconstrain_fixed() for param in self.params] + unconstrain_fixed.__doc__ = Param.unconstrain_fixed.__doc__ + unfix = unconstrain_fixed + + def unconstrain_bounded(self, lower, upper): + [param.unconstrain_bounded(lower, upper) for param in self.params] + unconstrain_bounded.__doc__ = Param.unconstrain_bounded.__doc__ + + def untie(self, *ties): + [param.untie(*ties) for param in self.params] + + def checkgrad(self, verbose=0, step=1e-6, tolerance=1e-3): + return self.params[0]._highest_parent_._checkgrad(self, verbose, step, tolerance) + #checkgrad.__doc__ = Gradcheckable.checkgrad.__doc__ + + __lt__ = lambda self, val: self.values() < val + __le__ = lambda self, val: self.values() <= val + __eq__ = lambda self, val: self.values() == val + __ne__ = lambda self, val: self.values() != val + __gt__ = lambda self, val: self.values() > val + __ge__ = lambda self, val: self.values() >= val + def __str__(self, *args, **kwargs): + def f(p): + ind = p._raveled_index() + return p.constraints.properties_for(ind), p._ties_for(ind), p.priors.properties_for(ind) + params = self.params + constr_matrices, ties_matrices, prior_matrices = zip(*map(f, params)) + indices = [p._indices() for p in params] + lc = max([p._max_len_names(cm, __constraints_name__) for p, cm in itertools.izip(params, constr_matrices)]) + lx = max([p._max_len_values() for p in params]) + li = max([p._max_len_index(i) for p, i in itertools.izip(params, indices)]) + lt = max([p._max_len_names(tm, __tie_name__) for p, tm in itertools.izip(params, ties_matrices)]) + lp = max([p._max_len_names(pm, __constraints_name__) for p, pm in itertools.izip(params, prior_matrices)]) + strings = [] + start = True + for p, cm, i, tm, pm in itertools.izip(params,constr_matrices,indices,ties_matrices,prior_matrices): + strings.append(p.__str__(constr_matrix=cm, indices=i, prirs=pm, ties=tm, lc=lc, lx=lx, li=li, lp=lp, lt=lt, only_name=(1-start))) + start = False + return "\n".join(strings) + def __repr__(self): + return "\n".join(map(repr,self.params)) + + def __ilshift__(self, *args, **kwargs): + self[:] = np.ndarray.__ilshift__(self.values(), *args, **kwargs) + + def __irshift__(self, *args, **kwargs): + self[:] = np.ndarray.__irshift__(self.values(), *args, **kwargs) + + def __ixor__(self, *args, **kwargs): + self[:] = np.ndarray.__ixor__(self.values(), *args, **kwargs) + + def __ipow__(self, *args, **kwargs): + self[:] = np.ndarray.__ipow__(self.values(), *args, **kwargs) + + def __ifloordiv__(self, *args, **kwargs): + self[:] = np.ndarray.__ifloordiv__(self.values(), *args, **kwargs) + + def __isub__(self, *args, **kwargs): + self[:] = np.ndarray.__isub__(self.values(), *args, **kwargs) + + def __ior__(self, *args, **kwargs): + self[:] = np.ndarray.__ior__(self.values(), *args, **kwargs) + + def __itruediv__(self, *args, **kwargs): + self[:] = np.ndarray.__itruediv__(self.values(), *args, **kwargs) + + def __idiv__(self, *args, **kwargs): + self[:] = np.ndarray.__idiv__(self.values(), *args, **kwargs) + + def __iand__(self, *args, **kwargs): + self[:] = np.ndarray.__iand__(self.values(), *args, **kwargs) + + def __imod__(self, *args, **kwargs): + self[:] = np.ndarray.__imod__(self.values(), *args, **kwargs) + + def __iadd__(self, *args, **kwargs): + self[:] = np.ndarray.__iadd__(self.values(), *args, **kwargs) + + def __imul__(self, *args, **kwargs): + self[:] = np.ndarray.__imul__(self.values(), *args, **kwargs) diff --git a/GPy/core/parameterization/parameter_core.py b/GPy/core/parameterization/parameter_core.py new file mode 100644 index 00000000..6add95b0 --- /dev/null +++ b/GPy/core/parameterization/parameter_core.py @@ -0,0 +1,1037 @@ +# Copyright (c) 2012, GPy authors (see AUTHORS.txt). +# Licensed under the BSD 3-clause license (see LICENSE.txt) +""" +Core module for parameterization. +This module implements all parameterization techniques, split up in modular bits. + +HierarchyError: +raised when an error with the hierarchy occurs (circles etc.) + +Observable: +Observable Pattern for patameterization + + +""" + +from transformations import Transformation,Logexp, NegativeLogexp, Logistic, __fixed__, FIXED, UNFIXED +import numpy as np +import re +import logging +from updateable import Updateable + +class HierarchyError(Exception): + """ + Gets thrown when something is wrong with the parameter hierarchy. + """ + +def adjust_name_for_printing(name): + """ + Make sure a name can be printed, alongside used as a variable name. + """ + if name is not None: + name2 = name + name = name.replace(" ", "_").replace(".", "_").replace("-", "_m_") + name = name.replace("+", "_p_").replace("!", "_I_") + name = name.replace("**", "_xx_").replace("*", "_x_") + name = name.replace("/", "_l_").replace("@", '_at_') + name = name.replace("(", "_of_").replace(")", "") + if re.match(r'^[a-zA-Z_][a-zA-Z0-9-_]*$', name) is None: + raise NameError, "name {} converted to {} cannot be further converted to valid python variable name!".format(name2, name) + return name + return '' + + + +class Parentable(object): + """ + Enable an Object to have a parent. + + Additionally this adds the parent_index, which is the index for the parent + to look for in its parameter list. + """ + _parent_ = None + _parent_index_ = None + def __init__(self, *args, **kwargs): + super(Parentable, self).__init__() + + def has_parent(self): + """ + Return whether this parentable object currently has a parent. + """ + return self._parent_ is not None + + def _parent_changed(self): + """ + Gets called, when the parent changed, so we can adjust our + inner attributes according to the new parent. + """ + raise NotImplementedError, "shouldnt happen, Parentable objects need to be able to change their parent" + + def _disconnect_parent(self, *args, **kw): + """ + Disconnect this object from its parent + """ + raise NotImplementedError, "Abstract superclass" + + @property + def _highest_parent_(self): + """ + Gets the highest parent by traversing up to the root node of the hierarchy. + """ + if self._parent_ is None: + return self + return self._parent_._highest_parent_ + + def _notify_parent_change(self): + """ + Dont do anything if in leaf node + """ + pass + +class Pickleable(object): + """ + Make an object pickleable (See python doc 'pickling'). + + This class allows for pickling support by Memento pattern. + _getstate returns a memento of the class, which gets pickled. + _setstate() (re-)sets the state of the class to the memento + """ + def __init__(self, *a, **kw): + super(Pickleable, self).__init__() + + #=========================================================================== + # Pickling operations + #=========================================================================== + def pickle(self, f, protocol=-1): + """ + :param f: either filename or open file object to write to. + if it is an open buffer, you have to make sure to close + it properly. + :param protocol: pickling protocol to use, python-pickle for details. + """ + import cPickle as pickle + if isinstance(f, str): + with open(f, 'wb') as f: + pickle.dump(self, f, protocol) + else: + pickle.dump(self, f, protocol) + + #=========================================================================== + # copy and pickling + #=========================================================================== + def copy(self, memo=None, which=None): + """ + Returns a (deep) copy of the current parameter handle. + + All connections to parents of the copy will be cut. + + :param dict memo: memo for deepcopy + :param Parameterized which: parameterized object which started the copy process [default: self] + """ + #raise NotImplementedError, "Copy is not yet implemented, TODO: Observable hierarchy" + if memo is None: + memo = {} + import copy + # the next part makes sure that we do not include parents in any form: + parents = [] + if which is None: + which = self + which.traverse_parents(parents.append) # collect parents + for p in parents: + if not memo.has_key(id(p)):memo[id(p)] = None # set all parents to be None, so they will not be copied + if not memo.has_key(id(self.gradient)):memo[id(self.gradient)] = None # reset the gradient + if not memo.has_key(id(self._fixes_)):memo[id(self._fixes_)] = None # fixes have to be reset, as this is now highest parent + copy = copy.deepcopy(self, memo) # and start the copy + copy._parent_index_ = None + copy._trigger_params_changed() + return copy + + def __deepcopy__(self, memo): + s = self.__new__(self.__class__) # fresh instance + memo[id(self)] = s # be sure to break all cycles --> self is already done + import copy + s.__setstate__(copy.deepcopy(self.__getstate__(), memo)) # standard copy + return s + + def __getstate__(self): + ignore_list = ['_param_array_', # parameters get set from bottom to top + '_gradient_array_', # as well as gradients + '_optimizer_copy_', + 'logger', + 'observers', + '_fixes_', # and fixes + '_Cacher_wrap__cachers', # never pickle cachers + ] + dc = dict() + for k,v in self.__dict__.iteritems(): + if k not in ignore_list: + dc[k] = v + return dc + + def __setstate__(self, state): + self.__dict__.update(state) + from lists_and_dicts import ObserverList + self.observers = ObserverList() + self._setup_observers() + self._optimizer_copy_transformed = False + + +class Gradcheckable(Pickleable, Parentable): + """ + Adds the functionality for an object to be gradcheckable. + It is just a thin wrapper of a call to the highest parent for now. + TODO: Can be done better, by only changing parameters of the current parameter handle, + such that object hierarchy only has to change for those. + """ + def __init__(self, *a, **kw): + super(Gradcheckable, self).__init__(*a, **kw) + + def checkgrad(self, verbose=0, step=1e-6, tolerance=1e-3, df_tolerance=1e-12): + """ + Check the gradient of this parameter with respect to the highest parent's + objective function. + This is a three point estimate of the gradient, wiggling at the parameters + with a stepsize step. + The check passes if either the ratio or the difference between numerical and + analytical gradient is smaller then tolerance. + + :param bool verbose: whether each parameter shall be checked individually. + :param float step: the stepsize for the numerical three point gradient estimate. + :param float tolerance: the tolerance for the gradient ratio or difference. + :param float df_tolerance: the tolerance for df_tolerance + + Note:- + The *dF_ratio* indicates the limit of accuracy of numerical gradients. + If it is too small, e.g., smaller than 1e-12, the numerical gradients + are usually not accurate enough for the tests (shown with blue). + """ + if self.has_parent(): + return self._highest_parent_._checkgrad(self, verbose=verbose, step=step, tolerance=tolerance, df_tolerance=df_tolerance) + return self._checkgrad(self, verbose=verbose, step=step, tolerance=tolerance, df_tolerance=df_tolerance) + + def _checkgrad(self, param, verbose=0, step=1e-6, tolerance=1e-3): + """ + Perform the checkgrad on the model. + TODO: this can be done more efficiently, when doing it inside here + """ + raise HierarchyError, "This parameter is not in a model with a likelihood, and, therefore, cannot be gradient checked!" + +class Nameable(Gradcheckable): + """ + Make an object nameable inside the hierarchy. + """ + def __init__(self, name, *a, **kw): + super(Nameable, self).__init__(*a, **kw) + self._name = name or self.__class__.__name__ + + @property + def name(self): + """ + The name of this object + """ + return self._name + @name.setter + def name(self, name): + """ + Set the name of this object. + Tell the parent if the name has changed. + """ + from_name = self.name + assert isinstance(name, str) + self._name = name + if self.has_parent(): + self._parent_._name_changed(self, from_name) + def hierarchy_name(self, adjust_for_printing=True): + """ + return the name for this object with the parents names attached by dots. + + :param bool adjust_for_printing: whether to call :func:`~adjust_for_printing()` + on the names, recursively + """ + if adjust_for_printing: adjust = lambda x: adjust_name_for_printing(x) + else: adjust = lambda x: x + if self.has_parent(): + return self._parent_.hierarchy_name() + "." + adjust(self.name) + return adjust(self.name) + + +class Indexable(Nameable, Updateable): + """ + Make an object constrainable with Priors and Transformations. + TODO: Mappings!! + Adding a constraint to a Parameter means to tell the highest parent that + the constraint was added and making sure that all parameters covered + by this object are indeed conforming to the constraint. + + :func:`constrain()` and :func:`unconstrain()` are main methods here + """ + def __init__(self, name, default_constraint=None, *a, **kw): + super(Indexable, self).__init__(name=name, *a, **kw) + self._default_constraint_ = default_constraint + from index_operations import ParameterIndexOperations + self.constraints = ParameterIndexOperations() + self.priors = ParameterIndexOperations() + if self._default_constraint_ is not None: + self.constrain(self._default_constraint_) + + def _disconnect_parent(self, constr=None, *args, **kw): + """ + From Parentable: + disconnect the parent and set the new constraints to constr + """ + if constr is None: + constr = self.constraints.copy() + self.constraints.clear() + self.constraints = constr + self._parent_ = None + self._parent_index_ = None + self._connect_fixes() + self._notify_parent_change() + + #=========================================================================== + # Indexable + #=========================================================================== + def _offset_for(self, param): + """ + Return the offset of the param inside this parameterized object. + This does not need to account for shaped parameters, as it + basically just sums up the parameter sizes which come before param. + """ + if param.has_parent(): + p = param._parent_._get_original(param) + if p in self.parameters: + return reduce(lambda a,b: a + b.size, self.parameters[:p._parent_index_], 0) + return self._offset_for(param._parent_) + param._parent_._offset_for(param) + return 0 + + def _raveled_index_for(self, param): + """ + get the raveled index for a param + that is an int array, containing the indexes for the flattened + param inside this parameterized logic. + """ + from param import ParamConcatenation + if isinstance(param, ParamConcatenation): + return np.hstack((self._raveled_index_for(p) for p in param.params)) + return param._raveled_index() + self._offset_for(param) + + def _raveled_index(self): + """ + Flattened array of ints, specifying the index of this object. + This has to account for shaped parameters! + """ + return np.r_[:self.size] + + #=========================================================================== + # Fixing Parameters: + #=========================================================================== + def constrain_fixed(self, value=None, warning=True, trigger_parent=True): + """ + Constrain this parameter to be fixed to the current value it carries. + + :param warning: print a warning for overwriting constraints. + """ + if value is not None: + self[:] = value + + index = self.unconstrain() + index = self._add_to_index_operations(self.constraints, index, __fixed__, warning) + self._highest_parent_._set_fixed(self, index) + self.notify_observers(self, None if trigger_parent else -np.inf) + return index + fix = constrain_fixed + + def unconstrain_fixed(self): + """ + This parameter will no longer be fixed. + """ + unconstrained = self.unconstrain(__fixed__) + self._highest_parent_._set_unfixed(self, unconstrained) + return unconstrained + unfix = unconstrain_fixed + + def _ensure_fixes(self): + # Ensure that the fixes array is set: + # Parameterized: ones(self.size) + # Param: ones(self._realsize_ + if not self._has_fixes(): self._fixes_ = np.ones(self.size, dtype=bool) + + def _set_fixed(self, param, index): + self._ensure_fixes() + offset = self._offset_for(param) + self._fixes_[index+offset] = FIXED + if np.all(self._fixes_): self._fixes_ = None # ==UNFIXED + + def _set_unfixed(self, param, index): + self._ensure_fixes() + offset = self._offset_for(param) + self._fixes_[index+offset] = UNFIXED + if np.all(self._fixes_): self._fixes_ = None # ==UNFIXED + + def _connect_fixes(self): + fixed_indices = self.constraints[__fixed__] + if fixed_indices.size > 0: + self._ensure_fixes() + self._fixes_[fixed_indices] = FIXED + else: + self._fixes_ = None + del self.constraints[__fixed__] + + #=========================================================================== + # Convenience for fixed + #=========================================================================== + def _has_fixes(self): + return hasattr(self, "_fixes_") and self._fixes_ is not None and self._fixes_.size == self.size + + @property + def is_fixed(self): + for p in self.parameters: + if not p.is_fixed: return False + return True + + def _get_original(self, param): + # if advanced indexing is activated it happens that the array is a copy + # you can retrieve the original param through this method, by passing + # the copy here + return self.parameters[param._parent_index_] + + #=========================================================================== + # Prior Operations + #=========================================================================== + def set_prior(self, prior, warning=True): + """ + Set the prior for this object to prior. + :param :class:`~GPy.priors.Prior` prior: a prior to set for this parameter + :param bool warning: whether to warn if another prior was set for this parameter + """ + repriorized = self.unset_priors() + self._add_to_index_operations(self.priors, repriorized, prior, warning) + + from domains import _REAL, _POSITIVE, _NEGATIVE + if prior.domain is _POSITIVE: + self.constrain_positive(warning) + elif prior.domain is _NEGATIVE: + self.constrain_negative(warning) + elif prior.domain is _REAL: + rav_i = self._raveled_index() + assert all(all(False if c is __fixed__ else c.domain is _REAL for c in con) for con in self.constraints.properties_for(rav_i)), 'Domain of prior and constraint have to match, please unconstrain if you REALLY wish to use this prior' + + def unset_priors(self, *priors): + """ + Un-set all priors given (in *priors) from this parameter handle. + """ + return self._remove_from_index_operations(self.priors, priors) + + def log_prior(self): + """evaluate the prior""" + if self.priors.size > 0: + x = self.param_array + return reduce(lambda a, b: a + b, (p.lnpdf(x[ind]).sum() for p, ind in self.priors.iteritems()), 0) + return 0. + + def _log_prior_gradients(self): + """evaluate the gradients of the priors""" + if self.priors.size > 0: + x = self.param_array + ret = np.zeros(x.size) + [np.put(ret, ind, p.lnpdf_grad(x[ind])) for p, ind in self.priors.iteritems()] + return ret + return 0. + + #=========================================================================== + # Tie parameters together + #=========================================================================== + + def _has_ties(self): + if self._highest_parent_.tie.tied_param is None: + return False + if self.has_parent(): + return self._highest_parent_.tie.label_buf[self._highest_parent_._raveled_index_for(self)].sum()>0 + return True + + def tie_together(self): + self._highest_parent_.tie.add_tied_parameter(self) + self._highest_parent_._set_fixed(self,self._raveled_index()) + self._trigger_params_changed() + + #=========================================================================== + # Constrain operations -> done + #=========================================================================== + + def constrain(self, transform, warning=True, trigger_parent=True): + """ + :param transform: the :py:class:`GPy.core.transformations.Transformation` + to constrain the this parameter to. + :param warning: print a warning if re-constraining parameters. + + Constrain the parameter to the given + :py:class:`GPy.core.transformations.Transformation`. + """ + if isinstance(transform, Transformation): + self.param_array[...] = transform.initialize(self.param_array) + reconstrained = self.unconstrain() + added = self._add_to_index_operations(self.constraints, reconstrained, transform, warning) + self.notify_observers(self, None if trigger_parent else -np.inf) + return added + + def unconstrain(self, *transforms): + """ + :param transforms: The transformations to unconstrain from. + + remove all :py:class:`GPy.core.transformations.Transformation` + transformats of this parameter object. + """ + return self._remove_from_index_operations(self.constraints, transforms) + + def constrain_positive(self, warning=True, trigger_parent=True): + """ + :param warning: print a warning if re-constraining parameters. + + Constrain this parameter to the default positive constraint. + """ + self.constrain(Logexp(), warning=warning, trigger_parent=trigger_parent) + + def constrain_negative(self, warning=True, trigger_parent=True): + """ + :param warning: print a warning if re-constraining parameters. + + Constrain this parameter to the default negative constraint. + """ + self.constrain(NegativeLogexp(), warning=warning, trigger_parent=trigger_parent) + + def constrain_bounded(self, lower, upper, warning=True, trigger_parent=True): + """ + :param lower, upper: the limits to bound this parameter to + :param warning: print a warning if re-constraining parameters. + + Constrain this parameter to lie within the given range. + """ + self.constrain(Logistic(lower, upper), warning=warning, trigger_parent=trigger_parent) + + def unconstrain_positive(self): + """ + Remove positive constraint of this parameter. + """ + self.unconstrain(Logexp()) + + def unconstrain_negative(self): + """ + Remove negative constraint of this parameter. + """ + self.unconstrain(NegativeLogexp()) + + def unconstrain_bounded(self, lower, upper): + """ + :param lower, upper: the limits to unbound this parameter from + + Remove (lower, upper) bounded constrain from this parameter/ + """ + self.unconstrain(Logistic(lower, upper)) + + def _parent_changed(self, parent): + """ + From Parentable: + Called when the parent changed + + update the constraints and priors view, so that + constraining is automized for the parent. + """ + from index_operations import ParameterIndexOperationsView + #if getattr(self, "_in_init_"): + #import ipdb;ipdb.set_trace() + #self.constraints.update(param.constraints, start) + #self.priors.update(param.priors, start) + offset = parent._offset_for(self) + self.constraints = ParameterIndexOperationsView(parent.constraints, offset, self.size) + self.priors = ParameterIndexOperationsView(parent.priors, offset, self.size) + self._fixes_ = None + for p in self.parameters: + p._parent_changed(parent) + + def _add_to_index_operations(self, which, reconstrained, what, warning): + """ + Helper preventing copy code. + This adds the given what (transformation, prior etc) to parameter index operations which. + reconstrained are reconstrained indices. + warn when reconstraining parameters if warning is True. + TODO: find out which parameters have changed specifically + """ + if warning and reconstrained.size > 0: + # TODO: figure out which parameters have changed and only print those + print "WARNING: reconstraining parameters {}".format(self.hierarchy_name() or self.name) + index = self._raveled_index() + which.add(what, index) + return index + + def _remove_from_index_operations(self, which, transforms): + """ + Helper preventing copy code. + Remove given what (transform prior etc) from which param index ops. + """ + if len(transforms) == 0: + transforms = which.properties() + removed = np.empty((0,), dtype=int) + for t in transforms: + unconstrained = which.remove(t, self._raveled_index()) + removed = np.union1d(removed, unconstrained) + if t is __fixed__: + self._highest_parent_._set_unfixed(self, unconstrained) + + return removed + +class OptimizationHandlable(Indexable): + """ + This enables optimization handles on an Object as done in GPy 0.4. + + `..._optimizer_copy_transformed`: make sure the transformations and constraints etc are handled + """ + def __init__(self, name, default_constraint=None, *a, **kw): + super(OptimizationHandlable, self).__init__(name, default_constraint=default_constraint, *a, **kw) + self._optimizer_copy_ = None + self._optimizer_copy_transformed = False + + #=========================================================================== + # Optimizer copy + #=========================================================================== + @property + def optimizer_array(self): + """ + Array for the optimizer to work on. + This array always lives in the space for the optimizer. + Thus, it is untransformed, going from Transformations. + + Setting this array, will make sure the transformed parameters for this model + will be set accordingly. It has to be set with an array, retrieved from + this method, as e.g. fixing will resize the array. + + The optimizer should only interfere with this array, such that transformations + are secured. + """ + if self.__dict__.get('_optimizer_copy_', None) is None or self.size != self._optimizer_copy_.size: + self._optimizer_copy_ = np.empty(self.size) + + if not self._optimizer_copy_transformed: + self._optimizer_copy_.flat = self.param_array.flat + [np.put(self._optimizer_copy_, ind, c.finv(self.param_array[ind])) for c, ind in self.constraints.iteritems() if c != __fixed__] + if self.has_parent() and (self.constraints[__fixed__].size != 0 or self._has_ties()): + fixes = np.ones(self.size).astype(bool) + fixes[self.constraints[__fixed__]] = FIXED + return self._optimizer_copy_[np.logical_and(fixes, self._highest_parent_.tie.getTieFlag(self))] + elif self._has_fixes(): + return self._optimizer_copy_[self._fixes_] + + self._optimizer_copy_transformed = True + + return self._optimizer_copy_ + + @optimizer_array.setter + def optimizer_array(self, p): + """ + Make sure the optimizer copy does not get touched, thus, we only want to + set the values *inside* not the array itself. + + Also we want to update param_array in here. + """ + f = None + if self.has_parent() and self.constraints[__fixed__].size != 0: + f = np.ones(self.size).astype(bool) + f[self.constraints[__fixed__]] = FIXED + elif self._has_fixes(): + f = self._fixes_ + if f is None: + self.param_array.flat = p + [np.put(self.param_array, ind, c.f(self.param_array.flat[ind])) + for c, ind in self.constraints.iteritems() if c != __fixed__] + else: + self.param_array.flat[f] = p + [np.put(self.param_array, ind[f[ind]], c.f(self.param_array.flat[ind[f[ind]]])) + for c, ind in self.constraints.iteritems() if c != __fixed__] + #self._highest_parent_.tie.propagate_val() + + self._optimizer_copy_transformed = False + self.trigger_update() + + def _get_params_transformed(self): + raise DeprecationWarning, "_get|set_params{_optimizer_copy_transformed} is deprecated, use self.optimizer array insetad!" +# + def _set_params_transformed(self, p): + raise DeprecationWarning, "_get|set_params{_optimizer_copy_transformed} is deprecated, use self.optimizer array insetad!" + + def _trigger_params_changed(self, trigger_parent=True): + """ + First tell all children to update, + then update yourself. + + If trigger_parent is True, we will tell the parent, otherwise not. + """ + [p._trigger_params_changed(trigger_parent=False) for p in self.parameters if not p.is_fixed] + self.notify_observers(None, None if trigger_parent else -np.inf) + + def _size_transformed(self): + """ + As fixes are not passed to the optimiser, the size of the model for the optimiser + is the size of all parameters minus the size of the fixes. + """ + return self.size - self.constraints[__fixed__].size + + def _transform_gradients(self, g): + """ + Transform the gradients by multiplying the gradient factor for each + constraint to it. + """ + self._highest_parent_.tie.collate_gradient() + [np.put(g, i, c.gradfactor(self.param_array[i], g[i])) for c, i in self.constraints.iteritems() if c != __fixed__] + if self._has_fixes(): return g[self._fixes_] + return g + + @property + def num_params(self): + """ + Return the number of parameters of this parameter_handle. + Param objects will always return 0. + """ + raise NotImplemented, "Abstract, please implement in respective classes" + + def parameter_names(self, add_self=False, adjust_for_printing=False, recursive=True): + """ + Get the names of all parameters of this model. + + :param bool add_self: whether to add the own name in front of names + :param bool adjust_for_printing: whether to call `adjust_name_for_printing` on names + :param bool recursive: whether to traverse through hierarchy and append leaf node names + """ + if adjust_for_printing: adjust = lambda x: adjust_name_for_printing(x) + else: adjust = lambda x: x + if recursive: names = [xi for x in self.parameters for xi in x.parameter_names(add_self=True, adjust_for_printing=adjust_for_printing)] + else: names = [adjust(x.name) for x in self.parameters] + if add_self: names = map(lambda x: adjust(self.name) + "." + x, names) + return names + + def _get_param_names(self): + n = np.array([p.hierarchy_name() + '[' + str(i) + ']' for p in self.flattened_parameters for i in p._indices()]) + return n + + def _get_param_names_transformed(self): + n = self._get_param_names() + if self._has_fixes(): + return n[self._fixes_] + return n + + #=========================================================================== + # Randomizeable + #=========================================================================== + def randomize(self, rand_gen=None, *args, **kwargs): + """ + Randomize the model. + Make this draw from the prior if one exists, else draw from given random generator + + :param rand_gen: np random number generator which takes args and kwargs + :param flaot loc: loc parameter for random number generator + :param float scale: scale parameter for random number generator + :param args, kwargs: will be passed through to random number generator + """ + if rand_gen is None: + rand_gen = np.random.normal + # first take care of all parameters (from N(0,1)) + x = rand_gen(size=self._size_transformed(), *args, **kwargs) + updates = self.update_model() + self.update_model(False) # Switch off the updates + self.optimizer_array = x # makes sure all of the tied parameters get the same init (since there's only one prior object...) + # now draw from prior where possible + x = self.param_array.copy() + [np.put(x, ind, p.rvs(ind.size)) for p, ind in self.priors.iteritems() if not p is None] + unfixlist = np.ones((self.size,),dtype=np.bool) + unfixlist[self.constraints[__fixed__]] = False + self.param_array.flat[unfixlist] = x.view(np.ndarray).ravel()[unfixlist] + self.update_model(updates) + + #=========================================================================== + # For shared memory arrays. This does nothing in Param, but sets the memory + # for all parameterized objects + #=========================================================================== + @property + def gradient_full(self): + """ + Note to users: + This does not return the gradient in the right shape! Use self.gradient + for the right gradient array. + + To work on the gradient array, use this as the gradient handle. + This method exists for in memory use of parameters. + When trying to access the true gradient array, use this. + """ + self.gradient # <<< ensure _gradient_array_ + return self._gradient_array_ + + def _propagate_param_grad(self, parray, garray): + """ + For propagating the param_array and gradient_array. + This ensures the in memory view of each subsequent array. + + 1.) connect param_array of children to self.param_array + 2.) tell all children to propagate further + """ + if self.param_array.size != self.size: + self._param_array_ = np.empty(self.size, dtype=np.float64) + if self.gradient.size != self.size: + self._gradient_array_ = np.empty(self.size, dtype=np.float64) + + pi_old_size = 0 + for pi in self.parameters: + pislice = slice(pi_old_size, pi_old_size + pi.size) + + self.param_array[pislice] = pi.param_array.flat # , requirements=['C', 'W']).flat + self.gradient_full[pislice] = pi.gradient_full.flat # , requirements=['C', 'W']).flat + + pi.param_array.data = parray[pislice].data + pi.gradient_full.data = garray[pislice].data + + pi._propagate_param_grad(parray[pislice], garray[pislice]) + pi_old_size += pi.size + + def _connect_parameters(self): + pass + +_name_digit = re.compile("(?P.*)_(?P\d+)$") +class Parameterizable(OptimizationHandlable): + """ + A parameterisable class. + + This class provides the parameters list (ArrayList) and standard parameter handling, + such as {add|remove}_parameter(), traverse hierarchy and param_array, gradient_array + and the empty parameters_changed(). + + This class is abstract and should not be instantiated. + Use GPy.core.Parameterized() as node (or leaf) in the parameterized hierarchy. + Use GPy.core.Param() for a leaf in the parameterized hierarchy. + """ + def __init__(self, *args, **kwargs): + super(Parameterizable, self).__init__(*args, **kwargs) + from GPy.core.parameterization.lists_and_dicts import ArrayList + self.parameters = ArrayList() + self._param_array_ = None + self._added_names_ = set() + self.logger = logging.getLogger(self.__class__.__name__) + self.__visited = False # for traversing in reverse order we need to know if we were here already + + @property + def param_array(self): + """ + Array representing the parameters of this class. + There is only one copy of all parameters in memory, two during optimization. + + !WARNING!: setting the parameter array MUST always be done in memory: + m.param_array[:] = m_copy.param_array + """ + if (self.__dict__.get('_param_array_', None) is None) or (self._param_array_.size != self.size): + self._param_array_ = np.empty(self.size, dtype=np.float64) + return self._param_array_ + + @property + def unfixed_param_array(self): + """ + Array representing the parameters of this class. + There is only one copy of all parameters in memory, two during optimization. + + !WARNING!: setting the parameter array MUST always be done in memory: + m.param_array[:] = m_copy.param_array + """ + if self.__dict__.get('_param_array_', None) is None: + self._param_array_ = np.empty(self.size, dtype=np.float64) + + if self.constraints[__fixed__].size !=0: + fixes = np.ones(self.size).astype(bool) + fixes[self.constraints[__fixed__]] = FIXED + return self._param_array_[fixes] + else: + return self._param_array_ + + @param_array.setter + def param_array(self, arr): + self._param_array_ = arr + + def traverse(self, visit, *args, **kwargs): + """ + Traverse the hierarchy performing visit(self, *args, **kwargs) + at every node passed by downwards. This function includes self! + + See "visitor pattern" in literature. This is implemented in pre-order fashion. + + Example: + Collect all children: + + children = [] + self.traverse(children.append) + print children + """ + if not self.__visited: + visit(self, *args, **kwargs) + self.__visited = True + for c in self.parameters: + c.traverse(visit, *args, **kwargs) + self.__visited = False + + def traverse_parents(self, visit, *args, **kwargs): + """ + Traverse the hierarchy upwards, visiting all parents and their children except self. + See "visitor pattern" in literature. This is implemented in pre-order fashion. + + Example: + + parents = [] + self.traverse_parents(parents.append) + print parents + """ + if self.has_parent(): + self.__visited = True + self._parent_._traverse_parents(visit, *args, **kwargs) + self.__visited = False + + def _traverse_parents(self, visit, *args, **kwargs): + if not self.__visited: + self.__visited = True + visit(self, *args, **kwargs) + if self.has_parent(): + self._parent_._traverse_parents(visit, *args, **kwargs) + self._parent_.traverse(visit, *args, **kwargs) + self.__visited = False + + #========================================================================= + # Gradient handling + #========================================================================= + @property + def gradient(self): + if (self.__dict__.get('_gradient_array_', None) is None) or self._gradient_array_.size != self.size: + self._gradient_array_ = np.empty(self.size, dtype=np.float64) + return self._gradient_array_ + + @gradient.setter + def gradient(self, val): + self._gradient_array_[:] = val + + @property + def num_params(self): + return len(self.parameters) + + def _add_parameter_name(self, param, ignore_added_names=False): + pname = adjust_name_for_printing(param.name) + if ignore_added_names: + self.__dict__[pname] = param + return + + def warn_and_retry(param, match=None): + #=================================================================== + # print """ + # WARNING: added a parameter with formatted name {}, + # which is already assigned to {}. + # Trying to change the parameter name to + # + # {}.{} + # """.format(pname, self.hierarchy_name(), self.hierarchy_name(), param.name + "_") + #=================================================================== + if match is None: + param.name += "_1" + else: + param.name = match.group('name') + "_" + str(int(match.group('digit'))+1) + self._add_parameter_name(param, ignore_added_names) + # and makes sure to not delete programmatically added parameters + for other in self.parameters[::-1]: + if other is not param and other.name.startswith(param.name): + warn_and_retry(param, _name_digit.match(other.name)) + return + if pname not in dir(self): + self.__dict__[pname] = param + self._added_names_.add(pname) + elif pname in self.__dict__: + if pname in self._added_names_: + other = self.__dict__[pname] + if not (param is other): + del self.__dict__[pname] + self._added_names_.remove(pname) + warn_and_retry(other) + warn_and_retry(param, _name_digit.match(other.name)) + return + + def _remove_parameter_name(self, param=None, pname=None): + assert param is None or pname is None, "can only delete either param by name, or the name of a param" + pname = adjust_name_for_printing(pname) or adjust_name_for_printing(param.name) + if pname in self._added_names_: + del self.__dict__[pname] + self._added_names_.remove(pname) + self._connect_parameters() + + def _name_changed(self, param, old_name): + self._remove_parameter_name(None, old_name) + self._add_parameter_name(param) + + def __setstate__(self, state): + super(Parameterizable, self).__setstate__(state) + self.logger = logging.getLogger(self.__class__.__name__) + return self + + #=========================================================================== + # notification system + #=========================================================================== + def _parameters_changed_notification(self, me, which=None): + """ + In parameterizable we just need to make sure, that the next call to optimizer_array + will update the optimizer_array to the latest parameters + """ + self._optimizer_copy_transformed = False # tells the optimizer array to update on next request + self.parameters_changed() + def _pass_through_notify_observers(self, me, which=None): + self.notify_observers(which=which) + def _setup_observers(self): + """ + Setup the default observers + + 1: parameters_changed_notify + 2: pass through to parent, if present + """ + self.add_observer(self, self._parameters_changed_notification, -100) + if self.has_parent(): + self.add_observer(self._parent_, self._parent_._pass_through_notify_observers, -np.inf) + #=========================================================================== + # From being parentable, we have to define the parent_change notification + #=========================================================================== + def _notify_parent_change(self): + """ + Notify all parameters that the parent has changed + """ + for p in self.parameters: + p._parent_changed(self) + + def parameters_changed(self): + """ + This method gets called when parameters have changed. + Another way of listening to param changes is to + add self as a listener to the param, such that + updates get passed through. See :py:function:``GPy.core.param.Observable.add_observer`` + """ + pass + + def save(self, filename, ftype='HDF5'): + """ + Save all the model parameters into a file (HDF5 by default). + """ + from . import Param + from ...util.misc import param_to_array + def gather_params(self, plist): + if isinstance(self,Param): + plist.append(self) + plist = [] + self.traverse(gather_params, plist) + names = self.parameter_names(adjust_for_printing=True) + if ftype=='HDF5': + try: + import h5py + f = h5py.File(filename,'w') + for p,n in zip(plist,names): + n = n.replace('.','_') + p = param_to_array(p) + d = f.create_dataset(n,p.shape,dtype=p.dtype) + d[:] = p + f.close() + except: + raise 'Fails to write the parameters into a HDF5 file!' + diff --git a/GPy/core/parameterization/parameterized.py b/GPy/core/parameterization/parameterized.py new file mode 100644 index 00000000..897c53e3 --- /dev/null +++ b/GPy/core/parameterization/parameterized.py @@ -0,0 +1,418 @@ +# Copyright (c) 2014, Max Zwiessele, James Hensman +# Licensed under the BSD 3-clause license (see LICENSE.txt) + + +import numpy; np = numpy +import itertools +from re import compile, _pattern_type +from param import ParamConcatenation +from parameter_core import HierarchyError, Parameterizable, adjust_name_for_printing + +import logging +from GPy.core.parameterization.index_operations import ParameterIndexOperationsView +logger = logging.getLogger("parameters changed meta") + +class ParametersChangedMeta(type): + def __call__(self, *args, **kw): + self._in_init_ = True + #import ipdb;ipdb.set_trace() + self = super(ParametersChangedMeta, self).__call__(*args, **kw) + logger.debug("finished init") + self._in_init_ = False + logger.debug("connecting parameters") + self._highest_parent_._connect_parameters() + #self._highest_parent_._notify_parent_change() + self._highest_parent_._connect_fixes() + logger.debug("calling parameters changed") + self.parameters_changed() + return self + +class Parameterized(Parameterizable): + """ + Parameterized class + + Say m is a handle to a parameterized class. + + Printing parameters: + + - print m: prints a nice summary over all parameters + - print m.name: prints details for param with name 'name' + - print m[regexp]: prints details for all the parameters + which match (!) regexp + - print m['']: prints details for all parameters + + Fields: + + Name: The name of the param, can be renamed! + Value: Shape or value, if one-valued + Constrain: constraint of the param, curly "{c}" brackets indicate + some parameters are constrained by c. See detailed print + to get exact constraints. + Tied_to: which paramter it is tied to. + + Getting and setting parameters: + + Set all values in param to one: + + m.name.to.param = 1 + + Handling of constraining, fixing and tieing parameters: + + You can constrain parameters by calling the constrain on the param itself, e.g: + + - m.name[:,1].constrain_positive() + - m.name[0].tie_to(m.name[1]) + + Fixing parameters will fix them to the value they are right now. If you change + the parameters value, the param will be fixed to the new value! + + If you want to operate on all parameters use m[''] to wildcard select all paramters + and concatenate them. Printing m[''] will result in printing of all parameters in detail. + """ + #=========================================================================== + # Metaclass for parameters changed after init. + # This makes sure, that parameters changed will always be called after __init__ + # **Never** call parameters_changed() yourself + __metaclass__ = ParametersChangedMeta + #=========================================================================== + def __init__(self, name=None, parameters=[], *a, **kw): + super(Parameterized, self).__init__(name=name, *a, **kw) + self.size = sum(p.size for p in self.parameters) + self.add_observer(self, self._parameters_changed_notification, -100) + if not self._has_fixes(): + self._fixes_ = None + self._param_slices_ = [] + #self._connect_parameters() + self.link_parameters(*parameters) + + def build_pydot(self, G=None): + import pydot # @UnresolvedImport + iamroot = False + if G is None: + G = pydot.Dot(graph_type='digraph', bgcolor=None) + iamroot=True + node = pydot.Node(id(self), shape='box', label=self.name)#, color='white') + G.add_node(node) + for child in self.parameters: + child_node = child.build_pydot(G) + G.add_edge(pydot.Edge(node, child_node))#, color='white')) + + for _, o, _ in self.observers: + label = o.name if hasattr(o, 'name') else str(o) + observed_node = pydot.Node(id(o), label=label) + G.add_node(observed_node) + edge = pydot.Edge(str(id(self)), str(id(o)), color='darkorange2', arrowhead='vee') + G.add_edge(edge) + + if iamroot: + return G + return node + + #=========================================================================== + # Add remove parameters: + #=========================================================================== + def link_parameter(self, param, index=None, _ignore_added_names=False): + """ + :param parameters: the parameters to add + :type parameters: list of or one :py:class:`GPy.core.param.Param` + :param [index]: index of where to put parameters + + :param bool _ignore_added_names: whether the name of the parameter overrides a possibly existing field + + Add all parameters to this param class, you can insert parameters + at any given index using the :func:`list.insert` syntax + """ + if param in self.parameters and index is not None: + self.unlink_parameter(param) + self.link_parameter(param, index) + # elif param.has_parent(): + # raise HierarchyError, "parameter {} already in another model ({}), create new object (or copy) for adding".format(param._short(), param._highest_parent_._short()) + elif param not in self.parameters: + if param.has_parent(): + def visit(parent, self): + if parent is self: + raise HierarchyError, "You cannot add a parameter twice into the hierarchy" + param.traverse_parents(visit, self) + param._parent_.unlink_parameter(param) + # make sure the size is set + if index is None: + start = sum(p.size for p in self.parameters) + self.constraints.shift_right(start, param.size) + self.priors.shift_right(start, param.size) + self.constraints.update(param.constraints, self.size) + self.priors.update(param.priors, self.size) + param._parent_ = self + param._parent_index_ = len(self.parameters) + self.parameters.append(param) + else: + start = sum(p.size for p in self.parameters[:index]) + self.constraints.shift_right(start, param.size) + self.priors.shift_right(start, param.size) + self.constraints.update(param.constraints, start) + self.priors.update(param.priors, start) + param._parent_ = self + param._parent_index_ = index if index>=0 else len(self.parameters[:index]) + for p in self.parameters[index:]: + p._parent_index_ += 1 + self.parameters.insert(index, param) + + param.add_observer(self, self._pass_through_notify_observers, -np.inf) + + parent = self + while parent is not None: + parent.size += param.size + parent = parent._parent_ + self._notify_parent_change() + + if not self._in_init_: + #self._connect_parameters() + #self._notify_parent_change() + + self._highest_parent_._connect_parameters(ignore_added_names=_ignore_added_names) + self._highest_parent_._notify_parent_change() + self._highest_parent_._connect_fixes() + + else: + raise HierarchyError, """Parameter exists already, try making a copy""" + + + def link_parameters(self, *parameters): + """ + convenience method for adding several + parameters without gradient specification + """ + [self.link_parameter(p) for p in parameters] + + def unlink_parameter(self, param): + """ + :param param: param object to remove from being a parameter of this parameterized object. + """ + if not param in self.parameters: + try: + raise RuntimeError, "{} does not belong to this object {}, remove parameters directly from their respective parents".format(param._short(), self.name) + except AttributeError: + raise RuntimeError, "{} does not seem to be a parameter, remove parameters directly from their respective parents".format(str(param)) + + start = sum([p.size for p in self.parameters[:param._parent_index_]]) + self._remove_parameter_name(param) + self.size -= param.size + del self.parameters[param._parent_index_] + + param._disconnect_parent() + param.remove_observer(self, self._pass_through_notify_observers) + self.constraints.shift_left(start, param.size) + + self._connect_parameters() + self._notify_parent_change() + + parent = self._parent_ + while parent is not None: + parent.size -= param.size + parent = parent._parent_ + + self._highest_parent_._connect_parameters() + self._highest_parent_._connect_fixes() + self._highest_parent_._notify_parent_change() + + def add_parameter(self, *args, **kwargs): + raise DeprecationWarning, "add_parameter was renamed to link_parameter to avoid confusion of setting variables" + def remove_parameter(self, *args, **kwargs): + raise DeprecationWarning, "remove_parameter was renamed to link_parameter to avoid confusion of setting variables" + + def _connect_parameters(self, ignore_added_names=False): + # connect parameterlist to this parameterized object + # This just sets up the right connection for the params objects + # to be used as parameters + # it also sets the constraints for each parameter to the constraints + # of their respective parents + if not hasattr(self, "parameters") or len(self.parameters) < 1: + # no parameters for this class + return + if self.param_array.size != self.size: + self._param_array_ = np.empty(self.size, dtype=np.float64) + if self.gradient.size != self.size: + self._gradient_array_ = np.empty(self.size, dtype=np.float64) + + old_size = 0 + self._param_slices_ = [] + for i, p in enumerate(self.parameters): + if not p.param_array.flags['C_CONTIGUOUS']: + raise ValueError, "This should not happen! Please write an email to the developers with the code, which reproduces this error. All parameter arrays must be C_CONTIGUOUS" + + p._parent_ = self + p._parent_index_ = i + + pslice = slice(old_size, old_size + p.size) + + # first connect all children + p._propagate_param_grad(self.param_array[pslice], self.gradient_full[pslice]) + + # then connect children to self + self.param_array[pslice] = p.param_array.flat # , requirements=['C', 'W']).ravel(order='C') + self.gradient_full[pslice] = p.gradient_full.flat # , requirements=['C', 'W']).ravel(order='C') + + p.param_array.data = self.param_array[pslice].data + p.gradient_full.data = self.gradient_full[pslice].data + + self._param_slices_.append(pslice) + + self._add_parameter_name(p, ignore_added_names=ignore_added_names) + old_size += p.size + + #=========================================================================== + # Get/set parameters: + #=========================================================================== + def grep_param_names(self, regexp): + """ + create a list of parameters, matching regular expression regexp + """ + if not isinstance(regexp, _pattern_type): regexp = compile(regexp) + found_params = [] + for n, p in itertools.izip(self.parameter_names(False, False, True), self.flattened_parameters): + if regexp.match(n) is not None: + found_params.append(p) + return found_params + + def __getitem__(self, name, paramlist=None): + if isinstance(name, (int, slice, tuple, np.ndarray)): + return self.param_array[name] + else: + if paramlist is None: + paramlist = self.grep_param_names(name) + if len(paramlist) < 1: raise AttributeError, name + if len(paramlist) == 1: + if isinstance(paramlist[-1], Parameterized): + paramlist = paramlist[-1].flattened_parameters + if len(paramlist) != 1: + return ParamConcatenation(paramlist) + return paramlist[-1] + return ParamConcatenation(paramlist) + + def __setitem__(self, name, value, paramlist=None): + if value is None: + return # nothing to do here + if isinstance(name, (slice, tuple, np.ndarray)): + try: + self.param_array[name] = value + except: + raise ValueError, "Setting by slice or index only allowed with array-like" + self._trigger_params_changed() + else: + try: param = self.__getitem__(name, paramlist) + except: raise + param[:] = value + + def __setattr__(self, name, val): + # override the default behaviour, if setting a param, so broadcasting can by used + if hasattr(self, "parameters"): + try: + pnames = self.parameter_names(False, adjust_for_printing=True, recursive=False) + if name in pnames: + param = self.parameters[pnames.index(name)] + param[:] = val; return + except AttributeError: + pass + object.__setattr__(self, name, val); + + #=========================================================================== + # Pickling + #=========================================================================== + def __setstate__(self, state): + super(Parameterized, self).__setstate__(state) + try: + self._connect_parameters() + self._connect_fixes() + self._notify_parent_change() + self.parameters_changed() + except Exception as e: + print "WARNING: caught exception {!s}, trying to continue".format(e) + + def copy(self, memo=None): + if memo is None: + memo = {} + memo[id(self.optimizer_array)] = None # and param_array + memo[id(self.param_array)] = None # and param_array + copy = super(Parameterized, self).copy(memo) + copy._connect_parameters() + copy._connect_fixes() + copy._notify_parent_change() + return copy + + #=========================================================================== + # Printing: + #=========================================================================== + def _short(self): + return self.hierarchy_name() + @property + def flattened_parameters(self): + return [xi for x in self.parameters for xi in x.flattened_parameters] + @property + def _parameter_sizes_(self): + return [x.size for x in self.parameters] + @property + def parameter_shapes(self): + return [xi for x in self.parameters for xi in x.parameter_shapes] + @property + def _constraints_str(self): + return [cs for p in self.parameters for cs in p._constraints_str] + @property + def _priors_str(self): + return [cs for p in self.parameters for cs in p._priors_str] + @property + def _description_str(self): + return [xi for x in self.parameters for xi in x._description_str] + @property + def _ties_str(self): + return [','.join(x._ties_str) for x in self.flattened_parameters] + + def _repr_html_(self, header=True): + """Representation of the parameters in html for notebook display.""" + name = adjust_name_for_printing(self.name) + "." + constrs = self._constraints_str; + ts = self._ties_str + prirs = self._priors_str + desc = self._description_str; names = self.parameter_names() + nl = max([len(str(x)) for x in names + [name]]) + sl = max([len(str(x)) for x in desc + ["Value"]]) + cl = max([len(str(x)) if x else 0 for x in constrs + ["Constraint"]]) + tl = max([len(str(x)) if x else 0 for x in ts + ["Tied to"]]) + pl = max([len(str(x)) if x else 0 for x in prirs + ["Prior"]]) + format_spec = "{{name:<{0}s}}{{desc:>{1}s}}{{const:^{2}s}}{{pri:^{3}s}}{{t:^{4}s}}".format(nl, sl, cl, pl, tl) + to_print = [] + for n, d, c, t, p in itertools.izip(names, desc, constrs, ts, prirs): + to_print.append(format_spec.format(name=n, desc=d, const=c, t=t, pri=p)) + sep = '-' * (nl + sl + cl + + pl + tl + 8 * 2 + 3) + if header: + header = """ + + {name} + Value + Constraint + Prior + Tied to""".format(name=name) + to_print.insert(0, header) + return '' + '\n'.format(sep).join(to_print) + '\n
' + + def __str__(self, header=True): + name = adjust_name_for_printing(self.name) + "." + constrs = self._constraints_str; + ts = self._ties_str + prirs = self._priors_str + desc = self._description_str; names = self.parameter_names() + nl = max([len(str(x)) for x in names + [name]]) + sl = max([len(str(x)) for x in desc + ["Value"]]) + cl = max([len(str(x)) if x else 0 for x in constrs + ["Constraint"]]) + tl = max([len(str(x)) if x else 0 for x in ts + ["Tied to"]]) + pl = max([len(str(x)) if x else 0 for x in prirs + ["Prior"]]) + format_spec = " \033[1m{{name:<{0}s}}\033[0;0m | {{desc:>{1}s}} | {{const:^{2}s}} | {{pri:^{3}s}} | {{t:^{4}s}}".format(nl, sl, cl, pl, tl) + to_print = [] + for n, d, c, t, p in itertools.izip(names, desc, constrs, ts, prirs): + to_print.append(format_spec.format(name=n, desc=d, const=c, t=t, pri=p)) + sep = '-' * (nl + sl + cl + + pl + tl + 8 * 2 + 3) + if header: + header = " {{0:<{0}s}} | {{1:^{1}s}} | {{2:^{2}s}} | {{3:^{3}s}} | {{4:^{4}s}}".format(nl, sl, cl, pl, tl).format(name, "Value", "Constraint", "Prior", "Tied to") + to_print.insert(0, header) + return '\n'.format(sep).join(to_print) + pass + + diff --git a/GPy/core/parameterization/priors.py b/GPy/core/parameterization/priors.py new file mode 100644 index 00000000..84b6357e --- /dev/null +++ b/GPy/core/parameterization/priors.py @@ -0,0 +1,771 @@ +# Copyright (c) 2012 - 2014, GPy authors (see AUTHORS.txt). +# Licensed under the BSD 3-clause license (see LICENSE.txt) + + +import numpy as np +from scipy.special import gammaln, digamma +from ...util.linalg import pdinv +from domains import _REAL, _POSITIVE +import warnings +import weakref + + +class Prior(object): + domain = None + _instance = None + def __new__(cls, *args, **kwargs): + if not cls._instance or cls._instance.__class__ is not cls: + cls._instance = super(Prior, cls).__new__(cls, *args, **kwargs) + return cls._instance + + def pdf(self, x): + return np.exp(self.lnpdf(x)) + + def plot(self): + import sys + + assert "matplotlib" in sys.modules, "matplotlib package has not been imported." + from ...plotting.matplot_dep import priors_plots + + priors_plots.univariate_plot(self) + + def __repr__(self, *args, **kwargs): + return self.__str__() + + +class Gaussian(Prior): + """ + Implementation of the univariate Gaussian probability function, coupled with random variables. + + :param mu: mean + :param sigma: standard deviation + + .. Note:: Bishop 2006 notation is used throughout the code + + """ + domain = _REAL + _instances = [] + + def __new__(cls, mu=0, sigma=1): # Singleton: + if cls._instances: + cls._instances[:] = [instance for instance in cls._instances if instance()] + for instance in cls._instances: + if instance().mu == mu and instance().sigma == sigma: + return instance() + o = super(Prior, cls).__new__(cls, mu, sigma) + cls._instances.append(weakref.ref(o)) + return cls._instances[-1]() + + def __init__(self, mu, sigma): + self.mu = float(mu) + self.sigma = float(sigma) + self.sigma2 = np.square(self.sigma) + self.constant = -0.5 * np.log(2 * np.pi * self.sigma2) + + def __str__(self): + return "N({:.2g}, {:.2g})".format(self.mu, self.sigma) + + def lnpdf(self, x): + return self.constant - 0.5 * np.square(x - self.mu) / self.sigma2 + + def lnpdf_grad(self, x): + return -(x - self.mu) / self.sigma2 + + def rvs(self, n): + return np.random.randn(n) * self.sigma + self.mu + +# def __getstate__(self): +# return self.mu, self.sigma +# +# def __setstate__(self, state): +# self.mu = state[0] +# self.sigma = state[1] +# self.sigma2 = np.square(self.sigma) +# self.constant = -0.5 * np.log(2 * np.pi * self.sigma2) + +class Uniform(Prior): + domain = _REAL + _instances = [] + + def __new__(cls, lower=0, upper=1): # Singleton: + if cls._instances: + cls._instances[:] = [instance for instance in cls._instances if instance()] + for instance in cls._instances: + if instance().lower == lower and instance().upper == upper: + return instance() + o = super(Prior, cls).__new__(cls, lower, upper) + cls._instances.append(weakref.ref(o)) + return cls._instances[-1]() + + def __init__(self, lower, upper): + self.lower = float(lower) + self.upper = float(upper) + + def __str__(self): + return "[{:.2g}, {:.2g}]".format(self.lower, self.upper) + + def lnpdf(self, x): + region = (x >= self.lower) * (x <= self.upper) + return region + + def lnpdf_grad(self, x): + return np.zeros(x.shape) + + def rvs(self, n): + return np.random.uniform(self.lower, self.upper, size=n) + +# def __getstate__(self): +# return self.lower, self.upper +# +# def __setstate__(self, state): +# self.lower = state[0] +# self.upper = state[1] + +class LogGaussian(Gaussian): + """ + Implementation of the univariate *log*-Gaussian probability function, coupled with random variables. + + :param mu: mean + :param sigma: standard deviation + + .. Note:: Bishop 2006 notation is used throughout the code + + """ + domain = _POSITIVE + _instances = [] + + def __new__(cls, mu=0, sigma=1): # Singleton: + if cls._instances: + cls._instances[:] = [instance for instance in cls._instances if instance()] + for instance in cls._instances: + if instance().mu == mu and instance().sigma == sigma: + return instance() + o = super(Prior, cls).__new__(cls, mu, sigma) + cls._instances.append(weakref.ref(o)) + return cls._instances[-1]() + + def __init__(self, mu, sigma): + self.mu = float(mu) + self.sigma = float(sigma) + self.sigma2 = np.square(self.sigma) + self.constant = -0.5 * np.log(2 * np.pi * self.sigma2) + + def __str__(self): + return "lnN({:.2g}, {:.2g})".format(self.mu, self.sigma) + + def lnpdf(self, x): + return self.constant - 0.5 * np.square(np.log(x) - self.mu) / self.sigma2 - np.log(x) + + def lnpdf_grad(self, x): + return -((np.log(x) - self.mu) / self.sigma2 + 1.) / x + + def rvs(self, n): + return np.exp(np.random.randn(n) * self.sigma + self.mu) + + +class MultivariateGaussian(Prior): + """ + Implementation of the multivariate Gaussian probability function, coupled with random variables. + + :param mu: mean (N-dimensional array) + :param var: covariance matrix (NxN) + + .. Note:: Bishop 2006 notation is used throughout the code + + """ + domain = _REAL + _instances = [] + + def __new__(cls, mu=0, var=1): # Singleton: + if cls._instances: + cls._instances[:] = [instance for instance in cls._instances if instance()] + for instance in cls._instances: + if np.all(instance().mu == mu) and np.all(instance().var == var): + return instance() + o = super(Prior, cls).__new__(cls, mu, var) + cls._instances.append(weakref.ref(o)) + return cls._instances[-1]() + + def __init__(self, mu, var): + self.mu = np.array(mu).flatten() + self.var = np.array(var) + assert len(self.var.shape) == 2 + assert self.var.shape[0] == self.var.shape[1] + assert self.var.shape[0] == self.mu.size + self.input_dim = self.mu.size + self.inv, self.hld = pdinv(self.var) + self.constant = -0.5 * self.input_dim * np.log(2 * np.pi) - self.hld + + def summary(self): + raise NotImplementedError + + def pdf(self, x): + return np.exp(self.lnpdf(x)) + + def lnpdf(self, x): + d = x - self.mu + return self.constant - 0.5 * np.sum(d * np.dot(d, self.inv), 1) + + def lnpdf_grad(self, x): + d = x - self.mu + return -np.dot(self.inv, d) + + def rvs(self, n): + return np.random.multivariate_normal(self.mu, self.var, n) + + def plot(self): + import sys + + assert "matplotlib" in sys.modules, "matplotlib package has not been imported." + from ..plotting.matplot_dep import priors_plots + + priors_plots.multivariate_plot(self) + + def __getstate__(self): + return self.mu, self.var + + def __setstate__(self, state): + self.mu = state[0] + self.var = state[1] + assert len(self.var.shape) == 2 + assert self.var.shape[0] == self.var.shape[1] + assert self.var.shape[0] == self.mu.size + self.input_dim = self.mu.size + self.inv, self.hld = pdinv(self.var) + self.constant = -0.5 * self.input_dim * np.log(2 * np.pi) - self.hld + +def gamma_from_EV(E, V): + warnings.warn("use Gamma.from_EV to create Gamma Prior", FutureWarning) + return Gamma.from_EV(E, V) + + +class Gamma(Prior): + """ + Implementation of the Gamma probability function, coupled with random variables. + + :param a: shape parameter + :param b: rate parameter (warning: it's the *inverse* of the scale) + + .. Note:: Bishop 2006 notation is used throughout the code + + """ + domain = _POSITIVE + _instances = [] + + def __new__(cls, a=1, b=.5): # Singleton: + if cls._instances: + cls._instances[:] = [instance for instance in cls._instances if instance()] + for instance in cls._instances: + if instance().a == a and instance().b == b: + return instance() + o = super(Prior, cls).__new__(cls, a, b) + cls._instances.append(weakref.ref(o)) + return cls._instances[-1]() + + def __init__(self, a, b): + self.a = float(a) + self.b = float(b) + self.constant = -gammaln(self.a) + a * np.log(b) + + def __str__(self): + return "Ga({:.2g}, {:.2g})".format(self.a, self.b) + + def summary(self): + ret = {"E[x]": self.a / self.b, \ + "E[ln x]": digamma(self.a) - np.log(self.b), \ + "var[x]": self.a / self.b / self.b, \ + "Entropy": gammaln(self.a) - (self.a - 1.) * digamma(self.a) - np.log(self.b) + self.a} + if self.a > 1: + ret['Mode'] = (self.a - 1.) / self.b + else: + ret['mode'] = np.nan + return ret + + def lnpdf(self, x): + return self.constant + (self.a - 1) * np.log(x) - self.b * x + + def lnpdf_grad(self, x): + return (self.a - 1.) / x - self.b + + def rvs(self, n): + return np.random.gamma(scale=1. / self.b, shape=self.a, size=n) + + @staticmethod + def from_EV(E, V): + """ + Creates an instance of a Gamma Prior by specifying the Expected value(s) + and Variance(s) of the distribution. + + :param E: expected value + :param V: variance + """ + a = np.square(E) / V + b = E / V + return Gamma(a, b) + + def __getstate__(self): + return self.a, self.b + + def __setstate__(self, state): + self.a = state[0] + self.b = state[1] + self.constant = -gammaln(self.a) + self.a * np.log(self.b) + +class InverseGamma(Gamma): + """ + Implementation of the inverse-Gamma probability function, coupled with random variables. + + :param a: shape parameter + :param b: rate parameter (warning: it's the *inverse* of the scale) + + .. Note:: Bishop 2006 notation is used throughout the code + + """ + domain = _POSITIVE + _instances = [] + def __new__(cls, a=1, b=.5): # Singleton: + if cls._instances: + cls._instances[:] = [instance for instance in cls._instances if instance()] + for instance in cls._instances: + if instance().a == a and instance().b == b: + return instance() + o = super(Prior, cls).__new__(cls, a, b) + cls._instances.append(weakref.ref(o)) + return cls._instances[-1]() + + def __init__(self, a, b): + self.a = float(a) + self.b = float(b) + self.constant = -gammaln(self.a) + a * np.log(b) + + def __str__(self): + return "iGa({:.2g}, {:.2g})".format(self.a, self.b) + + def lnpdf(self, x): + return self.constant - (self.a + 1) * np.log(x) - self.b / x + + def lnpdf_grad(self, x): + return -(self.a + 1.) / x + self.b / x ** 2 + + def rvs(self, n): + return 1. / np.random.gamma(scale=1. / self.b, shape=self.a, size=n) + +class DGPLVM_KFDA(Prior): + """ + Implementation of the Discriminative Gaussian Process Latent Variable function using + Kernel Fisher Discriminant Analysis by Seung-Jean Kim for implementing Face paper + by Chaochao Lu. + + :param lambdaa: constant + :param sigma2: constant + + .. Note:: Surpassing Human-Level Face paper dgplvm implementation + + """ + domain = _REAL + # _instances = [] + # def __new__(cls, lambdaa, sigma2): # Singleton: + # if cls._instances: + # cls._instances[:] = [instance for instance in cls._instances if instance()] + # for instance in cls._instances: + # if instance().mu == mu and instance().sigma == sigma: + # return instance() + # o = super(Prior, cls).__new__(cls, mu, sigma) + # cls._instances.append(weakref.ref(o)) + # return cls._instances[-1]() + + def __init__(self, lambdaa, sigma2, lbl, kern, x_shape): + """A description for init""" + self.datanum = lbl.shape[0] + self.classnum = lbl.shape[1] + self.lambdaa = lambdaa + self.sigma2 = sigma2 + self.lbl = lbl + self.kern = kern + lst_ni = self.compute_lst_ni() + self.a = self.compute_a(lst_ni) + self.A = self.compute_A(lst_ni) + self.x_shape = x_shape + + def get_class_label(self, y): + for idx, v in enumerate(y): + if v == 1: + return idx + return -1 + + # This function assigns each data point to its own class + # and returns the dictionary which contains the class name and parameters. + def compute_cls(self, x): + cls = {} + # Appending each data point to its proper class + for j in xrange(self.datanum): + class_label = self.get_class_label(self.lbl[j]) + if class_label not in cls: + cls[class_label] = [] + cls[class_label].append(x[j]) + if len(cls) > 2: + for i in range(2, self.classnum): + del cls[i] + return cls + + def x_reduced(self, cls): + x1 = cls[0] + x2 = cls[1] + x = np.concatenate((x1, x2), axis=0) + return x + + def compute_lst_ni(self): + lst_ni = [] + lst_ni1 = [] + lst_ni2 = [] + f1 = (np.where(self.lbl[:, 0] == 1)[0]) + f2 = (np.where(self.lbl[:, 1] == 1)[0]) + for idx in f1: + lst_ni1.append(idx) + for idx in f2: + lst_ni2.append(idx) + lst_ni.append(len(lst_ni1)) + lst_ni.append(len(lst_ni2)) + return lst_ni + + def compute_a(self, lst_ni): + a = np.ones((self.datanum, 1)) + count = 0 + for N_i in lst_ni: + if N_i == lst_ni[0]: + a[count:count + N_i] = (float(1) / N_i) * a[count] + count += N_i + else: + if N_i == lst_ni[1]: + a[count: count + N_i] = -(float(1) / N_i) * a[count] + count += N_i + return a + + def compute_A(self, lst_ni): + A = np.zeros((self.datanum, self.datanum)) + idx = 0 + for N_i in lst_ni: + B = float(1) / np.sqrt(N_i) * (np.eye(N_i) - ((float(1) / N_i) * np.ones((N_i, N_i)))) + A[idx:idx + N_i, idx:idx + N_i] = B + idx += N_i + return A + + # Here log function + def lnpdf(self, x): + x = x.reshape(self.x_shape) + K = self.kern.K(x) + a_trans = np.transpose(self.a) + paran = self.lambdaa * np.eye(x.shape[0]) + self.A.dot(K).dot(self.A) + inv_part = pdinv(paran)[0] + J = a_trans.dot(K).dot(self.a) - a_trans.dot(K).dot(self.A).dot(inv_part).dot(self.A).dot(K).dot(self.a) + J_star = (1. / self.lambdaa) * J + return (-1. / self.sigma2) * J_star + + # Here gradient function + def lnpdf_grad(self, x): + x = x.reshape(self.x_shape) + K = self.kern.K(x) + paran = self.lambdaa * np.eye(x.shape[0]) + self.A.dot(K).dot(self.A) + inv_part = pdinv(paran)[0] + b = self.A.dot(inv_part).dot(self.A).dot(K).dot(self.a) + a_Minus_b = self.a - b + a_b_trans = np.transpose(a_Minus_b) + DJ_star_DK = (1. / self.lambdaa) * (a_Minus_b.dot(a_b_trans)) + DJ_star_DX = self.kern.gradients_X(DJ_star_DK, x) + return (-1. / self.sigma2) * DJ_star_DX + + def rvs(self, n): + return np.random.rand(n) # A WRONG implementation + + def __str__(self): + return 'DGPLVM_prior' + + def __getstate___(self): + return self.lbl, self.lambdaa, self.sigma2, self.kern, self.x_shape + + def __setstate__(self, state): + lbl, lambdaa, sigma2, kern, a, A, x_shape = state + self.datanum = lbl.shape[0] + self.classnum = lbl.shape[1] + self.lambdaa = lambdaa + self.sigma2 = sigma2 + self.lbl = lbl + self.kern = kern + lst_ni = self.compute_lst_ni() + self.a = self.compute_a(lst_ni) + self.A = self.compute_A(lst_ni) + self.x_shape = x_shape + +class DGPLVM(Prior): + """ + Implementation of the Discriminative Gaussian Process Latent Variable model paper, by Raquel. + + :param sigma2: constant + + .. Note:: DGPLVM for Classification paper implementation + + """ + domain = _REAL + # _instances = [] + # def __new__(cls, mu, sigma): # Singleton: + # if cls._instances: + # cls._instances[:] = [instance for instance in cls._instances if instance()] + # for instance in cls._instances: + # if instance().mu == mu and instance().sigma == sigma: + # return instance() + # o = super(Prior, cls).__new__(cls, mu, sigma) + # cls._instances.append(weakref.ref(o)) + # return cls._instances[-1]() + + def __init__(self, sigma2, lbl, x_shape): + self.sigma2 = sigma2 + # self.x = x + self.lbl = lbl + self.classnum = lbl.shape[1] + self.datanum = lbl.shape[0] + self.x_shape = x_shape + self.dim = x_shape[1] + + def get_class_label(self, y): + for idx, v in enumerate(y): + if v == 1: + return idx + return -1 + + # This function assigns each data point to its own class + # and returns the dictionary which contains the class name and parameters. + def compute_cls(self, x): + cls = {} + # Appending each data point to its proper class + for j in xrange(self.datanum): + class_label = self.get_class_label(self.lbl[j]) + if class_label not in cls: + cls[class_label] = [] + cls[class_label].append(x[j]) + return cls + + # This function computes mean of each class. The mean is calculated through each dimension + def compute_Mi(self, cls): + M_i = np.zeros((self.classnum, self.dim)) + for i in cls: + # Mean of each class + M_i[i] = np.mean(cls[i], axis=0) + return M_i + + # Adding data points as tuple to the dictionary so that we can access indices + def compute_indices(self, x): + data_idx = {} + for j in xrange(self.datanum): + class_label = self.get_class_label(self.lbl[j]) + if class_label not in data_idx: + data_idx[class_label] = [] + t = (j, x[j]) + data_idx[class_label].append(t) + return data_idx + + # Adding indices to the list so we can access whole the indices + def compute_listIndices(self, data_idx): + lst_idx = [] + lst_idx_all = [] + for i in data_idx: + if len(lst_idx) == 0: + pass + #Do nothing, because it is the first time list is created so is empty + else: + lst_idx = [] + # Here we put indices of each class in to the list called lst_idx_all + for m in xrange(len(data_idx[i])): + lst_idx.append(data_idx[i][m][0]) + lst_idx_all.append(lst_idx) + return lst_idx_all + + # This function calculates between classes variances + def compute_Sb(self, cls, M_i, M_0): + Sb = np.zeros((self.dim, self.dim)) + for i in cls: + B = (M_i[i] - M_0).reshape(self.dim, 1) + B_trans = B.transpose() + Sb += (float(len(cls[i])) / self.datanum) * B.dot(B_trans) + return Sb + + # This function calculates within classes variances + def compute_Sw(self, cls, M_i): + Sw = np.zeros((self.dim, self.dim)) + for i in cls: + N_i = float(len(cls[i])) + W_WT = np.zeros((self.dim, self.dim)) + for xk in cls[i]: + W = (xk - M_i[i]) + W_WT += np.outer(W, W) + Sw += (N_i / self.datanum) * ((1. / N_i) * W_WT) + return Sw + + # Calculating beta and Bi for Sb + def compute_sig_beta_Bi(self, data_idx, M_i, M_0, lst_idx_all): + # import pdb + # pdb.set_trace() + B_i = np.zeros((self.classnum, self.dim)) + Sig_beta_B_i_all = np.zeros((self.datanum, self.dim)) + for i in data_idx: + # pdb.set_trace() + # Calculating Bi + B_i[i] = (M_i[i] - M_0).reshape(1, self.dim) + for k in xrange(self.datanum): + for i in data_idx: + N_i = float(len(data_idx[i])) + if k in lst_idx_all[i]: + beta = (float(1) / N_i) - (float(1) / self.datanum) + Sig_beta_B_i_all[k] += float(N_i) / self.datanum * (beta * B_i[i]) + else: + beta = -(float(1) / self.datanum) + Sig_beta_B_i_all[k] += float(N_i) / self.datanum * (beta * B_i[i]) + Sig_beta_B_i_all = Sig_beta_B_i_all.transpose() + return Sig_beta_B_i_all + + + # Calculating W_j s separately so we can access all the W_j s anytime + def compute_wj(self, data_idx, M_i): + W_i = np.zeros((self.datanum, self.dim)) + for i in data_idx: + N_i = float(len(data_idx[i])) + for tpl in data_idx[i]: + xj = tpl[1] + j = tpl[0] + W_i[j] = (xj - M_i[i]) + return W_i + + # Calculating alpha and Wj for Sw + def compute_sig_alpha_W(self, data_idx, lst_idx_all, W_i): + Sig_alpha_W_i = np.zeros((self.datanum, self.dim)) + for i in data_idx: + N_i = float(len(data_idx[i])) + for tpl in data_idx[i]: + k = tpl[0] + for j in lst_idx_all[i]: + if k == j: + alpha = 1 - (float(1) / N_i) + Sig_alpha_W_i[k] += (alpha * W_i[j]) + else: + alpha = 0 - (float(1) / N_i) + Sig_alpha_W_i[k] += (alpha * W_i[j]) + Sig_alpha_W_i = (1. / self.datanum) * np.transpose(Sig_alpha_W_i) + return Sig_alpha_W_i + + # This function calculates log of our prior + def lnpdf(self, x): + x = x.reshape(self.x_shape) + cls = self.compute_cls(x) + M_0 = np.mean(x, axis=0) + M_i = self.compute_Mi(cls) + Sb = self.compute_Sb(cls, M_i, M_0) + Sw = self.compute_Sw(cls, M_i) + # Sb_inv_N = np.linalg.inv(Sb + np.eye(Sb.shape[0]) * (np.diag(Sb).min() * 0.1)) + #Sb_inv_N = np.linalg.inv(Sb+np.eye(Sb.shape[0])*0.1) + Sb_inv_N = pdinv(Sb+ np.eye(Sb.shape[0]) * (np.diag(Sb).min() * 0.1))[0] + return (-1 / self.sigma2) * np.trace(Sb_inv_N.dot(Sw)) + + # This function calculates derivative of the log of prior function + def lnpdf_grad(self, x): + x = x.reshape(self.x_shape) + cls = self.compute_cls(x) + M_0 = np.mean(x, axis=0) + M_i = self.compute_Mi(cls) + Sb = self.compute_Sb(cls, M_i, M_0) + Sw = self.compute_Sw(cls, M_i) + data_idx = self.compute_indices(x) + lst_idx_all = self.compute_listIndices(data_idx) + Sig_beta_B_i_all = self.compute_sig_beta_Bi(data_idx, M_i, M_0, lst_idx_all) + W_i = self.compute_wj(data_idx, M_i) + Sig_alpha_W_i = self.compute_sig_alpha_W(data_idx, lst_idx_all, W_i) + + # Calculating inverse of Sb and its transpose and minus + # Sb_inv_N = np.linalg.inv(Sb + np.eye(Sb.shape[0]) * (np.diag(Sb).min() * 0.1)) + # Sb_inv_N = np.linalg.inv(Sb+np.eye(Sb.shape[0])*0.1) + Sb_inv_N = pdinv(Sb+ np.eye(Sb.shape[0]) * (np.diag(Sb).min() * 0.1))[0] + Sb_inv_N_trans = np.transpose(Sb_inv_N) + Sb_inv_N_trans_minus = -1 * Sb_inv_N_trans + Sw_trans = np.transpose(Sw) + + # Calculating DJ/DXk + DJ_Dxk = 2 * ( + Sb_inv_N_trans_minus.dot(Sw_trans).dot(Sb_inv_N_trans).dot(Sig_beta_B_i_all) + Sb_inv_N_trans.dot( + Sig_alpha_W_i)) + # Calculating derivative of the log of the prior + DPx_Dx = ((-1 / self.sigma2) * DJ_Dxk) + return DPx_Dx.T + + # def frb(self, x): + # from functools import partial + # from GPy.models import GradientChecker + # f = partial(self.lnpdf) + # df = partial(self.lnpdf_grad) + # grad = GradientChecker(f, df, x, 'X') + # grad.checkgrad(verbose=1) + + def rvs(self, n): + return np.random.rand(n) # A WRONG implementation + + def __str__(self): + return 'DGPLVM_prior' + +class HalfT(Prior): + """ + Implementation of the half student t probability function, coupled with random variables. + + :param A: scale parameter + :param nu: degrees of freedom + + """ + domain = _POSITIVE + _instances = [] + def __new__(cls, A, nu): # Singleton: + if cls._instances: + cls._instances[:] = [instance for instance in cls._instances if instance()] + for instance in cls._instances: + if instance().A == A and instance().nu == nu: + return instance() + o = super(Prior, cls).__new__(cls, A, nu) + cls._instances.append(weakref.ref(o)) + return cls._instances[-1]() + def __init__(self, A, nu): + self.A = float(A) + self.nu = float(nu) + self.constant = gammaln(.5*(self.nu+1.)) - gammaln(.5*self.nu) - .5*np.log(np.pi*self.A*self.nu) + + def __str__(self): + return "hT({:.2g}, {:.2g})".format(self.A, self.nu) + + def lnpdf(self,theta): + return (theta>0) * ( self.constant -.5*(self.nu+1) * np.log( 1.+ (1./self.nu) * (theta/self.A)**2 ) ) + + #theta = theta if isinstance(theta,np.ndarray) else np.array([theta]) + #lnpdfs = np.zeros_like(theta) + #theta = np.array([theta]) + #above_zero = theta.flatten()>1e-6 + #v = self.nu + #sigma2=self.A + #stop + #lnpdfs[above_zero] = (+ gammaln((v + 1) * 0.5) + # - gammaln(v * 0.5) + # - 0.5*np.log(sigma2 * v * np.pi) + # - 0.5*(v + 1)*np.log(1 + (1/np.float(v))*((theta[above_zero][0]**2)/sigma2)) + #) + #return lnpdfs + + def lnpdf_grad(self,theta): + theta = theta if isinstance(theta,np.ndarray) else np.array([theta]) + grad = np.zeros_like(theta) + above_zero = theta>1e-6 + v = self.nu + sigma2=self.A + grad[above_zero] = -0.5*(v+1)*(2*theta[above_zero])/(v*sigma2 + theta[above_zero][0]**2) + return grad + + def rvs(self, n): + #return np.random.randn(n) * self.sigma + self.mu + from scipy.stats import t + #[np.abs(x) for x in t.rvs(df=4,loc=0,scale=50, size=10000)]) + ret = t.rvs(self.nu,loc=0,scale=self.A, size=n) + ret[ret<0] = 0 + return ret + diff --git a/GPy/core/parameterization/ties_and_remappings.py b/GPy/core/parameterization/ties_and_remappings.py new file mode 100644 index 00000000..a81b8d61 --- /dev/null +++ b/GPy/core/parameterization/ties_and_remappings.py @@ -0,0 +1,225 @@ +# Copyright (c) 2014, James Hensman, Max Zwiessele +# Licensed under the BSD 3-clause license (see LICENSE.txt) + +import numpy as np +from parameterized import Parameterized +from param import Param + +class Remapping(Parameterized): + def mapping(self): + """ + The return value of this function gives the values which the re-mapped + parameters should take. Implement in sub-classes. + """ + raise NotImplementedError + + def callback(self): + raise NotImplementedError + + def __str__(self): + return self.name + + def parameters_changed(self): + #ensure all out parameters have the correct value, as specified by our mapping + index = self._highest_parent_.constraints[self] + self._highest_parent_.param_array[index] = self.mapping() + [p.notify_observers(which=self) for p in self.tied_parameters] + +class Fix(Remapping): + pass + + + + +class Tie(Parameterized): + """ + The new parameter tie framework. (under development) + + All the parameters tied together get a new parameter inside the *Tie* object. + Its value should always be equal to all the tied parameters, and its gradient + is the sum of all the tied parameters. + + =====Implementation Details===== + The *Tie* object should only exist on the top of param tree (the highest parent). + + self.label_buf: + It uses a label buffer that has the same length as all the parameters (self._highest_parent_.param_array). + The buffer keeps track of all the tied parameters. All the tied parameters have a label (an interger) higher + than 0, and the parameters that have the same label are tied together. + + self.buf_index: + An auxiliary index list for the global index of the tie parameter inside the *Tie* object. + + ================================ + + TODO: + * EVERYTHING + + """ + def __init__(self, name='tie'): + super(Tie, self).__init__(name) + self.tied_param = None + # The buffer keeps track of tie status + self.label_buf = None + # The global indices of the 'tied' param + self.buf_idx = None + # A boolean array indicating non-tied parameters + self._tie_ = None + + def getTieFlag(self, p=None): + if self.tied_param is None: + if self._tie_ is None or self._tie_.size != self._highest_parent_.param_array.size: + self._tie_ = np.ones((self._highest_parent_.param_array.size,),dtype=np.bool) + if p is not None: + return self._tie_[p._highest_parent_._raveled_index_for(p)] + return self._tie_ + + def _init_labelBuf(self): + if self.label_buf is None: + self.label_buf = np.zeros(self._highest_parent_.param_array.shape, dtype=np.int) + if self._tie_ is None or self._tie_.size != self._highest_parent_.param_array.size: + self._tie_ = np.ones((self._highest_parent_.param_array.size,),dtype=np.bool) + + def _updateTieFlag(self): + if self._tie_.size != self.label_buf.size: + self._tie_ = np.ones((self._highest_parent_.param_array.size,),dtype=np.bool) + self._tie_[self.label_buf>0] = False + self._tie_[self.buf_idx] = True + + def add_tied_parameter(self, p, p2=None): + """ + Tie the list of parameters p together (p2==None) or + Tie the list of parameters p with the list of parameters p2 (p2!=None) + """ + self._init_labelBuf() + if p2 is None: + idx = self._highest_parent_._raveled_index_for(p) + val = self._sync_val_group(idx) + if np.all(self.label_buf[idx]==0): + # None of p has been tied before. + tie_idx = self._expandTieParam(1) + print tie_idx + tie_id = self.label_buf.max()+1 + self.label_buf[tie_idx] = tie_id + else: + b = self.label_buf[idx] + ids = np.unique(b[b>0]) + tie_id, tie_idx = self._merge_tie_param(ids) + self._highest_parent_.param_array[tie_idx] = val + idx = self._highest_parent_._raveled_index_for(p) + self.label_buf[idx] = tie_id + else: + pass + self._updateTieFlag() + + def _merge_tie_param(self, ids): + """Merge the tie parameters with ids in the list.""" + if len(ids)==1: + id_final_idx = self.buf_idx[self.label_buf[self.buf_idx]==ids[0]][0] + return ids[0],id_final_idx + id_final = ids[0] + ids_rm = ids[1:] + label_buf_param = self.label_buf[self.buf_idx] + idx_param = [np.where(label_buf_param==i)[0][0] for i in ids_rm] + self._removeTieParam(idx_param) + [np.put(self.label_buf, np.where(self.label_buf==i), id_final) for i in ids_rm] + id_final_idx = self.buf_idx[self.label_buf[self.buf_idx]==id_final][0] + return id_final, id_final_idx + + def _sync_val_group(self, idx): + self._highest_parent_.param_array[idx] = self._highest_parent_.param_array[idx].mean() + return self._highest_parent_.param_array[idx][0] + + def _expandTieParam(self, num): + """Expand the tie param with the number of *num* parameters""" + if self.tied_param is None: + new_buf = np.empty((num,)) + else: + new_buf = np.empty((self.tied_param.size+num,)) + new_buf[:self.tied_param.size] = self.tied_param.param_array.copy() + self.remove_parameter(self.tied_param) + self.tied_param = Param('tied',new_buf) + self.add_parameter(self.tied_param) + buf_idx_new = self._highest_parent_._raveled_index_for(self.tied_param) + self._expand_label_buf(self.buf_idx, buf_idx_new) + self.buf_idx = buf_idx_new + return self.buf_idx[-num:] + + def _removeTieParam(self, idx): + """idx within tied_param""" + new_buf = np.empty((self.tied_param.size-len(idx),)) + bool_list = np.ones((self.tied_param.size,),dtype=np.bool) + bool_list[idx] = False + new_buf[:] = self.tied_param.param_array[bool_list] + self.remove_parameter(self.tied_param) + self.tied_param = Param('tied',new_buf) + self.add_parameter(self.tied_param) + buf_idx_new = self._highest_parent_._raveled_index_for(self.tied_param) + self._shrink_label_buf(self.buf_idx, buf_idx_new, bool_list) + self.buf_idx = buf_idx_new + + def _expand_label_buf(self, idx_old, idx_new): + """Expand label buffer accordingly""" + if idx_old is None: + self.label_buf = np.zeros(self._highest_parent_.param_array.shape, dtype=np.int) + else: + bool_old = np.zeros((self.label_buf.size,),dtype=np.bool) + bool_old[idx_old] = True + bool_new = np.zeros((self._highest_parent_.param_array.size,),dtype=np.bool) + bool_new[idx_new] = True + label_buf_new = np.zeros(self._highest_parent_.param_array.shape, dtype=np.int) + label_buf_new[np.logical_not(bool_new)] = self.label_buf[np.logical_not(bool_old)] + label_buf_new[idx_new[:len(idx_old)]] = self.label_buf[idx_old] + self.label_buf = label_buf_new + + def _shrink_label_buf(self, idx_old, idx_new, bool_list): + bool_old = np.zeros((self.label_buf.size,),dtype=np.bool) + bool_old[idx_old] = True + bool_new = np.zeros((self._highest_parent_.param_array.size,),dtype=np.bool) + bool_new[idx_new] = True + label_buf_new = np.empty(self._highest_parent_.param_array.shape, dtype=np.int) + label_buf_new[np.logical_not(bool_new)] = self.label_buf[np.logical_not(bool_old)] + label_buf_new[idx_new] = self.label_buf[idx_old[bool_list]] + self.label_buf = label_buf_new + + def _check_change(self): + changed = False + if self.tied_param is not None: + for i in xrange(self.tied_param.size): + b0 = self.label_buf==self.label_buf[self.buf_idx[i]] + b = self._highest_parent_.param_array[b0]!=self.tied_param[i] + if b.sum()==0: + print 'XXX' + continue + elif b.sum()==1: + print '!!!' + val = self._highest_parent_.param_array[b0][b][0] + self._highest_parent_.param_array[b0] = val + else: + print '@@@' + self._highest_parent_.param_array[b0] = self.tied_param[i] + changed = True + return changed + + def parameters_changed(self): + #ensure all out parameters have the correct value, as specified by our mapping + changed = self._check_change() + if changed: + self._highest_parent_._trigger_params_changed() + self.collate_gradient() + + def collate_gradient(self): + if self.tied_param is not None: + self.tied_param.gradient = 0. + [np.put(self.tied_param.gradient, i, self._highest_parent_.gradient[self.label_buf==self.label_buf[self.buf_idx[i]]].sum()) + for i in xrange(self.tied_param.size)] + + def propagate_val(self): + if self.tied_param is not None: + for i in xrange(self.tied_param.size): + self._highest_parent_.param_array[self.label_buf==self.label_buf[self.buf_idx[i]]] = self.tied_param[i] + + + + + diff --git a/GPy/core/parameterization/transformations.py b/GPy/core/parameterization/transformations.py new file mode 100644 index 00000000..291076a1 --- /dev/null +++ b/GPy/core/parameterization/transformations.py @@ -0,0 +1,433 @@ +# Copyright (c) 2012, GPy authors (see AUTHORS.txt). +# Licensed under the BSD 3-clause license (see LICENSE.txt) + + +import numpy as np +from domains import _POSITIVE,_NEGATIVE, _BOUNDED +import weakref + +import sys + +_exp_lim_val = np.finfo(np.float64).max +_lim_val = 36.0 +epsilon = np.finfo(np.float64).resolution + +#=============================================================================== +# Fixing constants +__fixed__ = "fixed" +FIXED = False +UNFIXED = True +#=============================================================================== + + +class Transformation(object): + domain = None + _instance = None + def __new__(cls, *args, **kwargs): + if not cls._instance or cls._instance.__class__ is not cls: + cls._instance = super(Transformation, cls).__new__(cls, *args, **kwargs) + return cls._instance + def f(self, opt_param): + raise NotImplementedError + def finv(self, model_param): + raise NotImplementedError + def gradfactor(self, model_param, dL_dmodel_param): + """ df(opt_param)_dopt_param evaluated at self.f(opt_param)=model_param, times the gradient dL_dmodel_param, + + i.e.: + define + + .. math:: + + \frac{\frac{\partial L}{\partial f}\left(\left.\partial f(x)}{\partial x}\right|_{x=f^{-1}(f)\right)} + """ + raise NotImplementedError + def initialize(self, f): + """ produce a sensible initial value for f(x)""" + raise NotImplementedError + def plot(self, xlabel=r'transformed $\theta$', ylabel=r'$\theta$', axes=None, *args,**kw): + assert "matplotlib" in sys.modules, "matplotlib package has not been imported." + import matplotlib.pyplot as plt + from ...plotting.matplot_dep import base_plots + x = np.linspace(-8,8) + base_plots.meanplot(x, self.f(x),axes=axes*args,**kw) + axes = plt.gca() + axes.set_xlabel(xlabel) + axes.set_ylabel(ylabel) + def __str__(self): + raise NotImplementedError + def __repr__(self): + return self.__class__.__name__ + +class Logexp(Transformation): + domain = _POSITIVE + def f(self, x): + return np.where(x>_lim_val, x, np.log1p(np.exp(np.clip(x, -_lim_val, _lim_val)))) + epsilon + #raises overflow warning: return np.where(x>_lim_val, x, np.log(1. + np.exp(x))) + def finv(self, f): + return np.where(f>_lim_val, f, np.log(np.exp(f+1e-20) - 1.)) + def gradfactor(self, f, df): + return np.einsum('i,i->i', df, np.where(f>_lim_val, 1., 1. - np.exp(-f))) + def initialize(self, f): + if np.any(f < 0.): + print "Warning: changing parameters to satisfy constraints" + return np.abs(f) + def __str__(self): + return '+ve' + + +class NormalTheta(Transformation): + _instances = [] + def __new__(cls, mu_indices, var_indices): + if cls._instances: + cls._instances[:] = [instance for instance in cls._instances if instance()] + for instance in cls._instances: + if np.all(instance().mu_indices==mu_indices, keepdims=False) and np.all(instance().var_indices==var_indices, keepdims=False): + return instance() + o = super(Transformation, cls).__new__(cls, mu_indices, var_indices) + cls._instances.append(weakref.ref(o)) + return cls._instances[-1]() + + def __init__(self, mu_indices, var_indices): + self.mu_indices = mu_indices + self.var_indices = var_indices + + def f(self, theta): + # In here abs is only a trick to make sure the numerics are ok. + # The variance will never go below zero, but at initialization we need to make sure + # that the values are ok + # Before: + theta[self.var_indices] = np.abs(-.5/theta[self.var_indices]) + theta[self.mu_indices] *= theta[self.var_indices] + return theta # which is now {mu, var} + + def finv(self, muvar): + # before: + varp = muvar[self.var_indices] + muvar[self.mu_indices] /= varp + muvar[self.var_indices] = -.5/varp + + return muvar # which is now {theta1, theta2} + + def gradfactor(self, muvar, dmuvar): + mu = muvar[self.mu_indices] + var = muvar[self.var_indices] + #======================================================================= + # theta gradients + # This works and the gradient checks! + dmuvar[self.mu_indices] *= var + dmuvar[self.var_indices] *= 2*(var)**2 + dmuvar[self.var_indices] += 2*dmuvar[self.mu_indices]*mu + #======================================================================= + + return dmuvar # which is now the gradient multiplicator for {theta1, theta2} + + def initialize(self, f): + if np.any(f[self.var_indices] < 0.): + print "Warning: changing parameters to satisfy constraints" + f[self.var_indices] = np.abs(f[self.var_indices]) + return f + + def __str__(self): + return "theta" + + def __getstate__(self): + return [self.mu_indices, self.var_indices] + + def __setstate__(self, state): + self.mu_indices = state[0] + self.var_indices = state[1] + +class NormalNaturalAntti(NormalTheta): + _instances = [] + _logexp = Logexp() + def __new__(cls, mu_indices, var_indices): + if cls._instances: + cls._instances[:] = [instance for instance in cls._instances if instance()] + for instance in cls._instances: + if np.all(instance().mu_indices==mu_indices, keepdims=False) and np.all(instance().var_indices==var_indices, keepdims=False): + return instance() + o = super(Transformation, cls).__new__(cls, mu_indices, var_indices) + cls._instances.append(weakref.ref(o)) + return cls._instances[-1]() + + def __init__(self, mu_indices, var_indices): + self.mu_indices = mu_indices + self.var_indices = var_indices + + def gradfactor(self, muvar, dmuvar): + mu = muvar[self.mu_indices] + var = muvar[self.var_indices] + + #======================================================================= + # theta gradients + # This works and the gradient checks! + dmuvar[self.mu_indices] *= var + dmuvar[self.var_indices] *= 2*var**2#np.einsum('i,i,i,i->i', dmuvar[self.var_indices], [2], var, var) + #======================================================================= + + return dmuvar # which is now the gradient multiplicator + + def initialize(self, f): + if np.any(f[self.var_indices] < 0.): + print "Warning: changing parameters to satisfy constraints" + f[self.var_indices] = np.abs(f[self.var_indices]) + return f + + def __str__(self): + return "natantti" + +class NormalEta(Transformation): + _instances = [] + def __new__(cls, mu_indices, var_indices): + if cls._instances: + cls._instances[:] = [instance for instance in cls._instances if instance()] + for instance in cls._instances: + if np.all(instance().mu_indices==mu_indices, keepdims=False) and np.all(instance().var_indices==var_indices, keepdims=False): + return instance() + o = super(Transformation, cls).__new__(cls, mu_indices, var_indices) + cls._instances.append(weakref.ref(o)) + return cls._instances[-1]() + + def __init__(self, mu_indices, var_indices): + self.mu_indices = mu_indices + self.var_indices = var_indices + + def f(self, theta): + theta[self.var_indices] = np.abs(theta[self.var_indices] - theta[self.mu_indices]**2) + return theta # which is now {mu, var} + + def finv(self, muvar): + muvar[self.var_indices] += muvar[self.mu_indices]**2 + return muvar # which is now {eta1, eta2} + + def gradfactor(self, muvar, dmuvar): + mu = muvar[self.mu_indices] + #======================================================================= + # Lets try natural gradients instead: Not working with bfgs... try stochastic! + dmuvar[self.mu_indices] -= 2*mu*dmuvar[self.var_indices] + #======================================================================= + return dmuvar # which is now the gradient multiplicator + + def initialize(self, f): + if np.any(f[self.var_indices] < 0.): + print "Warning: changing parameters to satisfy constraints" + f[self.var_indices] = np.abs(f[self.var_indices]) + return f + + def __str__(self): + return "eta" + +class NormalNaturalThroughTheta(NormalTheta): + _instances = [] + def __new__(cls, mu_indices, var_indices): + if cls._instances: + cls._instances[:] = [instance for instance in cls._instances if instance()] + for instance in cls._instances: + if np.all(instance().mu_indices==mu_indices, keepdims=False) and np.all(instance().var_indices==var_indices, keepdims=False): + return instance() + o = super(Transformation, cls).__new__(cls, mu_indices, var_indices) + cls._instances.append(weakref.ref(o)) + return cls._instances[-1]() + + def __init__(self, mu_indices, var_indices): + self.mu_indices = mu_indices + self.var_indices = var_indices + + def gradfactor(self, muvar, dmuvar): + mu = muvar[self.mu_indices] + var = muvar[self.var_indices] + + #======================================================================= + # This is just eta direction: + dmuvar[self.mu_indices] -= 2*mu*dmuvar[self.var_indices] + #======================================================================= + + + #======================================================================= + # This is by going through theta fully and then going into eta direction: + #dmu = dmuvar[self.mu_indices] + #dmuvar[self.var_indices] += dmu*mu*(var + 4/var) + #======================================================================= + return dmuvar # which is now the gradient multiplicator + + def __str__(self): + return "natgrad" + +class NormalNaturalThroughEta(NormalEta): + _instances = [] + def __new__(cls, mu_indices, var_indices): + if cls._instances: + cls._instances[:] = [instance for instance in cls._instances if instance()] + for instance in cls._instances: + if np.all(instance().mu_indices==mu_indices, keepdims=False) and np.all(instance().var_indices==var_indices, keepdims=False): + return instance() + o = super(Transformation, cls).__new__(cls, mu_indices, var_indices) + cls._instances.append(weakref.ref(o)) + return cls._instances[-1]() + + def __init__(self, mu_indices, var_indices): + self.mu_indices = mu_indices + self.var_indices = var_indices + + def gradfactor(self, muvar, dmuvar): + mu = muvar[self.mu_indices] + var = muvar[self.var_indices] + #======================================================================= + # theta gradients + # This works and the gradient checks! + dmuvar[self.mu_indices] *= var + dmuvar[self.var_indices] *= 2*(var)**2 + dmuvar[self.var_indices] += 2*dmuvar[self.mu_indices]*mu + #======================================================================= + return dmuvar + + def __str__(self): + return "natgrad" + + +class LogexpNeg(Transformation): + domain = _POSITIVE + def f(self, x): + return np.where(x>_lim_val, -x, -np.log(1. + np.exp(np.clip(x, -np.inf, _lim_val)))) + #raises overflow warning: return np.where(x>_lim_val, x, np.log(1. + np.exp(x))) + def finv(self, f): + return np.where(f>_lim_val, 0, np.log(np.exp(-f) - 1.)) + def gradfactor(self, f, df): + return np.einsum('i,i->i', df, np.where(f>_lim_val, -1, -1 + np.exp(-f))) + def initialize(self, f): + if np.any(f < 0.): + print "Warning: changing parameters to satisfy constraints" + return np.abs(f) + def __str__(self): + return '+ve' + + +class NegativeLogexp(Transformation): + domain = _NEGATIVE + logexp = Logexp() + def f(self, x): + return -self.logexp.f(x) # np.log(1. + np.exp(x)) + def finv(self, f): + return self.logexp.finv(-f) # np.log(np.exp(-f) - 1.) + def gradfactor(self, f, df): + return np.einsum('i,i->i', df, -self.logexp.gradfactor(-f)) + def initialize(self, f): + return -self.logexp.initialize(f) # np.abs(f) + def __str__(self): + return '-ve' + +class LogexpClipped(Logexp): + max_bound = 1e100 + min_bound = 1e-10 + log_max_bound = np.log(max_bound) + log_min_bound = np.log(min_bound) + domain = _POSITIVE + _instances = [] + def __new__(cls, lower=1e-6, *args, **kwargs): + if cls._instances: + cls._instances[:] = [instance for instance in cls._instances if instance()] + for instance in cls._instances: + if instance().lower == lower: + return instance() + o = super(Transformation, cls).__new__(cls, lower, *args, **kwargs) + cls._instances.append(weakref.ref(o)) + return cls._instances[-1]() + def __init__(self, lower=1e-6): + self.lower = lower + def f(self, x): + exp = np.exp(np.clip(x, self.log_min_bound, self.log_max_bound)) + f = np.log(1. + exp) +# if np.isnan(f).any(): +# import ipdb;ipdb.set_trace() + return np.clip(f, self.min_bound, self.max_bound) + def finv(self, f): + return np.log(np.exp(f - 1.)) + def gradfactor(self, f, df): + ef = np.exp(f) # np.clip(f, self.min_bound, self.max_bound)) + gf = (ef - 1.) / ef + return np.einsum('i,i->i', df, gf) # np.where(f < self.lower, 0, gf) + def initialize(self, f): + if np.any(f < 0.): + print "Warning: changing parameters to satisfy constraints" + return np.abs(f) + def __str__(self): + return '+ve_c' + +class Exponent(Transformation): + # TODO: can't allow this to go to zero, need to set a lower bound. Similar with negative Exponent below. See old MATLAB code. + domain = _POSITIVE + def f(self, x): + return np.where(x<_lim_val, np.where(x>-_lim_val, np.exp(x), np.exp(-_lim_val)), np.exp(_lim_val)) + def finv(self, x): + return np.log(x) + def gradfactor(self, f, df): + return np.einsum('i,i->i', df, f) + def initialize(self, f): + if np.any(f < 0.): + print "Warning: changing parameters to satisfy constraints" + return np.abs(f) + def __str__(self): + return '+ve' + +class NegativeExponent(Exponent): + domain = _NEGATIVE + def f(self, x): + return -Exponent.f(x) + def finv(self, f): + return Exponent.finv(-f) + def gradfactor(self, f, df): + return np.einsum('i,i->i', df, f) + def initialize(self, f): + return -Exponent.initialize(f) #np.abs(f) + def __str__(self): + return '-ve' + +class Square(Transformation): + domain = _POSITIVE + def f(self, x): + return x ** 2 + def finv(self, x): + return np.sqrt(x) + def gradfactor(self, f, df): + return np.einsum('i,i->i', df, 2 * np.sqrt(f)) + def initialize(self, f): + return np.abs(f) + def __str__(self): + return '+sq' + +class Logistic(Transformation): + domain = _BOUNDED + _instances = [] + def __new__(cls, lower=1e-6, upper=1e-6, *args, **kwargs): + if cls._instances: + cls._instances[:] = [instance for instance in cls._instances if instance()] + for instance in cls._instances: + if instance().lower == lower and instance().upper == upper: + return instance() + o = super(Transformation, cls).__new__(cls, lower, upper, *args, **kwargs) + cls._instances.append(weakref.ref(o)) + return cls._instances[-1]() + def __init__(self, lower, upper): + assert lower < upper + self.lower, self.upper = float(lower), float(upper) + self.difference = self.upper - self.lower + def f(self, x): + if (x<-300.).any(): + x = x.copy() + x[x<-300.] = -300. + return self.lower + self.difference / (1. + np.exp(-x)) + def finv(self, f): + return np.log(np.clip(f - self.lower, 1e-10, np.inf) / np.clip(self.upper - f, 1e-10, np.inf)) + def gradfactor(self, f, df): + return np.einsum('i,i->i', df, (f - self.lower) * (self.upper - f) / self.difference) + def initialize(self, f): + if np.any(np.logical_or(f < self.lower, f > self.upper)): + print "Warning: changing parameters to satisfy constraints" + #return np.where(np.logical_or(f < self.lower, f > self.upper), self.f(f * 0.), f) + #FIXME: Max, zeros_like right? + return np.where(np.logical_or(f < self.lower, f > self.upper), self.f(np.zeros_like(f)), f) + def __str__(self): + return '{},{}'.format(self.lower, self.upper) + + diff --git a/GPy/core/parameterization/updateable.py b/GPy/core/parameterization/updateable.py new file mode 100644 index 00000000..daf07d3c --- /dev/null +++ b/GPy/core/parameterization/updateable.py @@ -0,0 +1,63 @@ +''' +Created on 11 Nov 2014 + +@author: maxz +''' +from observable import Observable + + +class Updateable(Observable): + """ + A model can be updated or not. + Make sure updates can be switched on and off. + """ + _updates = True + def __init__(self, *args, **kwargs): + super(Updateable, self).__init__(*args, **kwargs) + + @property + def updates(self): + raise DeprecationWarning("updates is now a function, see update(True|False|None)") + + @updates.setter + def updates(self, ups): + raise DeprecationWarning("updates is now a function, see update(True|False|None)") + + def update_model(self, updates=None): + """ + Get or set, whether automatic updates are performed. When updates are + off, the model might be in a non-working state. To make the model work + turn updates on again. + + :param bool|None updates: + + bool: whether to do updates + None: get the current update state + """ + if updates is None: + p = getattr(self, '_highest_parent_', None) + if p is not None: + self._updates = p._updates + return self._updates + assert isinstance(updates, bool), "updates are either on (True) or off (False)" + p = getattr(self, '_highest_parent_', None) + if p is not None: + p._updates = updates + self._updates = updates + self.trigger_update() + + def toggle_update(self): + self.update_model(not self.update_model()) + + def trigger_update(self, trigger_parent=True): + """ + Update the model from the current state. + Make sure that updates are on, otherwise this + method will do nothing + + :param bool trigger_parent: Whether to trigger the parent, after self has updated + """ + if not self.update_model() or (hasattr(self, "_in_init_") and self._in_init_): + #print "Warning: updates are off, updating the model will do nothing" + return + self._trigger_params_changed(trigger_parent) diff --git a/GPy/core/parameterization/variational.py b/GPy/core/parameterization/variational.py new file mode 100644 index 00000000..7cc5c99a --- /dev/null +++ b/GPy/core/parameterization/variational.py @@ -0,0 +1,220 @@ +''' +Created on 6 Nov 2013 + +@author: maxz +''' + +import numpy as np +from parameterized import Parameterized +from param import Param +from transformations import Logexp, Logistic,__fixed__ +from GPy.util.misc import param_to_array +from GPy.util.caching import Cache_this + +class VariationalPrior(Parameterized): + def __init__(self, name='latent space', **kw): + super(VariationalPrior, self).__init__(name=name, **kw) + + def KL_divergence(self, variational_posterior): + raise NotImplementedError, "override this for variational inference of latent space" + + def update_gradients_KL(self, variational_posterior): + """ + updates the gradients for mean and variance **in place** + """ + raise NotImplementedError, "override this for variational inference of latent space" + +class NormalPrior(VariationalPrior): + def KL_divergence(self, variational_posterior): + var_mean = np.square(variational_posterior.mean).sum() + var_S = (variational_posterior.variance - np.log(variational_posterior.variance)).sum() + return 0.5 * (var_mean + var_S) - 0.5 * variational_posterior.input_dim * variational_posterior.num_data + + def update_gradients_KL(self, variational_posterior): + # dL: + variational_posterior.mean.gradient -= variational_posterior.mean + variational_posterior.variance.gradient -= (1. - (1. / (variational_posterior.variance))) * 0.5 + +class SpikeAndSlabPrior(VariationalPrior): + def __init__(self, pi=None, learnPi=False, variance = 1.0, name='SpikeAndSlabPrior', **kw): + super(SpikeAndSlabPrior, self).__init__(name=name, **kw) + self.variance = Param('variance',variance) + self.learnPi = learnPi + if learnPi: + self.pi = Param('Pi', pi, Logistic(1e-10,1.-1e-10)) + else: + self.pi = Param('Pi', pi, __fixed__) + self.link_parameter(self.pi) + + + def KL_divergence(self, variational_posterior): + mu = variational_posterior.mean + S = variational_posterior.variance + gamma,gamma1 = variational_posterior.gamma_probabilities() + log_gamma,log_gamma1 = variational_posterior.gamma_log_prob() + if len(self.pi.shape)==2: + idx = np.unique(gamma._raveled_index()/gamma.shape[-1]) + pi = self.pi[idx] + else: + pi = self.pi + + var_mean = np.square(mu)/self.variance + var_S = (S/self.variance - np.log(S)) + var_gamma = (gamma*(log_gamma-np.log(pi))).sum()+(gamma1*(log_gamma1-np.log(1-pi))).sum() + return var_gamma+ (gamma* (np.log(self.variance)-1. +var_mean + var_S)).sum()/2. + + def update_gradients_KL(self, variational_posterior): + mu = variational_posterior.mean + S = variational_posterior.variance + gamma,gamma1 = variational_posterior.gamma_probabilities() + log_gamma,log_gamma1 = variational_posterior.gamma_log_prob() + if len(self.pi.shape)==2: + idx = np.unique(gamma._raveled_index()/gamma.shape[-1]) + pi = self.pi[idx] + else: + pi = self.pi + + variational_posterior.binary_prob.gradient -= (np.log((1-pi)/pi)+log_gamma-log_gamma1+((np.square(mu)+S)/self.variance-np.log(S)+np.log(self.variance)-1.)/2.)*gamma*gamma1 + mu.gradient -= gamma*mu/self.variance + S.gradient -= (1./self.variance - 1./S) * gamma /2. + if self.learnPi: + if len(self.pi)==1: + self.pi.gradient = (gamma/self.pi - (1.-gamma)/(1.-self.pi)).sum() + elif len(self.pi.shape)==1: + self.pi.gradient = (gamma/self.pi - (1.-gamma)/(1.-self.pi)).sum(axis=0) + else: + self.pi[idx].gradient = (gamma/self.pi[idx] - (1.-gamma)/(1.-self.pi[idx])) + +class VariationalPosterior(Parameterized): + def __init__(self, means=None, variances=None, name='latent space', *a, **kw): + super(VariationalPosterior, self).__init__(name=name, *a, **kw) + self.mean = Param("mean", means) + self.variance = Param("variance", variances, Logexp()) + self.ndim = self.mean.ndim + self.shape = self.mean.shape + self.num_data, self.input_dim = self.mean.shape + self.link_parameters(self.mean, self.variance) + self.num_data, self.input_dim = self.mean.shape + if self.has_uncertain_inputs(): + assert self.variance.shape == self.mean.shape, "need one variance per sample and dimenion" + + def set_gradients(self, grad): + self.mean.gradient, self.variance.gradient = grad + + def _raveled_index(self): + index = np.empty(dtype=int, shape=0) + size = 0 + for p in self.parameters: + index = np.hstack((index, p._raveled_index()+size)) + size += p._realsize_ if hasattr(p, '_realsize_') else p.size + return index + + def has_uncertain_inputs(self): + return not self.variance is None + + def __getitem__(self, s): + if isinstance(s, (int, slice, tuple, list, np.ndarray)): + import copy + n = self.__new__(self.__class__, self.name) + dc = self.__dict__.copy() + dc['mean'] = self.mean[s] + dc['variance'] = self.variance[s] + dc['parameters'] = copy.copy(self.parameters) + n.__dict__.update(dc) + n.parameters[dc['mean']._parent_index_] = dc['mean'] + n.parameters[dc['variance']._parent_index_] = dc['variance'] + n._gradient_array_ = None + oversize = self.size - self.mean.size - self.variance.size + n.size = n.mean.size + n.variance.size + oversize + n.ndim = n.mean.ndim + n.shape = n.mean.shape + n.num_data = n.mean.shape[0] + n.input_dim = n.mean.shape[1] if n.ndim != 1 else 1 + return n + else: + return super(VariationalPosterior, self).__getitem__(s) + +class NormalPosterior(VariationalPosterior): + ''' + NormalPosterior distribution for variational approximations. + + holds the means and variances for a factorizing multivariate normal distribution + ''' + + def plot(self, *args): + """ + Plot latent space X in 1D: + + See GPy.plotting.matplot_dep.variational_plots + """ + import sys + assert "matplotlib" in sys.modules, "matplotlib package has not been imported." + from ...plotting.matplot_dep import variational_plots + import matplotlib + return variational_plots.plot(self,*args) + +class SpikeAndSlabPosterior(VariationalPosterior): + ''' + The SpikeAndSlab distribution for variational approximations. + ''' + def __init__(self, means, variances, binary_prob, name='latent space'): + """ + binary_prob : the probability of the distribution on the slab part. + """ + super(SpikeAndSlabPosterior, self).__init__(means, variances, name) + self.gamma = Param("binary_prob",binary_prob) + self.link_parameter(self.gamma) + + @Cache_this(limit=5) + def gamma_probabilities(self): + prob = np.zeros_like(param_to_array(self.gamma)) + prob[self.gamma>-710] = 1./(1.+np.exp(-self.gamma[self.gamma>-710])) + prob1 = -np.zeros_like(param_to_array(self.gamma)) + prob1[self.gamma<710] = 1./(1.+np.exp(self.gamma[self.gamma<710])) + return prob, prob1 + + @Cache_this(limit=5) + def gamma_log_prob(self): + loggamma = param_to_array(self.gamma).copy() + loggamma[loggamma>-40] = -np.log1p(np.exp(-loggamma[loggamma>-40])) + loggamma1 = -param_to_array(self.gamma).copy() + loggamma1[loggamma1>-40] = -np.log1p(np.exp(-loggamma1[loggamma1>-40])) + return loggamma,loggamma1 + + def set_gradients(self, grad): + self.mean.gradient, self.variance.gradient, self.gamma.gradient = grad + + def __getitem__(self, s): + if isinstance(s, (int, slice, tuple, list, np.ndarray)): + import copy + n = self.__new__(self.__class__, self.name) + dc = self.__dict__.copy() + dc['mean'] = self.mean[s] + dc['variance'] = self.variance[s] + dc['binary_prob'] = self.binary_prob[s] + dc['parameters'] = copy.copy(self.parameters) + n.__dict__.update(dc) + n.parameters[dc['mean']._parent_index_] = dc['mean'] + n.parameters[dc['variance']._parent_index_] = dc['variance'] + n.parameters[dc['binary_prob']._parent_index_] = dc['binary_prob'] + n._gradient_array_ = None + oversize = self.size - self.mean.size - self.variance.size + n.size = n.mean.size + n.variance.size + oversize + n.ndim = n.mean.ndim + n.shape = n.mean.shape + n.num_data = n.mean.shape[0] + n.input_dim = n.mean.shape[1] if n.ndim != 1 else 1 + return n + else: + return super(VariationalPrior, self).__getitem__(s) + + def plot(self, *args, **kwargs): + """ + Plot latent space X in 1D: + + See GPy.plotting.matplot_dep.variational_plots + """ + import sys + assert "matplotlib" in sys.modules, "matplotlib package has not been imported." + from ...plotting.matplot_dep import variational_plots + return variational_plots.plot_SpikeSlab(self,*args, **kwargs) diff --git a/GPy/core/parameterized.py b/GPy/core/parameterized.py deleted file mode 100644 index 35d2795c..00000000 --- a/GPy/core/parameterized.py +++ /dev/null @@ -1,465 +0,0 @@ -# Copyright (c) 2012, GPy authors (see AUTHORS.txt). -# Licensed under the BSD 3-clause license (see LICENSE.txt) - - -import numpy as np -import re -import copy -import cPickle -import warnings -import transformations - -class Parameterized(object): - def __init__(self): - """ - This is the base class for model and kernel. Mostly just handles tieing and constraining of parameters - """ - self.tied_indices = [] - self.fixed_indices = [] - self.fixed_values = [] - self.constrained_indices = [] - self.constraints = [] - - def _get_params(self): - raise NotImplementedError, "this needs to be implemented to use the Parameterized class" - def _set_params(self, x): - raise NotImplementedError, "this needs to be implemented to use the Parameterized class" - - def _get_param_names(self): - raise NotImplementedError, "this needs to be implemented to use the Parameterized class" - #def _get_print_names(self): - # """ Override for which names to print out, when using print m """ - # return self._get_param_names() - - def pickle(self, filename, protocol=-1): - with open(filename, 'wb') as f: - cPickle.dump(self, f, protocol=protocol) - - def copy(self): - """Returns a (deep) copy of the current model """ - return copy.deepcopy(self) - - def __getstate__(self): - if self._has_get_set_state(): - return self.getstate() - return self.__dict__ - - def __setstate__(self, state): - if self._has_get_set_state(): - self.setstate(state) # set state - self._set_params(self._get_params()) # restore all values - return - self.__dict__ = state - - def _has_get_set_state(self): - return 'getstate' in vars(self.__class__) and 'setstate' in vars(self.__class__) - - def getstate(self): - """ - Get the current state of the class, - here just all the indices, rest can get recomputed - For inheriting from Parameterized: - - Allways append the state of the inherited object - and call down to the inherited object in setstate!! - """ - return [self.tied_indices, - self.fixed_indices, - self.fixed_values, - self.constrained_indices, - self.constraints] - - def setstate(self, state): - self.constraints = state.pop() - self.constrained_indices = state.pop() - self.fixed_values = state.pop() - self.fixed_indices = state.pop() - self.tied_indices = state.pop() - - def __getitem__(self, regexp, return_names=False): - """ - Get a model parameter by name. The name is applied as a regular - expression and all parameters that match that regular expression are - returned. - """ - matches = self.grep_param_names(regexp) - if len(matches): - if return_names: - return self._get_params()[matches], np.asarray(self._get_param_names())[matches].tolist() - else: - return self._get_params()[matches] - else: - raise AttributeError, "no parameter matches %s" % regexp - - def __setitem__(self, name, val): - """ - Set model parameter(s) by name. The name is provided as a regular - expression. All parameters matching that regular expression are set to - the given value. - """ - matches = self.grep_param_names(name) - if len(matches): - val = np.array(val) - assert (val.size == 1) or val.size == len(matches), "Shape mismatch: {}:({},)".format(val.size, len(matches)) - x = self._get_params() - x[matches] = val - self._set_params(x) - else: - raise AttributeError, "no parameter matches %s" % name - - def tie_params(self, regexp): - """ - Tie (all!) parameters matching the regular expression `regexp`. - """ - matches = self.grep_param_names(regexp) - assert matches.size > 0, "need at least something to tie together" - if len(self.tied_indices): - assert not np.any(matches[:, None] == np.hstack(self.tied_indices)), "Some indices are already tied!" - self.tied_indices.append(matches) - # TODO only one of the priors will be evaluated. Give a warning message if the priors are not identical - if hasattr(self, 'prior'): - pass - - self._set_params_transformed(self._get_params_transformed()) # sets tied parameters to single value - - def untie_everything(self): - """Unties all parameters by setting tied_indices to an empty list.""" - self.tied_indices = [] - - def grep_param_names(self, regexp, transformed=False, search=False): - """ - :param regexp: regular expression to select parameter names - :type regexp: re | str | int - :rtype: the indices of self._get_param_names which match the regular expression. - - Note:- - Other objects are passed through - i.e. integers which weren't meant for grepping - """ - - if transformed: - names = self._get_param_names_transformed() - else: - names = self._get_param_names() - - if type(regexp) in [str, np.string_, np.str]: - regexp = re.compile(regexp) - elif type(regexp) is re._pattern_type: - pass - else: - return regexp - if search: - return np.nonzero([regexp.search(name) for name in names])[0] - else: - return np.nonzero([regexp.match(name) for name in names])[0] - - def num_params_transformed(self): - removed = 0 - for tie in self.tied_indices: - removed += tie.size - 1 - - for fix in self.fixed_indices: - removed += fix.size - - return len(self._get_params()) - removed - - def unconstrain(self, regexp): - """Unconstrain matching parameters. Does not untie parameters""" - matches = self.grep_param_names(regexp) - - # tranformed contraints: - for match in matches: - self.constrained_indices = [i[i <> match] for i in self.constrained_indices] - - # remove empty constraints - tmp = zip(*[(i, t) for i, t in zip(self.constrained_indices, self.constraints) if len(i)]) - if tmp: - self.constrained_indices, self.constraints = zip(*[(i, t) for i, t in zip(self.constrained_indices, self.constraints) if len(i)]) - self.constrained_indices, self.constraints = list(self.constrained_indices), list(self.constraints) - - # fixed: - self.fixed_values = [np.delete(values, np.nonzero(np.sum(indices[:, None] == matches[None, :], 1))[0]) for indices, values in zip(self.fixed_indices, self.fixed_values)] - self.fixed_indices = [np.delete(indices, np.nonzero(np.sum(indices[:, None] == matches[None, :], 1))[0]) for indices in self.fixed_indices] - - # remove empty elements - tmp = [(i, v) for i, v in zip(self.fixed_indices, self.fixed_values) if len(i)] - if tmp: - self.fixed_indices, self.fixed_values = zip(*tmp) - self.fixed_indices, self.fixed_values = list(self.fixed_indices), list(self.fixed_values) - else: - self.fixed_indices, self.fixed_values = [], [] - - def constrain_negative(self, regexp, warning=True): - """ Set negative constraints. """ - self.constrain(regexp, transformations.negative_logexp(), warning=warning) - - def constrain_positive(self, regexp, warning=True): - """ Set positive constraints. """ - self.constrain(regexp, transformations.logexp(), warning=warning) - - def constrain_bounded(self, regexp, lower, upper, warning=True): - """ Set bounded constraints. """ - self.constrain(regexp, transformations.logistic(lower, upper), warning=warning) - - def all_constrained_indices(self): - if len(self.constrained_indices) or len(self.fixed_indices): - return np.hstack(self.constrained_indices + self.fixed_indices) - else: - return np.empty(shape=(0,)) - - def constrain(self, regexp, transform, warning=True): - assert isinstance(transform, transformations.transformation) - - matches = self.grep_param_names(regexp) - if warning: - overlap = set(matches).intersection(set(self.all_constrained_indices())) - if overlap: - self.unconstrain(np.asarray(list(overlap))) - print 'Warning: re-constraining these parameters' - pn = self._get_param_names() - for i in overlap: - print pn[i] - - self.constrained_indices.append(matches) - self.constraints.append(transform) - x = self._get_params() - x[matches] = transform.initialize(x[matches]) - self._set_params(x) - - def constrain_fixed(self, regexp, value=None, warning=True): - """ - - :param regexp: which parameters need to be fixed. - :type regexp: ndarray(dtype=int) or regular expression object or string - :param value: the vlaue to fix the parameters to. If the value is not specified, - the parameter is fixed to the current value - :type value: float - - **Notes** - - Fixing a parameter which is tied to another, or constrained in some way will result in an error. - - To fix multiple parameters to the same value, simply pass a regular expression which matches both parameter names, or pass both of the indexes. - - """ - matches = self.grep_param_names(regexp) - if warning: - overlap = set(matches).intersection(set(self.all_constrained_indices())) - if overlap: - self.unconstrain(np.asarray(list(overlap))) - print 'Warning: re-constraining these parameters' - pn = self._get_param_names() - for i in overlap: - print pn[i] - - self.fixed_indices.append(matches) - if value != None: - self.fixed_values.append(value) - else: - self.fixed_values.append(self._get_params()[self.fixed_indices[-1]]) - - # self.fixed_values.append(value) - self._set_params_transformed(self._get_params_transformed()) - - def _get_params_transformed(self): - """use self._get_params to get the 'true' parameters of the model, which are then tied, constrained and fixed""" - x = self._get_params() - [np.put(x, i, t.finv(x[i])) for i, t in zip(self.constrained_indices, self.constraints)] - - to_remove = self.fixed_indices + [t[1:] for t in self.tied_indices] - if len(to_remove): - return np.delete(x, np.hstack(to_remove)) - else: - return x - - def _set_params_transformed(self, x): - """ takes the vector x, which is then modified (by untying, reparameterising or inserting fixed values), and then call self._set_params""" - self._set_params(self._untransform_params(x)) - - def _untransform_params(self, x): - """ - The transformation required for _set_params_transformed. - - This moves the vector x seen by the optimiser (unconstrained) to the - valid parameter vector seen by the model - - Note: - - This function is separate from _set_params_transformed for downstream flexibility - """ - # work out how many places are fixed, and where they are. tricky logic! - fix_places = self.fixed_indices + [t[1:] for t in self.tied_indices] - if len(fix_places): - fix_places = np.hstack(fix_places) - Nfix_places = fix_places.size - else: - Nfix_places = 0 - - free_places = np.setdiff1d(np.arange(Nfix_places + x.size, dtype=np.int), fix_places) - - # put the models values in the vector xx - xx = np.zeros(Nfix_places + free_places.size, dtype=np.float64) - - xx[free_places] = x - [np.put(xx, i, v) for i, v in zip(self.fixed_indices, self.fixed_values)] - [np.put(xx, i, v) for i, v in [(t[1:], xx[t[0]]) for t in self.tied_indices] ] - - [np.put(xx, i, t.f(xx[i])) for i, t in zip(self.constrained_indices, self.constraints)] - if hasattr(self, 'debug'): - stop # @UndefinedVariable - - return xx - - def _get_param_names_transformed(self): - """ - Returns the parameter names as propagated after constraining, - tying or fixing, i.e. a list of the same length as _get_params_transformed() - """ - n = self._get_param_names() - - # remove/concatenate the tied parameter names - if len(self.tied_indices): - for t in self.tied_indices: - n[t[0]] = "".join([n[tt] for tt in t]) - remove = np.hstack([t[1:] for t in self.tied_indices]) - else: - remove = np.empty(shape=(0,), dtype=np.int) - - # also remove the fixed params - if len(self.fixed_indices): - remove = np.hstack((remove, np.hstack(self.fixed_indices))) - - # add markers to show that some variables are constrained - for i, t in zip(self.constrained_indices, self.constraints): - for ii in i: - n[ii] = n[ii] + t.__str__() - - n = [nn for i, nn in enumerate(n) if not i in remove] - return n - - #@property - #def all(self): - # return self.__str__(self._get_param_names()) - - - #def __str__(self, names=None, nw=30): - def __str__(self, nw=30): - """ - Return a string describing the parameter names and their ties and constraints - """ - names = self._get_param_names() - #if names is None: - # names = self._get_print_names() - #name_indices = self.grep_param_names("|".join(names)) - N = len(names) - - if not N: - return "This object has no free parameters." - header = ['Name', 'Value', 'Constraints', 'Ties'] - values = self._get_params() # map(str,self._get_params()) - #values = self._get_params()[name_indices] # map(str,self._get_params()) - # sort out the constraints - constraints = [''] * len(names) - #constraints = [''] * len(self._get_param_names()) - for i, t in zip(self.constrained_indices, self.constraints): - for ii in i: - constraints[ii] = t.__str__() - for i in self.fixed_indices: - for ii in i: - constraints[ii] = 'Fixed' - # sort out the ties - ties = [''] * len(names) - for i, tie in enumerate(self.tied_indices): - for j in tie: - ties[j] = '(' + str(i) + ')' - - if values.size == 1: - values = ['%.4f' %float(values)] - else: - values = ['%.4f' % float(v) for v in values] - max_names = max([len(names[i]) for i in range(len(names))] + [len(header[0])]) - max_values = max([len(values[i]) for i in range(len(values))] + [len(header[1])]) - max_constraint = max([len(constraints[i]) for i in range(len(constraints))] + [len(header[2])]) - max_ties = max([len(ties[i]) for i in range(len(ties))] + [len(header[3])]) - cols = np.array([max_names, max_values, max_constraint, max_ties]) + 4 - # columns = cols.sum() - - header_string = ["{h:^{col}}".format(h=header[i], col=cols[i]) for i in range(len(cols))] - header_string = map(lambda x: '|'.join(x), [header_string]) - separator = '-' * len(header_string[0]) - param_string = ["{n:^{c0}}|{v:^{c1}}|{c:^{c2}}|{t:^{c3}}".format(n=names[i], v=values[i], c=constraints[i], t=ties[i], c0=cols[0], c1=cols[1], c2=cols[2], c3=cols[3]) for i in range(len(values))] - - - return ('\n'.join([header_string[0], separator] + param_string)) + '\n' - - def grep_model(self,regexp): - regexp_indices = self.grep_param_names(regexp) - all_names = self._get_param_names() - - names = [all_names[pj] for pj in regexp_indices] - N = len(names) - - if not N: - return "Match not found." - - header = ['Name', 'Value', 'Constraints', 'Ties'] - all_values = self._get_params() - values = np.array([all_values[pj] for pj in regexp_indices]) - constraints = [''] * len(names) - - _constrained_indices,aux = self._pick_elements(regexp_indices,self.constrained_indices) - _constraints = [self.constraints[pj] for pj in aux] - - for i, t in zip(_constrained_indices, _constraints): - for ii in i: - iii = regexp_indices.tolist().index(ii) - constraints[iii] = t.__str__() - - _fixed_indices,aux = self._pick_elements(regexp_indices,self.fixed_indices) - for i in _fixed_indices: - for ii in i: - iii = regexp_indices.tolist().index(ii) - constraints[ii] = 'Fixed' - - _tied_indices,aux = self._pick_elements(regexp_indices,self.tied_indices) - ties = [''] * len(names) - for i,ti in zip(_tied_indices,aux): - for ii in i: - iii = regexp_indices.tolist().index(ii) - ties[iii] = '(' + str(ti) + ')' - - if values.size == 1: - values = ['%.4f' %float(values)] - else: - values = ['%.4f' % float(v) for v in values] - - max_names = max([len(names[i]) for i in range(len(names))] + [len(header[0])]) - max_values = max([len(values[i]) for i in range(len(values))] + [len(header[1])]) - max_constraint = max([len(constraints[i]) for i in range(len(constraints))] + [len(header[2])]) - max_ties = max([len(ties[i]) for i in range(len(ties))] + [len(header[3])]) - cols = np.array([max_names, max_values, max_constraint, max_ties]) + 4 - - header_string = ["{h:^{col}}".format(h=header[i], col=cols[i]) for i in range(len(cols))] - header_string = map(lambda x: '|'.join(x), [header_string]) - separator = '-' * len(header_string[0]) - param_string = ["{n:^{c0}}|{v:^{c1}}|{c:^{c2}}|{t:^{c3}}".format(n=names[i], v=values[i], c=constraints[i], t=ties[i], c0=cols[0], c1=cols[1], c2=cols[2], c3=cols[3]) for i in range(len(values))] - - print header_string[0] - print separator - for string in param_string: - print string - - def _pick_elements(self,regexp_ind,array_list): - """Removes from array_list the elements different from regexp_ind""" - new_array_list = [] #New list with elements matching regexp_ind - array_indices = [] #Indices that matches the arrays in new_array_list and array_list - - array_index = 0 - for array in array_list: - _new = [] - for ai in array: - if ai in regexp_ind: - _new.append(ai) - if len(_new): - new_array_list.append(np.array(_new)) - array_indices.append(array_index) - array_index += 1 - return new_array_list, array_indices diff --git a/GPy/core/priors.py b/GPy/core/priors.py deleted file mode 100644 index 43090ae3..00000000 --- a/GPy/core/priors.py +++ /dev/null @@ -1,217 +0,0 @@ -# Copyright (c) 2012, GPy authors (see AUTHORS.txt). -# Licensed under the BSD 3-clause license (see LICENSE.txt) - - -import numpy as np -import pylab as pb -from scipy.special import gammaln, digamma -from ..util.linalg import pdinv -from GPy.core.domains import REAL, POSITIVE -import warnings - -class Prior: - domain = None - def pdf(self, x): - return np.exp(self.lnpdf(x)) - - def plot(self): - rvs = self.rvs(1000) - pb.hist(rvs, 100, normed=True) - xmin, xmax = pb.xlim() - xx = np.linspace(xmin, xmax, 1000) - pb.plot(xx, self.pdf(xx), 'r', linewidth=2) - - -class Gaussian(Prior): - """ - Implementation of the univariate Gaussian probability function, coupled with random variables. - - :param mu: mean - :param sigma: standard deviation - - .. Note:: Bishop 2006 notation is used throughout the code - - """ - domain = REAL - def __init__(self, mu, sigma): - self.mu = float(mu) - self.sigma = float(sigma) - self.sigma2 = np.square(self.sigma) - self.constant = -0.5 * np.log(2 * np.pi * self.sigma2) - - def __str__(self): - return "N(" + str(np.round(self.mu)) + ', ' + str(np.round(self.sigma2)) + ')' - - def lnpdf(self, x): - return self.constant - 0.5 * np.square(x - self.mu) / self.sigma2 - - def lnpdf_grad(self, x): - return -(x - self.mu) / self.sigma2 - - def rvs(self, n): - return np.random.randn(n) * self.sigma + self.mu - - -class LogGaussian(Prior): - """ - Implementation of the univariate *log*-Gaussian probability function, coupled with random variables. - - :param mu: mean - :param sigma: standard deviation - - .. Note:: Bishop 2006 notation is used throughout the code - - """ - domain = POSITIVE - def __init__(self, mu, sigma): - self.mu = float(mu) - self.sigma = float(sigma) - self.sigma2 = np.square(self.sigma) - self.constant = -0.5 * np.log(2 * np.pi * self.sigma2) - - def __str__(self): - return "lnN(" + str(np.round(self.mu)) + ', ' + str(np.round(self.sigma2)) + ')' - - def lnpdf(self, x): - return self.constant - 0.5 * np.square(np.log(x) - self.mu) / self.sigma2 - np.log(x) - - def lnpdf_grad(self, x): - return -((np.log(x) - self.mu) / self.sigma2 + 1.) / x - - def rvs(self, n): - return np.exp(np.random.randn(n) * self.sigma + self.mu) - - -class MultivariateGaussian: - """ - Implementation of the multivariate Gaussian probability function, coupled with random variables. - - :param mu: mean (N-dimensional array) - :param var: covariance matrix (NxN) - - .. Note:: Bishop 2006 notation is used throughout the code - - """ - domain = REAL - def __init__(self, mu, var): - self.mu = np.array(mu).flatten() - self.var = np.array(var) - assert len(self.var.shape) == 2 - assert self.var.shape[0] == self.var.shape[1] - assert self.var.shape[0] == self.mu.size - self.input_dim = self.mu.size - self.inv, self.hld = pdinv(self.var) - self.constant = -0.5 * self.input_dim * np.log(2 * np.pi) - self.hld - - def summary(self): - raise NotImplementedError - - def pdf(self, x): - return np.exp(self.lnpdf(x)) - - def lnpdf(self, x): - d = x - self.mu - return self.constant - 0.5 * np.sum(d * np.dot(d, self.inv), 1) - - def lnpdf_grad(self, x): - d = x - self.mu - return -np.dot(self.inv, d) - - def rvs(self, n): - return np.random.multivariate_normal(self.mu, self.var, n) - - def plot(self): - if self.input_dim == 2: - rvs = self.rvs(200) - pb.plot(rvs[:, 0], rvs[:, 1], 'kx', mew=1.5) - xmin, xmax = pb.xlim() - ymin, ymax = pb.ylim() - xx, yy = np.mgrid[xmin:xmax:100j, ymin:ymax:100j] - xflat = np.vstack((xx.flatten(), yy.flatten())).T - zz = self.pdf(xflat).reshape(100, 100) - pb.contour(xx, yy, zz, linewidths=2) - - -def gamma_from_EV(E, V): - warnings.warn("use Gamma.from_EV to create Gamma Prior", FutureWarning) - return Gamma.from_EV(E, V) - - -class Gamma(Prior): - """ - Implementation of the Gamma probability function, coupled with random variables. - - :param a: shape parameter - :param b: rate parameter (warning: it's the *inverse* of the scale) - - .. Note:: Bishop 2006 notation is used throughout the code - - """ - domain = POSITIVE - def __init__(self, a, b): - self.a = float(a) - self.b = float(b) - self.constant = -gammaln(self.a) + a * np.log(b) - - def __str__(self): - return "Ga(" + str(np.round(self.a)) + ', ' + str(np.round(self.b)) + ')' - - def summary(self): - ret = {"E[x]": self.a / self.b, \ - "E[ln x]": digamma(self.a) - np.log(self.b), \ - "var[x]": self.a / self.b / self.b, \ - "Entropy": gammaln(self.a) - (self.a - 1.) * digamma(self.a) - np.log(self.b) + self.a} - if self.a > 1: - ret['Mode'] = (self.a - 1.) / self.b - else: - ret['mode'] = np.nan - return ret - - def lnpdf(self, x): - return self.constant + (self.a - 1) * np.log(x) - self.b * x - - def lnpdf_grad(self, x): - return (self.a - 1.) / x - self.b - - def rvs(self, n): - return np.random.gamma(scale=1. / self.b, shape=self.a, size=n) - @staticmethod - def from_EV(E, V): - """ - Creates an instance of a Gamma Prior by specifying the Expected value(s) - and Variance(s) of the distribution. - - :param E: expected value - :param V: variance - """ - a = np.square(E) / V - b = E / V - return Gamma(a, b) - -class inverse_gamma(Prior): - """ - Implementation of the inverse-Gamma probability function, coupled with random variables. - - :param a: shape parameter - :param b: rate parameter (warning: it's the *inverse* of the scale) - - .. Note:: Bishop 2006 notation is used throughout the code - - """ - domain = POSITIVE - def __init__(self, a, b): - self.a = float(a) - self.b = float(b) - self.constant = -gammaln(self.a) + a * np.log(b) - - def __str__(self): - return "iGa(" + str(np.round(self.a)) + ', ' + str(np.round(self.b)) + ')' - - def lnpdf(self, x): - return self.constant - (self.a + 1) * np.log(x) - self.b / x - - def lnpdf_grad(self, x): - return -(self.a + 1.) / x + self.b / x ** 2 - - def rvs(self, n): - return 1. / np.random.gamma(scale=1. / self.b, shape=self.a, size=n) diff --git a/GPy/core/sparse_gp.py b/GPy/core/sparse_gp.py index 92433f64..beb69138 100644 --- a/GPy/core/sparse_gp.py +++ b/GPy/core/sparse_gp.py @@ -1,16 +1,28 @@ -# Copyright (c) 2012, GPy authors (see AUTHORS.txt). +# Copyright (c) 2012-2014, GPy authors (see AUTHORS.txt). # Licensed under the BSD 3-clause license (see LICENSE.txt) import numpy as np -import pylab as pb -from ..util.linalg import mdot, jitchol, tdot, symmetrify, backsub_both_sides, chol_inv, dtrtrs, dpotrs, dpotri -from scipy import linalg -from ..likelihoods import Gaussian, EP,EP_Mixed_Noise -from gp_base import GPBase +from gp import GP +from parameterization.param import Param +from ..inference.latent_function_inference import var_dtc +from .. import likelihoods +from parameterization.variational import VariationalPosterior -class SparseGP(GPBase): +import logging +from GPy.inference.latent_function_inference.posterior import Posterior +from GPy.inference.optimization.stochastics import SparseGPStochastics,\ + SparseGPMissing +#no stochastics.py file added! from GPy.inference.optimization.stochastics import SparseGPStochastics,\ + #SparseGPMissing +logger = logging.getLogger("sparse gp") + +class SparseGP(GP): """ - Variational sparse GP model + A general purpose Sparse GP model + + This model allows (approximate) inference using variational DTC or FITC + (Gaussian likelihoods) as well as non-conjugate sparse methods based on + these. :param X: inputs :type X: np.ndarray (num_data x input_dim) @@ -20,478 +32,101 @@ class SparseGP(GPBase): :type kernel: a GPy.kern.kern instance :param X_variance: The uncertainty in the measurements of X (Gaussian variance) :type X_variance: np.ndarray (num_data x input_dim) | None - :param Z: inducing inputs (optional, see note) - :type Z: np.ndarray (num_inducing x input_dim) | None + :param Z: inducing inputs + :type Z: np.ndarray (num_inducing x input_dim) :param num_inducing: Number of inducing points (optional, default 10. Ignored if Z is not None) :type num_inducing: int - :param normalize_(X|Y): whether to normalize the data before computing (predictions will be in original scales) - :type normalize_(X|Y): bool """ - def __init__(self, X, likelihood, kernel, Z, X_variance=None, normalize_X=False): - GPBase.__init__(self, X, likelihood, kernel, normalize_X=normalize_X) + def __init__(self, X, Y, Z, kernel, likelihood, inference_method=None, + name='sparse gp', Y_metadata=None, normalizer=False): + #pick a sensible inference method + if inference_method is None: + if isinstance(likelihood, likelihoods.Gaussian): + inference_method = var_dtc.VarDTC(limit=1 if not self.missing_data else Y.shape[1]) + else: + #inference_method = ?? + raise NotImplementedError, "what to do what to do?" + print "defaulting to ", inference_method, "for latent function inference" - self.Z = Z + self.Z = Param('inducing inputs', Z) self.num_inducing = Z.shape[0] - self.backsub = 0 - - if X_variance is None: - self.has_uncertain_inputs = False - self.X_variance = None + + GP.__init__(self, X, Y, kernel, likelihood, inference_method=inference_method, name=name, Y_metadata=Y_metadata, normalizer=normalizer) + + logger.info("Adding Z as parameter") + self.link_parameter(self.Z, index=0) + self.posterior = None + + def has_uncertain_inputs(self): + return isinstance(self.X, VariationalPosterior) + + def parameters_changed(self): + self.posterior, self._log_marginal_likelihood, self.grad_dict = self.inference_method.inference(self.kern, self.X, self.Z, self.likelihood, self.Y, self.Y_metadata) + + self.likelihood.update_gradients(self.grad_dict['dL_dthetaL']) + + if isinstance(self.X, VariationalPosterior): + #gradients wrt kernel + dL_dKmm = self.grad_dict['dL_dKmm'] + self.kern.update_gradients_full(dL_dKmm, self.Z, None) + kerngrad = self.kern.gradient.copy() + self.kern.update_gradients_expectations(variational_posterior=self.X, + Z=self.Z, + dL_dpsi0=self.grad_dict['dL_dpsi0'], + dL_dpsi1=self.grad_dict['dL_dpsi1'], + dL_dpsi2=self.grad_dict['dL_dpsi2']) + self.kern.gradient += kerngrad + + #gradients wrt Z + self.Z.gradient = self.kern.gradients_X(dL_dKmm, self.Z) + self.Z.gradient += self.kern.gradients_Z_expectations( + self.grad_dict['dL_dpsi0'], + self.grad_dict['dL_dpsi1'], + self.grad_dict['dL_dpsi2'], + Z=self.Z, + variational_posterior=self.X) else: - assert X_variance.shape == X.shape - self.has_uncertain_inputs = True - self.X_variance = X_variance - - if normalize_X: - self.Z = (self.Z.copy() - self._Xoffset) / self._Xscale - - # normalize X uncertainty also - if self.has_uncertain_inputs: - self.X_variance /= np.square(self._Xscale) - - self._const_jitter = None - - def _compute_kernel_matrices(self): - # kernel computations, using BGPLVM notation - self.Kmm = self.kern.K(self.Z) - if self.has_uncertain_inputs: - self.psi0 = self.kern.psi0(self.Z, self.X, self.X_variance) - self.psi1 = self.kern.psi1(self.Z, self.X, self.X_variance) - self.psi2 = self.kern.psi2(self.Z, self.X, self.X_variance) - else: - self.psi0 = self.kern.Kdiag(self.X) - self.psi1 = self.kern.K(self.X, self.Z) - self.psi2 = None - - def _computations(self): - if self._const_jitter is None or not(self._const_jitter.shape[0] == self.num_inducing): - self._const_jitter = np.eye(self.num_inducing) * 1e-7 - - # factor Kmm - self._Lm = jitchol(self.Kmm + self._const_jitter) - if not self.backsub: - self._LmInv = linalg.lapack.dtrtri(self._Lm, lower=1)[0] # TODO: not needed in old version - - # The rather complex computations of self._A - if self.has_uncertain_inputs: - if self.likelihood.is_heteroscedastic: - psi2_beta = (self.psi2 * (self.likelihood.precision.flatten().reshape(self.num_data, 1, 1))).sum(0) - else: - psi2_beta = self.psi2.sum(0) * self.likelihood.precision - if self.backsub: - evals, evecs = linalg.eigh(psi2_beta) - clipped_evals = np.clip(evals, 0., 1e6) # TODO: make clipping configurable - if not np.array_equal(evals, clipped_evals): - pass # print evals - tmp = evecs * np.sqrt(clipped_evals) - tmp = tmp.T - tmp, _ = dtrtrs(self._Lm, np.asfortranarray(tmp.T), lower=1) - self._A = tdot(tmp) - else: - self._A = np.dot(np.dot(self._LmInv, - psi2_beta), - self._LmInv.T) - else: - if self.likelihood.is_heteroscedastic: - tmp = self.psi1 * (np.sqrt(self.likelihood.precision.flatten().reshape(self.num_data, 1))) - else: - tmp = self.psi1 * (np.sqrt(self.likelihood.precision)) - tmp, _ = dtrtrs(self._Lm, np.asfortranarray(tmp.T), lower=1) - self._A = tdot(tmp) - - # factor B - self.B = np.eye(self.num_inducing) + self._A - self.LB = jitchol(self.B) - - # VVT_factor is a matrix such that tdot(VVT_factor) = VVT...this is for efficiency! - self.psi1Vf = np.dot(self.psi1.T, self.likelihood.VVT_factor) - - if 1:#self.backsub: - # back substutue C into psi1Vf - tmp, info1 = dtrtrs(self._Lm, np.asfortranarray(self.psi1Vf), lower=1, trans=0) - self._LBi_Lmi_psi1Vf, _ = dtrtrs(self.LB, np.asfortranarray(tmp), lower=1, trans=0) - # tmp, info2 = dpotrs(self.LB, tmp, lower=1) - tmp, info2 = dtrtrs(self.LB, self._LBi_Lmi_psi1Vf, lower=1, trans=1) - self.Cpsi1Vf, info3 = dtrtrs(self._Lm, tmp, lower=1, trans=1) - else: - # slower, but more stable (?) version: - tmp = np.dot(self._LmInv, self.psi1Vf) - self._LBInv = linalg.lapack.dtrtri(self.LB, lower=True)[0] - self._LBi_Lmi_psi1Vf = np.dot(self._LBInv, tmp) - tmp = np.dot(self._LBInv.T, self._LBi_Lmi_psi1Vf) - self.Cpsi1Vf = np.dot(self._LmInv.T, tmp) - - #import ipdb;ipdb.set_trace() - - # Compute dL_dKmm - tmp = tdot(self._LBi_Lmi_psi1Vf) - self.data_fit = np.trace(tmp) - self.DBi_plus_BiPBi = backsub_both_sides(self.LB, self.output_dim * np.eye(self.num_inducing) + tmp) - tmp = -0.5 * self.DBi_plus_BiPBi - tmp += -0.5 * self.B * self.output_dim - tmp += self.output_dim * np.eye(self.num_inducing) - self.dL_dKmm = backsub_both_sides(self._Lm, tmp) - - # Compute dL_dpsi # FIXME: this is untested for the heterscedastic + uncertain inputs case - self.dL_dpsi0 = -0.5 * self.output_dim * (self.likelihood.precision * np.ones([self.num_data, 1])).flatten() - self.dL_dpsi1 = np.dot(self.likelihood.VVT_factor, self.Cpsi1Vf.T) - dL_dpsi2_beta = 0.5 * backsub_both_sides(self._Lm, self.output_dim * np.eye(self.num_inducing) - self.DBi_plus_BiPBi) - - if self.likelihood.is_heteroscedastic: - - if self.has_uncertain_inputs: - self.dL_dpsi2 = self.likelihood.precision.flatten()[:, None, None] * dL_dpsi2_beta[None, :, :] - else: - self.dL_dpsi1 += 2.*np.dot(dL_dpsi2_beta, (self.psi1 * self.likelihood.precision.reshape(self.num_data, 1)).T).T - self.dL_dpsi2 = None - else: - dL_dpsi2 = self.likelihood.precision * dL_dpsi2_beta - if self.has_uncertain_inputs: - # repeat for each of the N psi_2 matrices - self.dL_dpsi2 = np.repeat(dL_dpsi2[None, :, :], self.num_data, axis=0) - else: - # subsume back into psi1 (==Kmn) - self.dL_dpsi1 += 2.*np.dot(self.psi1, dL_dpsi2) - self.dL_dpsi2 = None + #gradients wrt kernel + self.kern.update_gradients_diag(self.grad_dict['dL_dKdiag'], self.X) + kerngrad = self.kern.gradient.copy() + self.kern.update_gradients_full(self.grad_dict['dL_dKnm'], self.X, self.Z) + kerngrad += self.kern.gradient + self.kern.update_gradients_full(self.grad_dict['dL_dKmm'], self.Z, None) + self.kern.gradient += kerngrad + #gradients wrt Z + self.Z.gradient = self.kern.gradients_X(self.grad_dict['dL_dKmm'], self.Z) + self.Z.gradient += self.kern.gradients_X(self.grad_dict['dL_dKnm'].T, self.Z, self.X) - # the partial derivative vector for the likelihood - if self.likelihood.num_params == 0: - # save computation here. - self.partial_for_likelihood = None - elif self.likelihood.is_heteroscedastic: - - if self.has_uncertain_inputs: - raise NotImplementedError, "heteroscedatic derivates with uncertain inputs not implemented" - - else: - - LBi = chol_inv(self.LB) - Lmi_psi1, nil = dtrtrs(self._Lm, np.asfortranarray(self.psi1.T), lower=1, trans=0) - _LBi_Lmi_psi1, _ = dtrtrs(self.LB, np.asfortranarray(Lmi_psi1), lower=1, trans=0) - - - self.partial_for_likelihood = -0.5 * self.likelihood.precision + 0.5 * self.likelihood.V**2 - self.partial_for_likelihood += 0.5 * self.output_dim * (self.psi0 - np.sum(Lmi_psi1**2,0))[:,None] * self.likelihood.precision**2 - - self.partial_for_likelihood += 0.5*np.sum(mdot(LBi.T,LBi,Lmi_psi1)*Lmi_psi1,0)[:,None]*self.likelihood.precision**2 - - self.partial_for_likelihood += -np.dot(self._LBi_Lmi_psi1Vf.T,_LBi_Lmi_psi1).T * self.likelihood.Y * self.likelihood.precision**2 - self.partial_for_likelihood += 0.5*np.dot(self._LBi_Lmi_psi1Vf.T,_LBi_Lmi_psi1).T**2 * self.likelihood.precision**2 - - else: - # likelihood is not heteroscedatic - self.partial_for_likelihood = -0.5 * self.num_data * self.output_dim * self.likelihood.precision + 0.5 * self.likelihood.trYYT * self.likelihood.precision ** 2 - self.partial_for_likelihood += 0.5 * self.output_dim * (self.psi0.sum() * self.likelihood.precision ** 2 - np.trace(self._A) * self.likelihood.precision) - self.partial_for_likelihood += self.likelihood.precision * (0.5 * np.sum(self._A * self.DBi_plus_BiPBi) - self.data_fit) - - def log_likelihood(self): - """ Compute the (lower bound on the) log marginal likelihood """ - if self.likelihood.is_heteroscedastic: - A = -0.5 * self.num_data * self.output_dim * np.log(2.*np.pi) + 0.5 * np.sum(np.log(self.likelihood.precision)) - 0.5 * np.sum(self.likelihood.V * self.likelihood.Y) - B = -0.5 * self.output_dim * (np.sum(self.likelihood.precision.flatten() * self.psi0) - np.trace(self._A)) - else: - A = -0.5 * self.num_data * self.output_dim * (np.log(2.*np.pi) - np.log(self.likelihood.precision)) - 0.5 * self.likelihood.precision * self.likelihood.trYYT - B = -0.5 * self.output_dim * (np.sum(self.likelihood.precision * self.psi0) - np.trace(self._A)) - C = -self.output_dim * (np.sum(np.log(np.diag(self.LB)))) # + 0.5 * self.num_inducing * np.log(sf2)) - D = 0.5 * self.data_fit - self._A_part, self._B_part, self._C_part, self._D_part = A, B, C, D - return A + B + C + D + self.likelihood.Z - - def _set_params(self, p): - self.Z = p[:self.num_inducing * self.input_dim].reshape(self.num_inducing, self.input_dim) - self.kern._set_params(p[self.Z.size:self.Z.size + self.kern.num_params]) - self.likelihood._set_params(p[self.Z.size + self.kern.num_params:]) - self._compute_kernel_matrices() - self._computations() - self.Cpsi1V = None - - def _get_params(self): - return np.hstack([self.Z.flatten(), self.kern._get_params_transformed(), self.likelihood._get_params()]) - - def _get_param_names(self): - return sum([['iip_%i_%i' % (i, j) for j in range(self.Z.shape[1])] for i in range(self.Z.shape[0])], [])\ - + self.kern._get_param_names_transformed() + self.likelihood._get_param_names() - - #def _get_print_names(self): - # return self.kern._get_param_names_transformed() + self.likelihood._get_param_names() - - def update_likelihood_approximation(self, **kwargs): + def _raw_predict(self, Xnew, full_cov=False, kern=None): """ - Approximates a non-gaussian likelihood using Expectation Propagation - - For a Gaussian likelihood, no iteration is required: - this function does nothing - """ - if not isinstance(self.likelihood, Gaussian): # Updates not needed for Gaussian likelihood - self.likelihood.restart() - if self.has_uncertain_inputs: - Lmi = chol_inv(self._Lm) - Kmmi = tdot(Lmi.T) - diag_tr_psi2Kmmi = np.array([np.trace(psi2_Kmmi) for psi2_Kmmi in np.dot(self.psi2, Kmmi)]) - - self.likelihood.fit_FITC(self.Kmm, self.psi1.T, diag_tr_psi2Kmmi, **kwargs) # This uses the fit_FITC code, but does not perfomr a FITC-EP.#TODO solve potential confusion - # raise NotImplementedError, "EP approximation not implemented for uncertain inputs" - else: - self.likelihood.fit_DTC(self.Kmm, self.psi1.T, **kwargs) - # self.likelihood.fit_FITC(self.Kmm,self.psi1,self.psi0) - self._set_params(self._get_params()) # update the GP - - def _log_likelihood_gradients(self): - return np.hstack((self.dL_dZ().flatten(), self.dL_dtheta(), self.likelihood._gradients(partial=self.partial_for_likelihood))) - - def dL_dtheta(self): - """ - Compute and return the derivative of the log marginal likelihood wrt the parameters of the kernel - """ - dL_dtheta = self.kern.dK_dtheta(self.dL_dKmm, self.Z) - if self.has_uncertain_inputs: - dL_dtheta += self.kern.dpsi0_dtheta(self.dL_dpsi0, self.Z, self.X, self.X_variance) - dL_dtheta += self.kern.dpsi1_dtheta(self.dL_dpsi1, self.Z, self.X, self.X_variance) - dL_dtheta += self.kern.dpsi2_dtheta(self.dL_dpsi2, self.Z, self.X, self.X_variance) - else: - dL_dtheta += self.kern.dK_dtheta(self.dL_dpsi1, self.X, self.Z) - dL_dtheta += self.kern.dKdiag_dtheta(self.dL_dpsi0, self.X) - - return dL_dtheta - - def dL_dZ(self): - """ - The derivative of the bound wrt the inducing inputs Z - """ - dL_dZ = self.kern.dK_dX(self.dL_dKmm, self.Z) - if self.has_uncertain_inputs: - dL_dZ += self.kern.dpsi1_dZ(self.dL_dpsi1, self.Z, self.X, self.X_variance) - dL_dZ += self.kern.dpsi2_dZ(self.dL_dpsi2, self.Z, self.X, self.X_variance) - else: - dL_dZ += self.kern.dK_dX(self.dL_dpsi1.T, self.Z, self.X) - return dL_dZ - - def _raw_predict(self, Xnew, X_variance_new=None, which_parts='all', full_cov=False): - """ - Internal helper function for making predictions, does not account for - normalization or likelihood function + Make a prediction for the latent function values """ - Bi, _ = dpotri(self.LB, lower=0) # WTH? this lower switch should be 1, but that doesn't work! - symmetrify(Bi) - Kmmi_LmiBLmi = backsub_both_sides(self._Lm, np.eye(self.num_inducing) - Bi) + if kern is None: kern = self.kern - if self.Cpsi1V is None: - psi1V = np.dot(self.psi1.T, self.likelihood.V) - tmp, _ = dtrtrs(self._Lm, np.asfortranarray(psi1V), lower=1, trans=0) - tmp, _ = dpotrs(self.LB, tmp, lower=1) - self.Cpsi1V, _ = dtrtrs(self._Lm, tmp, lower=1, trans=1) - - if X_variance_new is None: - Kx = self.kern.K(self.Z, Xnew, which_parts=which_parts) - mu = np.dot(Kx.T, self.Cpsi1V) + if not isinstance(Xnew, VariationalPosterior): + Kx = kern.K(self.Z, Xnew) + mu = np.dot(Kx.T, self.posterior.woodbury_vector) if full_cov: - Kxx = self.kern.K(Xnew, which_parts=which_parts) - var = Kxx - mdot(Kx.T, Kmmi_LmiBLmi, Kx) # NOTE this won't work for plotting + Kxx = kern.K(Xnew) + if self.posterior.woodbury_inv.ndim == 2: + var = Kxx - np.dot(Kx.T, np.dot(self.posterior.woodbury_inv, Kx)) + elif self.posterior.woodbury_inv.ndim == 3: + var = Kxx[:,:,None] - np.tensordot(np.dot(np.atleast_3d(self.posterior.woodbury_inv).T, Kx).T, Kx, [1,0]).swapaxes(1,2) + var = var else: - Kxx = self.kern.Kdiag(Xnew, which_parts=which_parts) - var = Kxx - np.sum(Kx * np.dot(Kmmi_LmiBLmi, Kx), 0) + Kxx = kern.Kdiag(Xnew) + var = (Kxx - np.sum(np.dot(np.atleast_3d(self.posterior.woodbury_inv).T, Kx) * Kx[None,:,:], 1)).T else: - # assert which_parts=='all', "swithching out parts of variational kernels is not implemented" - Kx = self.kern.psi1(self.Z, Xnew, X_variance_new) # , which_parts=which_parts) TODO: which_parts - mu = np.dot(Kx, self.Cpsi1V) + Kx = kern.psi1(self.Z, Xnew) + mu = np.dot(Kx, self.posterior.woodbury_vector) if full_cov: raise NotImplementedError, "TODO" else: - Kxx = self.kern.psi0(self.Z, Xnew, X_variance_new) - psi2 = self.kern.psi2(self.Z, Xnew, X_variance_new) + Kxx = kern.psi0(self.Z, Xnew) + psi2 = kern.psi2(self.Z, Xnew) var = Kxx - np.sum(np.sum(psi2 * Kmmi_LmiBLmi[None, :, :], 1), 1) - - return mu, var[:, None] - - def predict(self, Xnew, X_variance_new=None, which_parts='all', full_cov=False, **likelihood_args): - """ - Predict the function(s) at the new point(s) Xnew. - - **Arguments** - - :param Xnew: The points at which to make a prediction - :type Xnew: np.ndarray, Nnew x self.input_dim - :param X_variance_new: The uncertainty in the prediction points - :type X_variance_new: np.ndarray, Nnew x self.input_dim - :param which_parts: specifies which outputs kernel(s) to use in prediction - :type which_parts: ('all', list of bools) - :param full_cov: whether to return the full covariance matrix, or just the diagonal - :type full_cov: bool - :rtype: posterior mean, a Numpy array, Nnew x self.input_dim - :rtype: posterior variance, a Numpy array, Nnew x 1 if full_cov=False, Nnew x Nnew otherwise - :rtype: lower and upper boundaries of the 95% confidence intervals, Numpy arrays, Nnew x self.input_dim - - - If full_cov and self.input_dim > 1, the return shape of var is Nnew x Nnew x self.input_dim. If self.input_dim == 1, the return shape is Nnew x Nnew. - This is to allow for different normalizations of the output dimensions. - - """ - # normalize X values - Xnew = (Xnew.copy() - self._Xoffset) / self._Xscale - if X_variance_new is not None: - X_variance_new = X_variance_new / self._Xscale ** 2 - - # here's the actual prediction by the GP model - mu, var = self._raw_predict(Xnew, X_variance_new, full_cov=full_cov, which_parts=which_parts) - - # now push through likelihood - mean, var, _025pm, _975pm = self.likelihood.predictive_values(mu, var, full_cov, **likelihood_args) - - return mean, var, _025pm, _975pm - - - def plot_f(self, samples=0, plot_limits=None, which_data_rows='all', - which_data_ycols='all', which_parts='all', resolution=None, - full_cov=False, fignum=None, ax=None): - - """ - Plot the GP's view of the world, where the data is normalized and the - - In one dimension, the function is plotted with a shaded region identifying two standard deviations. - - In two dimsensions, a contour-plot shows the mean predicted function - - Not implemented in higher dimensions - - :param samples: the number of a posteriori samples to plot - :param plot_limits: The limits of the plot. If 1D [xmin,xmax], if 2D [[xmin,ymin],[xmax,ymax]]. Defaluts to data limits - :param which_data_rows: which if the training data to plot (default all) - :type which_data_rows: 'all' or a slice object to slice self.X, self.Y - :param which_parts: which of the kernel functions to plot (additively) - :type which_parts: 'all', or list of bools - :param resolution: the number of intervals to sample the GP on. Defaults to 200 in 1D and 50 (a 50x50 grid) in 2D - :type resolution: int - :param full_cov: - :type full_cov: bool - :param fignum: figure to plot on. - :type fignum: figure number - :param ax: axes to plot on. - :type ax: axes handle - - :param output: which output to plot (for multiple output models only) - :type output: integer (first output is 0) - """ - if ax is None: - fig = pb.figure(num=fignum) - ax = fig.add_subplot(111) - if fignum is None and ax is None: - fignum = fig.num - if which_data_rows is 'all': - which_data_rows = slice(None) - - GPBase.plot_f(self, samples=samples, plot_limits=plot_limits, which_data_rows=which_data_rows, which_data_ycols=which_data_ycols, which_parts=which_parts, resolution=resolution, fignum=fignum, ax=ax) - - if self.X.shape[1] == 1: - if self.has_uncertain_inputs: - Xu = self.X * self._Xscale + self._Xoffset # NOTE self.X are the normalized values now - ax.errorbar(Xu[which_data, 0], self.likelihood.data[which_data, 0], - xerr=2 * np.sqrt(self.X_variance[which_data, 0]), - ecolor='k', fmt=None, elinewidth=.5, alpha=.5) - Zu = self.Z * self._Xscale + self._Xoffset - ax.plot(Zu, np.zeros_like(Zu) + ax.get_ylim()[0], 'r|', mew=1.5, markersize=12) - - elif self.X.shape[1] == 2: - Zu = self.Z * self._Xscale + self._Xoffset - ax.plot(Zu[:, 0], Zu[:, 1], 'wo') - - else: - raise NotImplementedError, "Cannot define a frame with more than two input dimensions" - - def plot(self, plot_limits=None, which_data_rows='all', - which_data_ycols='all', which_parts='all', fixed_inputs=[], - plot_raw=False, - levels=20, samples=0, fignum=None, ax=None, resolution=None): - """ - Plot the posterior of the sparse GP. - - In one dimension, the function is plotted with a shaded region identifying two standard deviations. - - In two dimsensions, a contour-plot shows the mean predicted function - - In higher dimensions, use fixed_inputs to plot the GP with some of the inputs fixed. - - Can plot only part of the data and part of the posterior functions - using which_data_rowsm which_data_ycols and which_parts - - :param plot_limits: The limits of the plot. If 1D [xmin,xmax], if 2D [[xmin,ymin],[xmax,ymax]]. Defaluts to data limits - :type plot_limits: np.array - :param which_data_rows: which of the training data to plot (default all) - :type which_data_rows: 'all' or a slice object to slice self.X, self.Y - :param which_data_ycols: when the data has several columns (independant outputs), only plot these - :type which_data_rows: 'all' or a list of integers - :param which_parts: which of the kernel functions to plot (additively) - :type which_parts: 'all', or list of bools - :param fixed_inputs: a list of tuple [(i,v), (i,v)...], specifying that input index i should be set to value v. - :type fixed_inputs: a list of tuples - :param resolution: the number of intervals to sample the GP on. Defaults to 200 in 1D and 50 (a 50x50 grid) in 2D - :type resolution: int - :param levels: number of levels to plot in a contour plot. - :type levels: int - :param samples: the number of a posteriori samples to plot - :type samples: int - :param fignum: figure to plot on. - :type fignum: figure number - :param ax: axes to plot on. - :type ax: axes handle - :type output: integer (first output is 0) - :param linecol: color of line to plot. - :type linecol: - :param fillcol: color of fill - :param levels: for 2D plotting, the number of contour levels to use is ax is None, create a new figure - """ - #deal work out which ax to plot on - #Need these because we use which_data_rows in this function not just base - if which_data_rows == 'all': - which_data_rows = slice(None) - if which_data_ycols == 'all': - which_data_ycols = np.arange(self.output_dim) - if ax is None: - fig = pb.figure(num=fignum) - ax = fig.add_subplot(111) - - #work out what the inputs are for plotting (1D or 2D) - fixed_dims = np.array([i for i,v in fixed_inputs]) - free_dims = np.setdiff1d(np.arange(self.input_dim),fixed_dims) - - #call the base plotting - GPBase.plot(self, samples=samples, plot_limits=plot_limits, - which_data_rows=which_data_rows, - which_data_ycols=which_data_ycols, fixed_inputs=fixed_inputs, - which_parts=which_parts, resolution=resolution, levels=20, - fignum=fignum, ax=ax) - - if len(free_dims) == 1: - #plot errorbars for the uncertain inputs - if self.has_uncertain_inputs: - Xu = self.X * self._Xscale + self._Xoffset # NOTE self.X are the normalized values now - ax.errorbar(Xu[which_data_rows, 0], self.likelihood.data[which_data_rows, 0], - xerr=2 * np.sqrt(self.X_variance[which_data_rows, 0]), - ecolor='k', fmt=None, elinewidth=.5, alpha=.5) - - #plot the inducing inputs - Zu = self.Z * self._Xscale + self._Xoffset - ax.plot(Zu, np.zeros_like(Zu) + ax.get_ylim()[0], 'r|', mew=1.5, markersize=12) - - elif len(free_dims) == 2: - Zu = self.Z * self._Xscale + self._Xoffset - ax.plot(Zu[:, 0], Zu[:, 1], 'wo') - - else: - raise NotImplementedError, "Cannot define a frame with more than two input dimensions" - - def getstate(self): - """ - Get the current state of the class, - here just all the indices, rest can get recomputed - """ - return GPBase.getstate(self) + [self.Z, - self.num_inducing, - self.has_uncertain_inputs, - self.X_variance] - - def setstate(self, state): - self.X_variance = state.pop() - self.has_uncertain_inputs = state.pop() - self.num_inducing = state.pop() - self.Z = state.pop() - GPBase.setstate(self, state) - - + return mu, var diff --git a/GPy/core/sparse_gp_mpi.py b/GPy/core/sparse_gp_mpi.py new file mode 100644 index 00000000..15d3ad76 --- /dev/null +++ b/GPy/core/sparse_gp_mpi.py @@ -0,0 +1,120 @@ +# Copyright (c) 2012-2014, GPy authors (see AUTHORS.txt). +# Licensed under the BSD 3-clause license (see LICENSE.txt) + +import numpy as np +from sparse_gp import SparseGP +from numpy.linalg.linalg import LinAlgError +from ..inference.latent_function_inference.var_dtc_parallel import update_gradients, VarDTC_minibatch + +import logging +logger = logging.getLogger("sparse gp mpi") + +class SparseGP_MPI(SparseGP): + """ + A general purpose Sparse GP model with MPI parallelization support + + This model allows (approximate) inference using variational DTC or FITC + (Gaussian likelihoods) as well as non-conjugate sparse methods based on + these. + + :param X: inputs + :type X: np.ndarray (num_data x input_dim) + :param likelihood: a likelihood instance, containing the observed data + :type likelihood: GPy.likelihood.(Gaussian | EP | Laplace) + :param kernel: the kernel (covariance function). See link kernels + :type kernel: a GPy.kern.kern instance + :param X_variance: The uncertainty in the measurements of X (Gaussian variance) + :type X_variance: np.ndarray (num_data x input_dim) | None + :param Z: inducing inputs + :type Z: np.ndarray (num_inducing x input_dim) + :param num_inducing: Number of inducing points (optional, default 10. Ignored if Z is not None) + :type num_inducing: int + :param mpi_comm: The communication group of MPI, e.g. mpi4py.MPI.COMM_WORLD + :type mpi_comm: mpi4py.MPI.Intracomm + + """ + + def __init__(self, X, Y, Z, kernel, likelihood, variational_prior=None, inference_method=None, name='sparse gp mpi', Y_metadata=None, mpi_comm=None, normalizer=False): + self._IN_OPTIMIZATION_ = False + if mpi_comm != None: + if inference_method is None: + inference_method = VarDTC_minibatch(mpi_comm=mpi_comm) + else: + assert isinstance(inference_method, VarDTC_minibatch), 'inference_method has to support MPI!' + + super(SparseGP_MPI, self).__init__(X, Y, Z, kernel, likelihood, inference_method=inference_method, name=name, Y_metadata=Y_metadata, normalizer=normalizer) + self.update_model(False) + + if variational_prior is not None: + self.link_parameter(variational_prior) + + self.mpi_comm = mpi_comm + # Manage the data (Y) division + if mpi_comm != None: + from ..util.parallel import divide_data + N_start, N_end, N_list = divide_data(Y.shape[0], mpi_comm.rank, mpi_comm.size) + self.N_range = (N_start, N_end) + self.N_list = np.array(N_list) + self.Y_local = self.Y[N_start:N_end] + print 'MPI RANK '+str(self.mpi_comm.rank)+' with the data range '+str(self.N_range) + mpi_comm.Bcast(self.param_array, root=0) + self.update_model(True) + + def __getstate__(self): + dc = super(SparseGP_MPI, self).__getstate__() + dc['mpi_comm'] = None + if self.mpi_comm != None: + del dc['N_range'] + del dc['N_list'] + del dc['Y_local'] + if 'normalizer' not in dc: + dc['normalizer'] = None + dc['Y_normalized'] = dc['Y'] + return dc + + #===================================================== + # The MPI parallelization + # - can move to model at some point + #===================================================== + + @SparseGP.optimizer_array.setter + def optimizer_array(self, p): + if self.mpi_comm != None: + if self._IN_OPTIMIZATION_ and self.mpi_comm.rank==0: + self.mpi_comm.Bcast(np.int32(1),root=0) + self.mpi_comm.Bcast(p, root=0) + SparseGP.optimizer_array.fset(self,p) + + def optimize(self, optimizer=None, start=None, **kwargs): + self._IN_OPTIMIZATION_ = True + if self.mpi_comm==None: + super(SparseGP_MPI, self).optimize(optimizer,start,**kwargs) + elif self.mpi_comm.rank==0: + super(SparseGP_MPI, self).optimize(optimizer,start,**kwargs) + self.mpi_comm.Bcast(np.int32(-1),root=0) + elif self.mpi_comm.rank>0: + x = self.optimizer_array.copy() + flag = np.empty(1,dtype=np.int32) + while True: + self.mpi_comm.Bcast(flag,root=0) + if flag==1: + try: + self.optimizer_array = x + self._fail_count = 0 + except (LinAlgError, ZeroDivisionError, ValueError): + if self._fail_count >= self._allowed_failures: + raise + self._fail_count += 1 + elif flag==-1: + break + else: + self._IN_OPTIMIZATION_ = False + raise Exception("Unrecognizable flag for synchronization!") + self._IN_OPTIMIZATION_ = False + + def parameters_changed(self): + if isinstance(self.inference_method,VarDTC_minibatch): + update_gradients(self, mpi_comm=self.mpi_comm) + else: + super(SparseGP_MPI,self).parameters_changed() + diff --git a/GPy/core/svigp.py b/GPy/core/svigp.py deleted file mode 100644 index d47d46f1..00000000 --- a/GPy/core/svigp.py +++ /dev/null @@ -1,512 +0,0 @@ -# Copyright (c) 2012, James Hensman and Nicolo' Fusi -# Licensed under the BSD 3-clause license (see LICENSE.txt) - -import numpy as np -import pylab as pb -from .. import kern -from ..util.linalg import pdinv, mdot, tdot, dpotrs, dtrtrs, jitchol, backsub_both_sides -from ..likelihoods import EP -from gp_base import GPBase -from model import Model -import time -import sys - - -class SVIGP(GPBase): - """ - - Stochastic Variational inference in a Gaussian Process - - :param X: inputs - :type X: np.ndarray (num_data x num_inputs) - :param Y: observed data - :type Y: np.ndarray of observations (num_data x output_dim) - :param batchsize: the size of a minibatch - :param q_u: canonical parameters of the distribution squasehd into a 1D array - :type q_u: np.ndarray - :param kernel: the kernel/covariance function. See link kernels - :type kernel: a GPy kernel - :param Z: inducing inputs - :type Z: np.ndarray (num_inducing x num_inputs) - - """ - - def __init__(self, X, likelihood, kernel, Z, q_u=None, batchsize=10, X_variance=None): - GPBase.__init__(self, X, likelihood, kernel, normalize_X=False) - self.batchsize=batchsize - self.Y = self.likelihood.Y.copy() - self.Z = Z - self.num_inducing = Z.shape[0] - self.batchcounter = 0 - self.epochs = 0 - self.iterations = 0 - - self.vb_steplength = 0.05 - self.param_steplength = 1e-5 - self.momentum = 0.9 - - if X_variance is None: - self.has_uncertain_inputs = False - else: - self.has_uncertain_inputs = True - self.X_variance = X_variance - - - if q_u is None: - q_u = np.hstack((np.random.randn(self.num_inducing*self.output_dim),-.5*np.eye(self.num_inducing).flatten())) - self.set_vb_param(q_u) - - self._permutation = np.random.permutation(self.num_data) - self.load_batch() - - self._param_trace = [] - self._ll_trace = [] - self._grad_trace = [] - - #set the adaptive steplength parameters - self.hbar_t = 0.0 - self.tau_t = 100.0 - self.gbar_t = 0.0 - self.gbar_t1 = 0.0 - self.gbar_t2 = 0.0 - self.hbar_tp = 0.0 - self.tau_tp = 10000.0 - self.gbar_tp = 0.0 - self.adapt_param_steplength = True - self.adapt_vb_steplength = True - self._param_steplength_trace = [] - self._vb_steplength_trace = [] - - self.ensure_default_constraints() - - def getstate(self): - steplength_params = [self.hbar_t, self.tau_t, self.gbar_t, self.gbar_t1, self.gbar_t2, self.hbar_tp, self.tau_tp, self.gbar_tp, self.adapt_param_steplength, self.adapt_vb_steplength, self.vb_steplength, self.param_steplength] - return GPBase.getstate(self) + \ - [self.get_vb_param(), - self.Z, - self.num_inducing, - self.has_uncertain_inputs, - self.X_variance, - self.X_batch, - self.X_variance_batch, - steplength_params, - self.batchcounter, - self.batchsize, - self.epochs, - self.momentum, - self.data_prop, - self._param_trace, - self._param_steplength_trace, - self._vb_steplength_trace, - self._ll_trace, - self._grad_trace, - self.Y, - self._permutation, - self.iterations - ] - - def setstate(self, state): - self.iterations = state.pop() - self._permutation = state.pop() - self.Y = state.pop() - self._grad_trace = state.pop() - self._ll_trace = state.pop() - self._vb_steplength_trace = state.pop() - self._param_steplength_trace = state.pop() - self._param_trace = state.pop() - self.data_prop = state.pop() - self.momentum = state.pop() - self.epochs = state.pop() - self.batchsize = state.pop() - self.batchcounter = state.pop() - steplength_params = state.pop() - (self.hbar_t, self.tau_t, self.gbar_t, self.gbar_t1, self.gbar_t2, self.hbar_tp, self.tau_tp, self.gbar_tp, self.adapt_param_steplength, self.adapt_vb_steplength, self.vb_steplength, self.param_steplength) = steplength_params - self.X_variance_batch = state.pop() - self.X_batch = state.pop() - self.X_variance = state.pop() - self.has_uncertain_inputs = state.pop() - self.num_inducing = state.pop() - self.Z = state.pop() - vb_param = state.pop() - GPBase.setstate(self, state) - self.set_vb_param(vb_param) - - def _compute_kernel_matrices(self): - # kernel computations, using BGPLVM notation - self.Kmm = self.kern.K(self.Z) - if self.has_uncertain_inputs: - self.psi0 = self.kern.psi0(self.Z, self.X_batch, self.X_variance_batch) - self.psi1 = self.kern.psi1(self.Z, self.X_batch, self.X_variance_batch) - self.psi2 = self.kern.psi2(self.Z, self.X_batch, self.X_variance_batch) - else: - self.psi0 = self.kern.Kdiag(self.X_batch) - self.psi1 = self.kern.K(self.X_batch, self.Z) - self.psi2 = None - - def dL_dtheta(self): - dL_dtheta = self.kern.dK_dtheta(self.dL_dKmm, self.Z) - if self.has_uncertain_inputs: - dL_dtheta += self.kern.dpsi0_dtheta(self.dL_dpsi0, self.Z, self.X_batch, self.X_variance_batch) - dL_dtheta += self.kern.dpsi1_dtheta(self.dL_dpsi1, self.Z, self.X_batch, self.X_variance_batch) - dL_dtheta += self.kern.dpsi2_dtheta(self.dL_dpsi2, self.Z, self.X_batch, self.X_variance_batch) - else: - dL_dtheta += self.kern.dK_dtheta(self.dL_dpsi1, self.X_batch, self.Z) - dL_dtheta += self.kern.dKdiag_dtheta(self.dL_dpsi0, self.X_batch) - return dL_dtheta - - def _set_params(self, p, computations=True): - self.kern._set_params_transformed(p[:self.kern.num_params]) - self.likelihood._set_params(p[self.kern.num_params:]) - if computations: - self._compute_kernel_matrices() - self._computations() - - def _get_params(self): - return np.hstack((self.kern._get_params_transformed() , self.likelihood._get_params())) - - def _get_param_names(self): - return self.kern._get_param_names_transformed() + self.likelihood._get_param_names() - - def load_batch(self): - """ - load a batch of data (set self.X_batch and self.likelihood.Y from self.X, self.Y) - """ - - #if we've seen all the data, start again with them in a new random order - if self.batchcounter+self.batchsize > self.num_data: - self.batchcounter = 0 - self.epochs += 1 - self._permutation = np.random.permutation(self.num_data) - - this_perm = self._permutation[self.batchcounter:self.batchcounter+self.batchsize] - - self.X_batch = self.X[this_perm] - self.likelihood.set_data(self.Y[this_perm]) - if self.has_uncertain_inputs: - self.X_variance_batch = self.X_variance[this_perm] - - self.batchcounter += self.batchsize - - self.data_prop = float(self.batchsize)/self.num_data - - self._compute_kernel_matrices() - self._computations() - - def _computations(self,do_Kmm=True, do_Kmm_grad=True): - """ - All of the computations needed. Some are optional, see kwargs. - """ - - if do_Kmm: - self.Lm = jitchol(self.Kmm) - - # The rather complex computations of self.A - if self.has_uncertain_inputs: - if self.likelihood.is_heteroscedastic: - psi2_beta = (self.psi2 * (self.likelihood.precision.flatten().reshape(self.batchsize, 1, 1))).sum(0) - else: - psi2_beta = self.psi2.sum(0) * self.likelihood.precision - evals, evecs = np.linalg.eigh(psi2_beta) - clipped_evals = np.clip(evals, 0., 1e6) # TODO: make clipping configurable - tmp = evecs * np.sqrt(clipped_evals) - else: - if self.likelihood.is_heteroscedastic: - tmp = self.psi1.T * (np.sqrt(self.likelihood.precision.flatten().reshape(1, self.batchsize))) - else: - tmp = self.psi1.T * (np.sqrt(self.likelihood.precision)) - tmp, _ = dtrtrs(self.Lm, np.asfortranarray(tmp), lower=1) - self.A = tdot(tmp) - - self.V = self.likelihood.precision*self.likelihood.Y - self.VmT = np.dot(self.V,self.q_u_expectation[0].T) - self.psi1V = np.dot(self.psi1.T, self.V) - - self.B = np.eye(self.num_inducing)*self.data_prop + self.A - self.Lambda = backsub_both_sides(self.Lm, self.B.T) - self.LQL = backsub_both_sides(self.Lm,self.q_u_expectation[1].T,transpose='right') - - self.trace_K = self.psi0.sum() - np.trace(self.A)/self.likelihood.precision - self.Kmmi_m, _ = dpotrs(self.Lm, self.q_u_expectation[0], lower=1) - self.projected_mean = np.dot(self.psi1,self.Kmmi_m) - - # Compute dL_dpsi - self.dL_dpsi0 = - 0.5 * self.output_dim * self.likelihood.precision * np.ones(self.batchsize) - self.dL_dpsi1, _ = dpotrs(self.Lm,np.asfortranarray(self.VmT.T),lower=1) - self.dL_dpsi1 = self.dL_dpsi1.T - - dL_dpsi2 = -0.5 * self.likelihood.precision * backsub_both_sides(self.Lm, self.LQL - self.output_dim * np.eye(self.num_inducing)) - if self.has_uncertain_inputs: - self.dL_dpsi2 = np.repeat(dL_dpsi2[None,:,:],self.batchsize,axis=0) - else: - self.dL_dpsi1 += 2.*np.dot(dL_dpsi2,self.psi1.T).T - self.dL_dpsi2 = None - - # Compute dL_dKmm - if do_Kmm_grad: - tmp = np.dot(self.LQL,self.A) - backsub_both_sides(self.Lm,np.dot(self.q_u_expectation[0],self.psi1V.T),transpose='right') - tmp += tmp.T - tmp += -self.output_dim*self.B - tmp += self.data_prop*self.LQL - self.dL_dKmm = 0.5*backsub_both_sides(self.Lm,tmp) - - #Compute the gradient of the log likelihood wrt noise variance - self.partial_for_likelihood = -0.5*(self.batchsize*self.output_dim - np.sum(self.A*self.LQL))*self.likelihood.precision - self.partial_for_likelihood += (0.5*self.output_dim*self.trace_K + 0.5 * self.likelihood.trYYT - np.sum(self.likelihood.Y*self.projected_mean))*self.likelihood.precision**2 - - - def log_likelihood(self): - """ - As for uncollapsed sparse GP, but account for the proportion of data we're looking at right now. - - NB. self.batchsize is the size of the batch, not the size of X_all - """ - assert not self.likelihood.is_heteroscedastic - A = -0.5*self.batchsize*self.output_dim*(np.log(2.*np.pi) - np.log(self.likelihood.precision)) - B = -0.5*self.likelihood.precision*self.output_dim*self.trace_K - Kmm_logdet = 2.*np.sum(np.log(np.diag(self.Lm))) - C = -0.5*self.output_dim*self.data_prop*(Kmm_logdet-self.q_u_logdet - self.num_inducing) - C += -0.5*np.sum(self.LQL * self.B) - D = -0.5*self.likelihood.precision*self.likelihood.trYYT - E = np.sum(self.V*self.projected_mean) - return (A+B+C+D+E)/self.data_prop - - def _log_likelihood_gradients(self): - return np.hstack((self.dL_dtheta(), self.likelihood._gradients(partial=self.partial_for_likelihood)))/self.data_prop - - def vb_grad_natgrad(self): - """ - Compute the gradients of the lower bound wrt the canonical and - Expectation parameters of u. - - Note that the natural gradient in either is given by the gradient in the other (See Hensman et al 2012 Fast Variational inference in the conjugate exponential Family) - """ - - # Gradient for eta - dL_dmmT_S = -0.5*self.Lambda/self.data_prop + 0.5*self.q_u_prec - Kmmipsi1V,_ = dpotrs(self.Lm,self.psi1V,lower=1) - dL_dm = (Kmmipsi1V - np.dot(self.Lambda,self.q_u_mean))/self.data_prop - - # Gradients for theta - S = self.q_u_cov - Si = self.q_u_prec - m = self.q_u_mean - dL_dSi = -mdot(S,dL_dmmT_S, S) - - dL_dmhSi = -2*dL_dSi - dL_dSim = np.dot(dL_dSi,m) + np.dot(Si, dL_dm) - - return np.hstack((dL_dm.flatten(),dL_dmmT_S.flatten())) , np.hstack((dL_dSim.flatten(), dL_dmhSi.flatten())) - - - def optimize(self, iterations, print_interval=10, callback=lambda:None, callback_interval=5): - - param_step = 0. - - #Iterate! - for i in range(iterations): - - #store the current configuration for plotting later - self._param_trace.append(self._get_params()) - self._ll_trace.append(self.log_likelihood() + self.log_prior()) - - #load a batch and do the appropriate computations (kernel matrices, etc) - self.load_batch() - - #compute the (stochastic) gradient - natgrads = self.vb_grad_natgrad() - grads = self._transform_gradients(self._log_likelihood_gradients() + self._log_prior_gradients()) - self._grad_trace.append(grads) - - #compute the steps in all parameters - vb_step = self.vb_steplength*natgrads[0] - #only move the parameters after the first epoch and only if the steplength is nonzero - if (self.epochs>=1) and (self.param_steplength > 0): - param_step = self.momentum*param_step + self.param_steplength*grads - else: - param_step = 0. - - self.set_vb_param(self.get_vb_param() + vb_step) - #Note: don't recompute everything here, wait until the next iteration when we have a new batch - self._set_params(self._untransform_params(self._get_params_transformed() + param_step), computations=False) - - #print messages if desired - if i and (not i%print_interval): - print i, np.mean(self._ll_trace[-print_interval:]) #, self.log_likelihood() - print np.round(np.mean(self._grad_trace[-print_interval:],0),3) - sys.stdout.flush() - - #callback - if i and not i%callback_interval: - callback(self) # Change this to callback() - time.sleep(0.01) - - if self.epochs > 10: - self._adapt_steplength() - self._vb_steplength_trace.append(self.vb_steplength) - self._param_steplength_trace.append(self.param_steplength) - - self.iterations += 1 - - - def _adapt_steplength(self): - if self.adapt_vb_steplength: - # self._adaptive_vb_steplength() - self._adaptive_vb_steplength_KL() - #self._vb_steplength_trace.append(self.vb_steplength) - assert self.vb_steplength >= 0 - - if self.adapt_param_steplength: - self._adaptive_param_steplength() - # self._adaptive_param_steplength_log() - # self._adaptive_param_steplength_from_vb() - #self._param_steplength_trace.append(self.param_steplength) - - def _adaptive_param_steplength(self): - if hasattr(self, 'adapt_param_steplength_decr'): - decr_factor = self.adapt_param_steplength_decr - else: - decr_factor = 0.02 - g_tp = self._transform_gradients(self._log_likelihood_gradients()) - self.gbar_tp = (1-1/self.tau_tp)*self.gbar_tp + 1/self.tau_tp * g_tp - self.hbar_tp = (1-1/self.tau_tp)*self.hbar_tp + 1/self.tau_tp * np.dot(g_tp.T, g_tp) - new_param_steplength = np.dot(self.gbar_tp.T, self.gbar_tp) / self.hbar_tp - #- hack - new_param_steplength *= decr_factor - self.param_steplength = (self.param_steplength + new_param_steplength)/2 - #- - self.tau_tp = self.tau_tp*(1-self.param_steplength) + 1 - - def _adaptive_param_steplength_log(self): - stp = np.logspace(np.log(0.0001), np.log(1e-6), base=np.e, num=18000) - self.param_steplength = stp[self.iterations] - - def _adaptive_param_steplength_log2(self): - self.param_steplength = (self.iterations + 0.001)**-0.5 - - def _adaptive_param_steplength_from_vb(self): - self.param_steplength = self.vb_steplength * 0.01 - - def _adaptive_vb_steplength(self): - decr_factor = 0.1 - g_t = self.vb_grad_natgrad()[0] - self.gbar_t = (1-1/self.tau_t)*self.gbar_t + 1/self.tau_t * g_t - self.hbar_t = (1-1/self.tau_t)*self.hbar_t + 1/self.tau_t * np.dot(g_t.T, g_t) - new_vb_steplength = np.dot(self.gbar_t.T, self.gbar_t) / self.hbar_t - #- hack - new_vb_steplength *= decr_factor - self.vb_steplength = (self.vb_steplength + new_vb_steplength)/2 - #- - self.tau_t = self.tau_t*(1-self.vb_steplength) + 1 - - def _adaptive_vb_steplength_KL(self): - decr_factor = 0.1 - natgrad = self.vb_grad_natgrad() - g_t1 = natgrad[0] - g_t2 = natgrad[1] - self.gbar_t1 = (1-1/self.tau_t)*self.gbar_t1 + 1/self.tau_t * g_t1 - self.gbar_t2 = (1-1/self.tau_t)*self.gbar_t2 + 1/self.tau_t * g_t2 - self.hbar_t = (1-1/self.tau_t)*self.hbar_t + 1/self.tau_t * np.dot(g_t1.T, g_t2) - self.vb_steplength = np.dot(self.gbar_t1.T, self.gbar_t2) / self.hbar_t - self.vb_steplength *= decr_factor - self.tau_t = self.tau_t*(1-self.vb_steplength) + 1 - - def _raw_predict(self, X_new, X_variance_new=None, which_parts='all',full_cov=False): - """Internal helper function for making predictions, does not account for normalization""" - - #TODO: make this more efficient! - self.Kmmi, self.Lm, self.Lmi, self.Kmm_logdet = pdinv(self.Kmm) - tmp = self.Kmmi- mdot(self.Kmmi,self.q_u_cov,self.Kmmi) - - if X_variance_new is None: - Kx = self.kern.K(X_new,self.Z) - mu = np.dot(Kx,self.Kmmi_m) - if full_cov: - Kxx = self.kern.K(X_new) - var = Kxx - mdot(Kx,tmp,Kx.T) - else: - Kxx = self.kern.Kdiag(X_new) - var = (Kxx - np.sum(Kx*np.dot(Kx,tmp),1))[:,None] - return mu, var - else: - assert X_variance_new.shape == X_new.shape - Kx = self.kern.psi1(self.Z,X_new, X_variance_new) - mu = np.dot(Kx,self.Kmmi_m) - Kxx = self.kern.psi0(self.Z,X_new,X_variance_new) - psi2 = self.kern.psi2(self.Z,X_new,X_variance_new) - diag_var = Kxx - np.sum(np.sum(psi2*tmp[None,:,:],1),1) - if full_cov: - raise NotImplementedError - else: - return mu, diag_var[:,None] - - def predict(self, Xnew, X_variance_new=None, which_parts='all', full_cov=False, sampling=False, num_samples=15000): - # normalize X values - Xnew = (Xnew.copy() - self._Xoffset) / self._Xscale - if X_variance_new is not None: - X_variance_new = X_variance_new / self._Xscale ** 2 - - # here's the actual prediction by the GP model - mu, var = self._raw_predict(Xnew, X_variance_new, full_cov=full_cov, which_parts=which_parts) - - # now push through likelihood - mean, var, _025pm, _975pm = self.likelihood.predictive_values(mu, var, full_cov, sampling=sampling, num_samples=num_samples) - - return mean, var, _025pm, _975pm - - - def set_vb_param(self,vb_param): - """set the distribution q(u) from the canonical parameters""" - self.q_u_canonical_flat = vb_param.copy() - self.q_u_canonical = self.q_u_canonical_flat[:self.num_inducing*self.output_dim].reshape(self.num_inducing,self.output_dim),self.q_u_canonical_flat[self.num_inducing*self.output_dim:].reshape(self.num_inducing,self.num_inducing) - - self.q_u_prec = -2.*self.q_u_canonical[1] - self.q_u_cov, q_u_Li, q_u_L, tmp = pdinv(self.q_u_prec) - self.q_u_Li = q_u_Li - self.q_u_logdet = -tmp - self.q_u_mean, _ = dpotrs(q_u_Li, np.asfortranarray(self.q_u_canonical[0]),lower=1) - - self.q_u_expectation = (self.q_u_mean, np.dot(self.q_u_mean,self.q_u_mean.T)+self.q_u_cov*self.output_dim) - - - def get_vb_param(self): - """ - Return the canonical parameters of the distribution q(u) - """ - return self.q_u_canonical_flat - - - def plot(self, ax=None, fignum=None, Z_height=None, **kwargs): - - if ax is None: - fig = pb.figure(num=fignum) - ax = fig.add_subplot(111) - - #horrible hack here: - data = self.likelihood.data.copy() - self.likelihood.data = self.Y - GPBase.plot(self, ax=ax, **kwargs) - self.likelihood.data = data - - Zu = self.Z * self._Xscale + self._Xoffset - if self.input_dim==1: - ax.plot(self.X_batch, self.likelihood.data, 'gx',mew=2) - if Z_height is None: - Z_height = ax.get_ylim()[0] - ax.plot(Zu, np.zeros_like(Zu) + Z_height, 'r|', mew=1.5, markersize=12) - - if self.input_dim==2: - ax.scatter(self.X[:,0], self.X[:,1], 20., self.Y[:,0], linewidth=0, cmap=pb.cm.jet) - ax.plot(Zu[:,0], Zu[:,1], 'w^') - - def plot_traces(self): - pb.figure() - t = np.array(self._param_trace) - pb.subplot(2,1,1) - for l,ti in zip(self._get_param_names(),t.T): - if not l[:3]=='iip': - pb.plot(ti,label=l) - pb.legend(loc=0) - - pb.subplot(2,1,2) - pb.plot(np.asarray(self._ll_trace),label='stochastic likelihood') - pb.legend(loc=0) diff --git a/GPy/core/symbolic.py b/GPy/core/symbolic.py new file mode 100644 index 00000000..ed3a9d59 --- /dev/null +++ b/GPy/core/symbolic.py @@ -0,0 +1,420 @@ +# Copyright (c) 2014, GPy authors (see AUTHORS.txt). +# Licensed under the BSD 3-clause license (see LICENSE.txt) + +import sys +import re +from ..core.parameterization import Parameterized +import numpy as np +import sympy as sym +from ..core.parameterization import Param +from sympy.utilities.lambdify import lambdastr, _imp_namespace, _get_namespace +from sympy.utilities.iterables import numbered_symbols +import scipy +import GPy + + +def getFromDict(dataDict, mapList): + return reduce(lambda d, k: d[k], mapList, dataDict) + +def setInDict(dataDict, mapList, value): + getFromDict(dataDict, mapList[:-1])[mapList[-1]] = value + +class Symbolic_core(): + """ + Base model symbolic class. + """ + + def __init__(self, expressions, cacheable, derivatives=None, parameters=None, func_modules=[]): + # Base class init, do some basic derivatives etc. + + # Func_modules sets up the right mapping for functions. + func_modules += [{'gamma':scipy.special.gamma, + 'gammaln':scipy.special.gammaln, + 'erf':scipy.special.erf, 'erfc':scipy.special.erfc, + 'erfcx':scipy.special.erfcx, + 'polygamma':scipy.special.polygamma, + 'normcdf':GPy.util.functions.normcdf, + 'normcdfln':GPy.util.functions.normcdfln, + 'logistic':GPy.util.functions.logistic, + 'logisticln':GPy.util.functions.logisticln}, + 'numpy'] + + self._set_expressions(expressions) + self._set_variables(cacheable) + self._set_derivatives(derivatives) + self._set_parameters(parameters) + # Convert the expressions to a list for common sub expression elimination + # We should find the following type of expressions: 'function', 'derivative', 'second_derivative', 'third_derivative'. + self.update_expression_list() + + # Apply any global stabilisation operations to expressions. + self.global_stabilize() + + # Helper functions to get data in and out of dictionaries. + # this code from http://stackoverflow.com/questions/14692690/access-python-nested-dictionary-items-via-a-list-of-keys + + self.extract_sub_expressions() + self._gen_code() + self._set_namespace(func_modules) + + def _set_namespace(self, namespaces): + """Set the name space for use when calling eval. This needs to contain all the relvant functions for mapping from symbolic python to the numerical python. It also contains variables, cached portions etc.""" + self.namespace = {} + for m in namespaces[::-1]: + buf = _get_namespace(m) + self.namespace.update(buf) + self.namespace.update(self.__dict__) + + def _set_expressions(self, expressions): + """Extract expressions and variables from the user provided expressions.""" + self.expressions = {} + for key, item in expressions.items(): + self.expressions[key] = {'function': item} + + def _set_variables(self, cacheable): + """Pull the variable names out of the provided expressions and separate into cacheable expressions and normal parameters. Those that are only stored in the cache, the parameters are stored in this object.""" + # pull the parameters and inputs out of the symbolic pdf + def extract_vars(expr): + return [e for e in expr.atoms() if e.is_Symbol and e not in vars] + self.cacheable = cacheable + self.variables = {} + vars = [] + for expression in self.expressions.values(): + vars += extract_vars(expression['function']) + # inputs are assumed to be those things that are + # cacheable. I.e. those things that aren't stored within the + # object except as cached. For covariance functions this is X + # and Z, for likelihoods F and for mapping functions X. + self.cacheable_vars = [] # list of everything that's cacheable + for var in cacheable: + self.variables[var] = [e for e in vars if e.name.split('_')[0]==var.lower()] + self.cacheable_vars += self.variables[var] + for var in cacheable: + if not self.variables[var]: + raise ValueError('Variable ' + var + ' was specified as cacheable but is not in expression. Expected to find symbols of the form ' + var.lower() + '_0 to represent ' + var) + + # things that aren't cacheable are assumed to be parameters. + self.variables['theta'] = sorted([e for e in vars if not e in self.cacheable_vars],key=lambda e:e.name) + + def _set_derivatives(self, derivatives): + # these are arguments for computing derivatives. + def extract_derivative(function, derivative_arguments): + return {theta.name : self.stabilize(sym.diff(function,theta)) for theta in derivative_arguments} + derivative_arguments = [] + if derivatives is not None: + for derivative in derivatives: + derivative_arguments += self.variables[derivative] + + # Do symbolic work to compute derivatives. + for key, func in self.expressions.items(): + # if func['function'].is_Matrix: + # rows = func['function'].shape[0] + # cols = func['function'].shape[1] + # self.expressions[key]['derivative'] = sym.zeros(rows, cols) + # for i in xrange(rows): + # for j in xrange(cols): + # self.expressions[key]['derivative'][i, j] = extract_derivative(func['function'][i, j], derivative_arguments) + # else: + self.expressions[key]['derivative'] = extract_derivative(func['function'], derivative_arguments) + + def _set_parameters(self, parameters): + """Add parameters to the model and initialize with given values.""" + for theta in self.variables['theta']: + val = 1.0 + # TODO: improve approach for initializing parameters. + if parameters is not None: + if parameters.has_key(theta.name): + val = parameters[theta.name] + # Add parameter. + + self.link_parameters(Param(theta.name, val, None)) + #self._set_attribute(theta.name, ) + + def eval_parameters_changed(self): + # TODO: place checks for inf/nan in here + # do all the precomputation codes. + self.eval_update_cache() + + def eval_update_cache(self, **kwargs): + # TODO: place checks for inf/nan in here + # for all provided keywords + + for var, code in self.variable_sort(self.code['parameters_changed']): + self._set_attribute(var, eval(code, self.namespace)) + + for var, value in kwargs.items(): + # update their cached values + if value is not None: + if var == 'X' or var == 'F' or var == 'M': + value = np.atleast_2d(value) + for i, theta in enumerate(self.variables[var]): + self._set_attribute(theta.name, value[:, i][:, None]) + elif var == 'Y': + # Y values can be missing. + value = np.atleast_2d(value) + for i, theta in enumerate(self.variables[var]): + self._set_attribute('missing' + str(i), np.isnan(value[:, i])) + self._set_attribute(theta.name, value[:, i][:, None]) + elif var == 'Z': + value = np.atleast_2d(value) + for i, theta in enumerate(self.variables[var]): + self._set_attribute(theta.name, value[:, i][None, :]) + else: + value = np.atleast_1d(value) + for i, theta in enumerate(self.variables[var]): + self._set_attribute(theta.name, value[i]) + for var, code in self.variable_sort(self.code['update_cache']): + self._set_attribute(var, eval(code, self.namespace)) + + def eval_update_gradients(self, function, partial, **kwargs): + # TODO: place checks for inf/nan in here? + self.eval_update_cache(**kwargs) + gradient = {} + for theta in self.variables['theta']: + code = self.code[function]['derivative'][theta.name] + gradient[theta.name] = (partial*eval(code, self.namespace)).sum() + return gradient + + def eval_gradients_X(self, function, partial, **kwargs): + if kwargs.has_key('X'): + gradients_X = np.zeros_like(kwargs['X']) + self.eval_update_cache(**kwargs) + for i, theta in enumerate(self.variables['X']): + code = self.code[function]['derivative'][theta.name] + gradients_X[:, i:i+1] = partial*eval(code, self.namespace) + return gradients_X + + def eval_function(self, function, **kwargs): + self.eval_update_cache(**kwargs) + return eval(self.code[function]['function'], self.namespace) + + def code_parameters_changed(self): + # do all the precomputation codes. + lcode = '' + for variable, code in self.variable_sort(self.code['parameters_changed']): + lcode += self._print_code(variable) + ' = ' + self._print_code(code) + '\n' + return lcode + + def code_update_cache(self): + lcode = '' + for var in self.cacheable: + lcode += 'if ' + var + ' is not None:\n' + if var == 'X': + reorder = '[:, None]' + elif var == 'Z': + reorder = '[None, :]' + else: + reorder = '' + for i, theta in enumerate(self.variables[var]): + lcode+= "\t" + var + '= np.atleast_2d(' + var + ')\n' + lcode+= "\t" + self._print_code(theta.name) + ' = ' + var + '[:, ' + str(i) + "]" + reorder + "\n" + + for variable, code in self.variable_sort(self.code['update_cache']): + lcode+= self._print_code(variable) + ' = ' + self._print_code(code) + "\n" + + return lcode + + def code_update_gradients(self, function): + lcode = '' + for theta in self.variables['theta']: + code = self.code[function]['derivative'][theta.name] + lcode += self._print_code(theta.name) + '.gradient = (partial*(' + self._print_code(code) + ')).sum()\n' + return lcode + + def code_gradients_cacheable(self, function, variable): + if variable not in self.cacheable: + raise RuntimeError, variable + ' must be a cacheable.' + lcode = 'gradients_' + variable + ' = np.zeros_like(' + variable + ')\n' + lcode += 'self.update_cache(' + ', '.join(self.cacheable) + ')\n' + for i, theta in enumerate(self.variables[variable]): + code = self.code[function]['derivative'][theta.name] + lcode += 'gradients_' + variable + '[:, ' + str(i) + ':' + str(i) + '+1] = partial*' + self._print_code(code) + '\n' + lcode += 'return gradients_' + variable + '\n' + return lcode + + def code_function(self, function): + lcode = 'self.update_cache(' + ', '.join(self.cacheable) + ')\n' + lcode += 'return ' + self._print_code(self.code[function]['function']) + return lcode + + def stabilize(self, expr): + """Stabilize the code in the model.""" + # this code is applied to expressions in the model in an attempt to sabilize them. + return expr + + def global_stabilize(self): + """Stabilize all code in the model.""" + pass + + def _set_attribute(self, name, value): + """Make sure namespace gets updated when setting attributes.""" + setattr(self, name, value) + self.namespace.update({name: getattr(self, name)}) + + + def update_expression_list(self): + """Extract a list of expressions from the dictionary of expressions.""" + self.expression_list = [] # code arrives in dictionary, but is passed in this list + self.expression_keys = [] # Keep track of the dictionary keys. + self.expression_order = [] # This may be unecessary. It's to give ordering for cse + for fname, fexpressions in self.expressions.items(): + for type, texpressions in fexpressions.items(): + if type == 'function': + self.expression_list.append(texpressions) + self.expression_keys.append([fname, type]) + self.expression_order.append(1) + elif type[-10:] == 'derivative': + for dtype, expression in texpressions.items(): + self.expression_list.append(expression) + self.expression_keys.append([fname, type, dtype]) + if type[:-10] == 'first_' or type[:-10] == '': + self.expression_order.append(3) #sym.count_ops(self.expressions[type][dtype])) + elif type[:-10] == 'second_': + self.expression_order.append(4) #sym.count_ops(self.expressions[type][dtype])) + elif type[:-10] == 'third_': + self.expression_order.append(5) #sym.count_ops(self.expressions[type][dtype])) + else: + self.expression_list.append(fexpressions[type]) + self.expression_keys.append([fname, type]) + self.expression_order.append(2) + + # This step may be unecessary. + # Not 100% sure if the sub expression elimination is order sensitive. This step orders the list with the 'function' code first and derivatives after. + self.expression_order, self.expression_list, self.expression_keys = zip(*sorted(zip(self.expression_order, self.expression_list, self.expression_keys))) + + def extract_sub_expressions(self, cache_prefix='cache', sub_prefix='sub', prefix='XoXoXoX'): + # Do the common sub expression elimination. + common_sub_expressions, expression_substituted_list = sym.cse(self.expression_list, numbered_symbols(prefix=prefix)) + + self.variables[cache_prefix] = [] + self.variables[sub_prefix] = [] + + # Create dictionary of new sub expressions + sub_expression_dict = {} + for var, void in common_sub_expressions: + sub_expression_dict[var.name] = var + + # Sort out any expression that's dependent on something that scales with data size (these are listed in cacheable). + cacheable_list = [] + params_change_list = [] + # common_sube_expressions contains a list of paired tuples with the new variable and what it equals + for var, expr in common_sub_expressions: + arg_list = [e for e in expr.atoms() if e.is_Symbol] + # List any cacheable dependencies of the sub-expression + cacheable_symbols = [e for e in arg_list if e in cacheable_list or e in self.cacheable_vars] + if cacheable_symbols: + # list which ensures dependencies are cacheable. + cacheable_list.append(var) + else: + params_change_list.append(var) + + replace_dict = {} + for i, expr in enumerate(cacheable_list): + sym_var = sym.var(cache_prefix + str(i)) + self.variables[cache_prefix].append(sym_var) + replace_dict[expr.name] = sym_var + + for i, expr in enumerate(params_change_list): + sym_var = sym.var(sub_prefix + str(i)) + self.variables[sub_prefix].append(sym_var) + replace_dict[expr.name] = sym_var + + for replace, void in common_sub_expressions: + for expr, keys in zip(expression_substituted_list, self.expression_keys): + setInDict(self.expressions, keys, expr.subs(replace, replace_dict[replace.name])) + for void, expr in common_sub_expressions: + expr = expr.subs(replace, replace_dict[replace.name]) + + # Replace original code with code including subexpressions. + for keys in self.expression_keys: + for replace, void in common_sub_expressions: + setInDict(self.expressions, keys, getFromDict(self.expressions, keys).subs(replace, replace_dict[replace.name])) + + self.expressions['parameters_changed'] = {} + self.expressions['update_cache'] = {} + for var, expr in common_sub_expressions: + for replace, void in common_sub_expressions: + expr = expr.subs(replace, replace_dict[replace.name]) + if var in cacheable_list: + self.expressions['update_cache'][replace_dict[var.name].name] = expr + else: + self.expressions['parameters_changed'][replace_dict[var.name].name] = expr + + + def _gen_code(self): + """Generate code for the list of expressions provided using the common sub-expression eliminator to separate out portions that are computed multiple times.""" + # This is the dictionary that stores all the generated code. + + self.code = {} + def match_key(expr): + if type(expr) is dict: + code = {} + for key in expr.keys(): + code[key] = match_key(expr[key]) + else: + arg_list = [e for e in expr.atoms() if e.is_Symbol] + code = self._expr2code(arg_list, expr) + return code + + self.code = match_key(self.expressions) + + + def _expr2code(self, arg_list, expr): + """Convert the given symbolic expression into code.""" + code = lambdastr(arg_list, expr) + function_code = code.split(':')[1].strip() + #for arg in arg_list: + # function_code = function_code.replace(arg.name, 'self.'+arg.name) + + return function_code + + def _print_code(self, code): + """Prepare code for string writing.""" + # This needs a rewrite --- it doesn't check for match clashes! So sub11 would be replaced by sub1 before being replaced with sub11!! + for key in self.variables.keys(): + for arg in self.variables[key]: + code = code.replace(arg.name, 'self.'+arg.name) + return code + + def _display_expression(self, keys, user_substitutes={}): + """Helper function for human friendly display of the symbolic components.""" + # Create some pretty maths symbols for the display. + sigma, alpha, nu, omega, l, variance = sym.var('\sigma, \alpha, \nu, \omega, \ell, \sigma^2') + substitutes = {'scale': sigma, 'shape': alpha, 'lengthscale': l, 'variance': variance} + substitutes.update(user_substitutes) + + function_substitutes = {normcdfln : lambda arg : sym.log(normcdf(arg)), + logisticln : lambda arg : -sym.log(1+sym.exp(-arg)), + logistic : lambda arg : 1/(1+sym.exp(-arg)), + erfcx : lambda arg : erfc(arg)/sym.exp(arg*arg), + gammaln : lambda arg : sym.log(sym.gamma(arg))} + expr = getFromDict(self.expressions, keys) + for var_name, sub in self.variable_sort(self.expressions['update_cache'], reverse=True): + for var in self.variables['cache']: + if var_name == var.name: + expr = expr.subs(var, sub) + break + for var_name, sub in self.variable_sort(self.expressions['parameters_changed'], reverse=True): + for var in self.variables['sub']: + if var_name == var.name: + expr = expr.subs(var, sub) + break + + for var_name, sub in self.variable_sort(substitutes, reverse=True): + for var in self.variables['theta']: + if var_name == var.name: + expr = expr.subs(var, sub) + break + for m, r in function_substitutes.iteritems(): + expr = expr.replace(m, r)#normcdfln, lambda arg : sym.log(normcdf(arg))) + return expr.simplify() + + def variable_sort(self, var_dict, reverse=False): + def sort_key(x): + digits = re.findall(r'\d+$', x[0]) + if digits: + return int(digits[0]) + else: + return x[0] + + return sorted(var_dict.iteritems(), key=sort_key, reverse=reverse) diff --git a/GPy/core/transformations.py b/GPy/core/transformations.py deleted file mode 100644 index 73a9837b..00000000 --- a/GPy/core/transformations.py +++ /dev/null @@ -1,143 +0,0 @@ -# Copyright (c) 2012, GPy authors (see AUTHORS.txt). -# Licensed under the BSD 3-clause license (see LICENSE.txt) - - -import numpy as np -from GPy.core.domains import POSITIVE, NEGATIVE, BOUNDED -import sys -lim_val = -np.log(sys.float_info.epsilon) - -class transformation(object): - domain = None - def f(self, x): - raise NotImplementedError - - def finv(self, x): - raise NotImplementedError - - def gradfactor(self, f): - """ df_dx evaluated at self.f(x)=f""" - raise NotImplementedError - - def initialize(self, f): - """ produce a sensible initial value for f(x)""" - raise NotImplementedError - - def __str__(self): - raise NotImplementedError - -class logexp(transformation): - domain = POSITIVE - def f(self, x): - return np.where(x<-lim_val, np.log(1+np.exp(-lim_val)), np.where(x>lim_val, x, np.log(1. + np.exp(x)))) - def finv(self, f): - return np.where(f>lim_val, f, np.log(np.exp(f) - 1.)) - def gradfactor(self, f): - return np.where(f>lim_val, 1., 1 - np.exp(-f)) - def initialize(self, f): - if np.any(f < 0.): - print "Warning: changing parameters to satisfy constraints" - return np.abs(f) - def __str__(self): - return '(+ve)' - -class negative_logexp(transformation): - domain = NEGATIVE - def f(self, x): - return -logexp.f(x) - def finv(self, f): - return logexp.finv(-f) - def gradfactor(self, f): - return -logexp.gradfactor(-f) - def initialize(self, f): - return -logexp.initialize(f) - def __str__(self): - return '(-ve)' - -class logexp_clipped(logexp): - max_bound = 1e100 - min_bound = 1e-10 - log_max_bound = np.log(max_bound) - log_min_bound = np.log(min_bound) - domain = POSITIVE - def __init__(self, lower=1e-6): - self.lower = lower - def f(self, x): - exp = np.exp(np.clip(x, self.log_min_bound, self.log_max_bound)) - f = np.log(1. + exp) -# if np.isnan(f).any(): -# import ipdb;ipdb.set_trace() - return np.clip(f, self.min_bound, self.max_bound) - def finv(self, f): - return np.log(np.exp(f - 1.)) - def gradfactor(self, f): - ef = np.exp(f) # np.clip(f, self.min_bound, self.max_bound)) - gf = (ef - 1.) / ef - return gf # np.where(f < self.lower, 0, gf) - def initialize(self, f): - if np.any(f < 0.): - print "Warning: changing parameters to satisfy constraints" - return np.abs(f) - def __str__(self): - return '(+ve_c)' - -class exponent(transformation): - domain = POSITIVE - def f(self, x): - return np.where(x-lim_val, np.exp(x), np.exp(-lim_val)), np.exp(lim_val)) - def finv(self, x): - return np.log(x) - def gradfactor(self, f): - return f - def initialize(self, f): - if np.any(f < 0.): - print "Warning: changing parameters to satisfy constraints" - return np.abs(f) - def __str__(self): - return '(+ve)' - -class negative_exponent(exponent): - domain = NEGATIVE - def f(self, x): - return -exponent.f(x) - def finv(self, f): - return exponent.finv(-f) - def gradfactor(self, f): - return f - def initialize(self, f): - return -exponent.initialize(f) #np.abs(f) - def __str__(self): - return '(-ve)' - -class square(transformation): - domain = POSITIVE - def f(self, x): - return x ** 2 - def finv(self, x): - return np.sqrt(x) - def gradfactor(self, f): - return 2 * np.sqrt(f) - def initialize(self, f): - return np.abs(f) - def __str__(self): - return '(+sq)' - -class logistic(transformation): - domain = BOUNDED - def __init__(self, lower, upper): - assert lower < upper - self.lower, self.upper = float(lower), float(upper) - self.difference = self.upper - self.lower - def f(self, x): - return self.lower + self.difference / (1. + np.exp(-x)) - def finv(self, f): - return np.log(np.clip(f - self.lower, 1e-10, np.inf) / np.clip(self.upper - f, 1e-10, np.inf)) - def gradfactor(self, f): - return (f - self.lower) * (self.upper - f) / self.difference - def initialize(self, f): - if np.any(np.logical_or(f < self.lower, f > self.upper)): - print "Warning: changing parameters to satisfy constraints" - return np.where(np.logical_or(f < self.lower, f > self.upper), self.f(f * 0.), f) - def __str__(self): - return '({},{})'.format(self.lower, self.upper) - diff --git a/GPy/defaults.cfg b/GPy/defaults.cfg new file mode 100644 index 00000000..306543ed --- /dev/null +++ b/GPy/defaults.cfg @@ -0,0 +1,27 @@ +# This is the default configuration file for GPy + +# Do note edit this file. + +# For machine specific changes (i.e. those specific to a given installation) edit GPy/installation.cfg + +# For user specific changes edit $HOME/.gpy_user.cfg +[parallel] +# Enable openmp support. This speeds up some computations, depending on the number +# of cores available. Setting up a compiler with openmp support can be difficult on +# some platforms, hence by default it is off. +openmp=False + +[datasets] +# location for the local data cache +dir=$HOME/tmp/GPy-datasets/ + +[anaconda] +# if you have an anaconda python installation please specify it here. +installed = False +location = None + # set this to true if you have the MKL optimizations installed: +MKL = False + +[weave] +#if true, try to use weave, and fall back to numpy. if false, just use numpy. +working = True diff --git a/GPy/examples/__init__.py b/GPy/examples/__init__.py index 2f74858a..968333e0 100644 --- a/GPy/examples/__init__.py +++ b/GPy/examples/__init__.py @@ -1,8 +1,7 @@ -# Copyright (c) 2012, GPy authors (see AUTHORS.txt). +# Copyright (c) 2012-2014, GPy authors (see AUTHORS.txt). # Licensed under the BSD 3-clause license (see LICENSE.txt) import classification import regression import dimensionality_reduction -import tutorials -import stochastic +import non_gaussian diff --git a/GPy/examples/classification.py b/GPy/examples/classification.py index f9aaddd1..b3780073 100644 --- a/GPy/examples/classification.py +++ b/GPy/examples/classification.py @@ -1,11 +1,10 @@ -# Copyright (c) 2012, GPy authors (see AUTHORS.txt). +# Copyright (c) 2012-2014, GPy authors (see AUTHORS.txt). # Licensed under the BSD 3-clause license (see LICENSE.txt) """ -Gaussian Processes classification +Gaussian Processes classification examples """ -import pylab as pb import GPy default_seed = 10000 @@ -15,7 +14,9 @@ def oil(num_inducing=50, max_iters=100, kernel=None, optimize=True, plot=True): Run a Gaussian process classification on the three phase oil data. The demonstration calls the basic GP classification model and uses EP to approximate the likelihood. """ - data = GPy.util.datasets.oil() + try:import pods + except ImportError:print 'pods unavailable, see https://github.com/sods/ods for example datasets' + data = pods.datasets.oil() X = data['X'] Xtest = data['Xtest'] Y = data['Y'][:, 0:1] @@ -27,13 +28,13 @@ def oil(num_inducing=50, max_iters=100, kernel=None, optimize=True, plot=True): m = GPy.models.SparseGPClassification(X, Y, kernel=kernel, num_inducing=num_inducing) # Contrain all parameters to be positive - m.tie_params('.*len') + #m.tie_params('.*len') m['.*len'] = 10. - m.update_likelihood_approximation() # Optimize if optimize: - m.optimize(max_iters=max_iters) + for _ in range(5): + m.optimize(max_iters=int(max_iters/5)) print(m) #Test @@ -50,7 +51,9 @@ def toy_linear_1d_classification(seed=default_seed, optimize=True, plot=True): """ - data = GPy.util.datasets.toy_linear_1d_classification(seed=seed) + try:import pods + except ImportError:print 'pods unavailable, see https://github.com/sods/ods for example datasets' + data = pods.datasets.toy_linear_1d_classification(seed=seed) Y = data['Y'][:, 0:1] Y[Y.flatten() == -1] = 0 @@ -61,13 +64,14 @@ def toy_linear_1d_classification(seed=default_seed, optimize=True, plot=True): if optimize: #m.update_likelihood_approximation() # Parameters optimization: - #m.optimize() + m.optimize() #m.update_likelihood_approximation() - m.pseudo_EM() + #m.pseudo_EM() # Plot if plot: - fig, axes = pb.subplots(2, 1) + from matplotlib import pyplot as plt + fig, axes = plt.subplots(2, 1) m.plot_f(ax=axes[0]) m.plot(ax=axes[1]) @@ -83,27 +87,30 @@ def toy_linear_1d_classification_laplace(seed=default_seed, optimize=True, plot= """ - data = GPy.util.datasets.toy_linear_1d_classification(seed=seed) + try:import pods + except ImportError:print 'pods unavailable, see https://github.com/sods/ods for example datasets' + data = pods.datasets.toy_linear_1d_classification(seed=seed) Y = data['Y'][:, 0:1] Y[Y.flatten() == -1] = 0 - bern_noise_model = GPy.likelihoods.bernoulli() - laplace_likelihood = GPy.likelihoods.Laplace(Y.copy(), bern_noise_model) + likelihood = GPy.likelihoods.Bernoulli() + laplace_inf = GPy.inference.latent_function_inference.Laplace() + kernel = GPy.kern.RBF(1) # Model definition - m = GPy.models.GPClassification(data['X'], Y, likelihood=laplace_likelihood) - print m + m = GPy.core.GP(data['X'], Y, kernel=kernel, likelihood=likelihood, inference_method=laplace_inf) # Optimize if optimize: - #m.update_likelihood_approximation() - # Parameters optimization: - m.optimize('bfgs', messages=1) - #m.pseudo_EM() + try: + m.optimize('scg', messages=1) + except Exception as e: + return m # Plot if plot: - fig, axes = pb.subplots(2, 1) + from matplotlib import pyplot as plt + fig, axes = plt.subplots(2, 1) m.plot_f(ax=axes[0]) m.plot(ax=axes[1]) @@ -119,7 +126,9 @@ def sparse_toy_linear_1d_classification(num_inducing=10, seed=default_seed, opti """ - data = GPy.util.datasets.toy_linear_1d_classification(seed=seed) + try:import pods + except ImportError:print 'pods unavailable, see https://github.com/sods/ods for example datasets' + data = pods.datasets.toy_linear_1d_classification(seed=seed) Y = data['Y'][:, 0:1] Y[Y.flatten() == -1] = 0 @@ -129,21 +138,19 @@ def sparse_toy_linear_1d_classification(num_inducing=10, seed=default_seed, opti # Optimize if optimize: - #m.update_likelihood_approximation() - # Parameters optimization: - #m.optimize() - m.pseudo_EM() + m.optimize() # Plot if plot: - fig, axes = pb.subplots(2, 1) + from matplotlib import pyplot as plt + fig, axes = plt.subplots(2, 1) m.plot_f(ax=axes[0]) m.plot(ax=axes[1]) print m return m -def toy_heaviside(seed=default_seed, optimize=True, plot=True): +def toy_heaviside(seed=default_seed, max_iters=100, optimize=True, plot=True): """ Simple 1D classification example using a heavy side gp transformation @@ -152,25 +159,30 @@ def toy_heaviside(seed=default_seed, optimize=True, plot=True): """ - data = GPy.util.datasets.toy_linear_1d_classification(seed=seed) + try:import pods + except ImportError:print 'pods unavailable, see https://github.com/sods/ods for example datasets' + data = pods.datasets.toy_linear_1d_classification(seed=seed) Y = data['Y'][:, 0:1] Y[Y.flatten() == -1] = 0 # Model definition - noise_model = GPy.likelihoods.bernoulli(GPy.likelihoods.noise_models.gp_transformations.Heaviside()) - likelihood = GPy.likelihoods.EP(Y, noise_model) - m = GPy.models.GPClassification(data['X'], likelihood=likelihood) + kernel = GPy.kern.RBF(1) + likelihood = GPy.likelihoods.Bernoulli(gp_link=GPy.likelihoods.link_functions.Heaviside()) + ep = GPy.inference.latent_function_inference.expectation_propagation.EP() + m = GPy.core.GP(X=data['X'], Y=Y, kernel=kernel, likelihood=likelihood, inference_method=ep, name='gp_classification_heaviside') + #m = GPy.models.GPClassification(data['X'], likelihood=likelihood) # Optimize if optimize: - m.update_likelihood_approximation() # Parameters optimization: - m.optimize() - #m.pseudo_EM() + for _ in range(5): + m.optimize(max_iters=int(max_iters/5)) + print m # Plot if plot: - fig, axes = pb.subplots(2, 1) + from matplotlib import pyplot as plt + fig, axes = plt.subplots(2, 1) m.plot_f(ax=axes[0]) m.plot(ax=axes[1]) @@ -189,7 +201,9 @@ def crescent_data(model_type='Full', num_inducing=10, seed=default_seed, kernel= :param kernel: kernel to use in the model :type kernel: a GPy kernel """ - data = GPy.util.datasets.crescent_data(seed=seed) + try:import pods + except ImportError:print 'pods unavailable, see https://github.com/sods/ods for example datasets' + data = pods.datasets.crescent_data(seed=seed) Y = data['Y'] Y[Y.flatten()==-1] = 0 diff --git a/GPy/examples/coreg_example.py b/GPy/examples/coreg_example.py new file mode 100644 index 00000000..4e9566dc --- /dev/null +++ b/GPy/examples/coreg_example.py @@ -0,0 +1,89 @@ +# Copyright (c) 2012-2014, GPy authors (see AUTHORS.txt). +# Licensed under the BSD 3-clause license (see LICENSE.txt) + +import numpy as np +try: + import pylab as pb +except: + pass +import GPy +pb.ion() +pb.close('all') + +X1 = np.arange(3)[:,None] +X2 = np.arange(4)[:,None] +I1 = np.zeros_like(X1) +I2 = np.ones_like(X2) + +_X = np.vstack([ X1, X2 ]) +_I = np.vstack([ I1, I2 ]) + +X = np.hstack([ _X, _I ]) + +Y1 = np.sin(X1/8.) +Y2 = np.cos(X2/8.) + +Bias = GPy.kern.Bias(1,active_dims=[0]) +Coreg = GPy.kern.Coregionalize(1,2,active_dims=[1]) +K = Bias.prod(Coreg,name='X') + +#K.coregion.W = 0 +#print K.coregion.W +#print Bias.K(_X,_X) +#print K.K(X,X) +#pb.matshow(K.K(X,X)) + +Mlist = [GPy.kern.Matern32(1,lengthscale=20.,name="Mat")] +kern = GPy.util.multioutput.LCM(input_dim=1,num_outputs=2,kernels_list=Mlist,name='H') +kern.B.W = 0 +kern.B.kappa = 1. +#kern.B.W.fix() +#kern.B.kappa.fix() +#m = GPy.models.GPCoregionalizedRegression(X_list=[X1,X2], Y_list=[Y1,Y2], kernel=kern) + + +Z1 = np.array([1.5,2.5])[:,None] + +m = GPy.models.SparseGPCoregionalizedRegression(X_list=[X1], Y_list=[Y1], Z_list = [Z1], kernel=kern) +#m.optimize() +m.checkgrad(verbose=1) + +""" +fig = pb.figure() +ax0 = fig.add_subplot(211) +ax1 = fig.add_subplot(212) +slices = GPy.util.multioutput.get_slices([Y1,Y2]) +m.plot(fixed_inputs=[(1,0)],which_data_rows=slices[0],ax=ax0) +#m.plot(fixed_inputs=[(1,1)],which_data_rows=slices[1],ax=ax1) +""" + + + +""" + +X1 = 100 * np.random.rand(100)[:,None] +X2 = 100 * np.random.rand(100)[:,None] +#X1.sort() +#X2.sort() + +Y1 = np.sin(X1/10.) + np.random.rand(100)[:,None] +Y2 = np.cos(X2/10.) + np.random.rand(100)[:,None] + + + + +Mlist = [GPy.kern.Matern32(1,lengthscale=20.,name="Mat")] +kern = GPy.util.multioutput.LCM(input_dim=1,num_outputs=12,kernels_list=Mlist,name='H') + + +m = GPy.models.GPCoregionalizedRegression(X_list=[X1,X2], Y_list=[Y1,Y2], kernel=kern) +m.optimize() + +fig = pb.figure() +ax0 = fig.add_subplot(211) +ax1 = fig.add_subplot(212) +slices = GPy.util.multioutput.get_slices([Y1,Y2]) +m.plot(fixed_inputs=[(1,0)],which_data_rows=slices[0],ax=ax0) +m.plot(fixed_inputs=[(1,1)],which_data_rows=slices[1],ax=ax1) + +""" diff --git a/GPy/examples/dimensionality_reduction.py b/GPy/examples/dimensionality_reduction.py index 83ee248e..eea3bb40 100644 --- a/GPy/examples/dimensionality_reduction.py +++ b/GPy/examples/dimensionality_reduction.py @@ -1,75 +1,79 @@ -# Copyright (c) 2012, GPy authors (see AUTHORS.txt). +# Copyright (c) 2012-2014, GPy authors (see AUTHORS.txt). # Licensed under the BSD 3-clause license (see LICENSE.txt) import numpy as _np -default_seed = _np.random.seed(123344) -def bgplvm_test_model(seed=default_seed, optimize=False, verbose=1, plot=False): +# default_seed = _np.random.seed(123344) + +def bgplvm_test_model(optimize=False, verbose=1, plot=False, output_dim=200, nan=False): """ model for testing purposes. Samples from a GP with rbf kernel and learns the samples with a new kernel. Normally not for optimization, just model cheking """ - from GPy.likelihoods.gaussian import Gaussian import GPy num_inputs = 13 num_inducing = 5 if plot: output_dim = 1 - input_dim = 2 + input_dim = 3 else: input_dim = 2 - output_dim = 25 + output_dim = output_dim # generate GPLVM-like data X = _np.random.rand(num_inputs, input_dim) lengthscales = _np.random.rand(input_dim) - k = (GPy.kern.rbf(input_dim, .5, lengthscales, ARD=True) - + GPy.kern.white(input_dim, 0.01)) + k = GPy.kern.RBF(input_dim, .5, lengthscales, ARD=True) K = k.K(X) - Y = _np.random.multivariate_normal(_np.zeros(num_inputs), K, output_dim).T - lik = Gaussian(Y, normalize=True) + Y = _np.random.multivariate_normal(_np.zeros(num_inputs), K, (output_dim,)).T - k = GPy.kern.rbf_inv(input_dim, .5, _np.ones(input_dim) * 2., ARD=True) + GPy.kern.bias(input_dim) + GPy.kern.white(input_dim) - # k = GPy.kern.linear(input_dim) + GPy.kern.bias(input_dim) + GPy.kern.white(input_dim, 0.00001) - # k = GPy.kern.rbf(input_dim, ARD = False) + GPy.kern.white(input_dim, 0.00001) - # k = GPy.kern.rbf(input_dim, .5, _np.ones(input_dim) * 2., ARD=True) + GPy.kern.rbf(input_dim, .3, _np.ones(input_dim) * .2, ARD=True) - # k = GPy.kern.rbf(input_dim, .5, 2., ARD=0) + GPy.kern.rbf(input_dim, .3, .2, ARD=0) - # k = GPy.kern.rbf(input_dim, .5, _np.ones(input_dim) * 2., ARD=True) + GPy.kern.linear(input_dim, _np.ones(input_dim) * .2, ARD=True) + # k = GPy.kern.RBF_inv(input_dim, .5, _np.ones(input_dim) * 2., ARD=True) + GPy.kern.bias(input_dim) + GPy.kern.white(input_dim) + # k = GPy.kern.linear(input_dim)# + GPy.kern.bias(input_dim) + GPy.kern.white(input_dim, 0.00001) + # k = GPy.kern.RBF(input_dim, ARD = False) + GPy.kern.white(input_dim, 0.00001) + # k = GPy.kern.RBF(input_dim, .5, _np.ones(input_dim) * 2., ARD=True) + GPy.kern.RBF(input_dim, .3, _np.ones(input_dim) * .2, ARD=True) + # k = GPy.kern.RBF(input_dim, .5, 2., ARD=0) + GPy.kern.RBF(input_dim, .3, .2, ARD=0) + # k = GPy.kern.RBF(input_dim, .5, _np.ones(input_dim) * 2., ARD=True) + GPy.kern.linear(input_dim, _np.ones(input_dim) * .2, ARD=True) + + p = .3 + + m = GPy.models.BayesianGPLVM(Y, input_dim, kernel=k, num_inducing=num_inducing) + + if nan: + m.inference_method = GPy.inference.latent_function_inference.var_dtc.VarDTCMissingData() + m.Y[_np.random.binomial(1, p, size=(Y.shape)).astype(bool)] = _np.nan + m.parameters_changed() - m = GPy.models.BayesianGPLVM(lik, input_dim, kernel=k, num_inducing=num_inducing) #=========================================================================== # randomly obstruct data with percentage p - p = .8 - Y_obstruct = Y.copy() - Y_obstruct[_np.random.uniform(size=(Y.shape)) < p] = _np.nan #=========================================================================== - m2 = GPy.models.BayesianGPLVMWithMissingData(Y_obstruct, input_dim, kernel=k, num_inducing=num_inducing) - m.lengthscales = lengthscales + # m2 = GPy.models.BayesianGPLVMWithMissingData(Y_obstruct, input_dim, kernel=k, num_inducing=num_inducing) + # m.lengthscales = lengthscales if plot: import matplotlib.pyplot as pb m.plot() pb.title('PCA initialisation') - m2.plot() - pb.title('PCA initialisation') + # m2.plot() + # pb.title('PCA initialisation') if optimize: m.optimize('scg', messages=verbose) - m2.optimize('scg', messages=verbose) + # m2.optimize('scg', messages=verbose) if plot: m.plot() pb.title('After optimisation') - m2.plot() - pb.title('After optimisation') + # m2.plot() + # pb.title('After optimisation') - return m, m2 + return m def gplvm_oil_100(optimize=True, verbose=1, plot=True): import GPy - data = GPy.util.datasets.oil_100() + import pods + data = pods.datasets.oil_100() Y = data['X'] # create simple GP model - kernel = GPy.kern.rbf(6, ARD=True) + GPy.kern.bias(6) + kernel = GPy.kern.RBF(6, ARD=True) + GPy.kern.Bias(6) m = GPy.models.GPLVM(Y, 6, kernel=kernel) m.data_labels = data['Y'].argmax(axis=1) if optimize: m.optimize('scg', messages=verbose) @@ -78,13 +82,15 @@ def gplvm_oil_100(optimize=True, verbose=1, plot=True): def sparse_gplvm_oil(optimize=True, verbose=0, plot=True, N=100, Q=6, num_inducing=15, max_iters=50): import GPy + import pods + _np.random.seed(0) - data = GPy.util.datasets.oil() + data = pods.datasets.oil() Y = data['X'][:N] Y = Y - Y.mean(0) Y /= Y.std(0) # Create the model - kernel = GPy.kern.rbf(Q, ARD=True) + GPy.kern.bias(Q) + kernel = GPy.kern.RBF(Q, ARD=True) + GPy.kern.Bias(Q) m = GPy.models.SparseGPLVM(Y, Q, kernel=kernel, num_inducing=num_inducing) m.data_labels = data['Y'][:N].argmax(axis=1) @@ -94,9 +100,9 @@ def sparse_gplvm_oil(optimize=True, verbose=0, plot=True, N=100, Q=6, num_induci m.kern.plot_ARD() return m -def swiss_roll(optimize=True, verbose=1, plot=True, N=1000, num_inducing=15, Q=4, sigma=.2): +def swiss_roll(optimize=True, verbose=1, plot=True, N=1000, num_inducing=25, Q=4, sigma=.2): import GPy - from GPy.util.datasets import swiss_roll_generated + from pods.datasets import swiss_roll_generated from GPy.models import BayesianGPLVM data = swiss_roll_generated(num_samples=N, sigma=sigma) @@ -134,93 +140,103 @@ def swiss_roll(optimize=True, verbose=1, plot=True, N=1000, num_inducing=15, Q=4 (1 - var))) + .001 Z = _np.random.permutation(X)[:num_inducing] - kernel = GPy.kern.rbf(Q, ARD=True) + GPy.kern.bias(Q, _np.exp(-2)) + GPy.kern.white(Q, _np.exp(-2)) + kernel = GPy.kern.RBF(Q, ARD=True) + GPy.kern.Bias(Q, _np.exp(-2)) + GPy.kern.White(Q, _np.exp(-2)) m = BayesianGPLVM(Y, Q, X=X, X_variance=S, num_inducing=num_inducing, Z=Z, kernel=kernel) m.data_colors = c m.data_t = t - m['noise_variance'] = Y.var() / 100. if optimize: - m.optimize('scg', messages=verbose, max_iters=2e3) + m.optimize('bfgs', messages=verbose, max_iters=2e3) if plot: fig = plt.figure('fitted') ax = fig.add_subplot(111) s = m.input_sensitivity().argsort()[::-1][:2] - ax.scatter(*m.X.T[s], c=c) + ax.scatter(*m.X.mean.T[s], c=c) return m def bgplvm_oil(optimize=True, verbose=1, plot=True, N=200, Q=7, num_inducing=40, max_iters=1000, **k): import GPy - from GPy.likelihoods import Gaussian from matplotlib import pyplot as plt - + import numpy as np _np.random.seed(0) - data = GPy.util.datasets.oil() + try: + import pods + data = pods.datasets.oil() + except ImportError: + data = GPy.util.datasets.oil() - kernel = GPy.kern.rbf_inv(Q, 1., [.1] * Q, ARD=True) + GPy.kern.bias(Q, _np.exp(-2)) + + kernel = GPy.kern.RBF(Q, 1., 1. / _np.random.uniform(0, 1, (Q,)), ARD=True) # + GPy.kern.Bias(Q, _np.exp(-2)) Y = data['X'][:N] - Yn = Gaussian(Y, normalize=True) - m = GPy.models.BayesianGPLVM(Yn, Q, kernel=kernel, num_inducing=num_inducing, **k) + m = GPy.models.BayesianGPLVM(Y, Q, kernel=kernel, num_inducing=num_inducing, **k) m.data_labels = data['Y'][:N].argmax(axis=1) - m['noise'] = Yn.Y.var() / 100. if optimize: - m.optimize('scg', messages=verbose, max_iters=max_iters, gtol=.05) + m.optimize('bfgs', messages=verbose, max_iters=max_iters, gtol=.05) if plot: - y = m.likelihood.Y[0, :] fig, (latent_axes, sense_axes) = plt.subplots(1, 2) - m.plot_latent(ax=latent_axes) - data_show = GPy.util.visualize.vector_show(y) - lvm_visualizer = GPy.util.visualize.lvm_dimselect(m.X[0, :], # @UnusedVariable - m, data_show, latent_axes=latent_axes, sense_axes=sense_axes) + m.plot_latent(ax=latent_axes, labels=m.data_labels) + data_show = GPy.plotting.matplot_dep.visualize.vector_show((m.Y[0, :])) + lvm_visualizer = GPy.plotting.matplot_dep.visualize.lvm_dimselect(m.X.mean.values[0:1, :], # @UnusedVariable + m, data_show, latent_axes=latent_axes, sense_axes=sense_axes, labels=m.data_labels) raw_input('Press enter to finish') plt.close(fig) return m -def _simulate_sincos(D1, D2, D3, N, num_inducing, Q, plot_sim=False): - x = _np.linspace(0, 4 * _np.pi, N)[:, None] - s1 = _np.vectorize(lambda x: _np.sin(x)) - s2 = _np.vectorize(lambda x: _np.cos(x)) - s3 = _np.vectorize(lambda x:-_np.exp(-_np.cos(2 * x))) - sS = _np.vectorize(lambda x: _np.sin(2 * x)) +def ssgplvm_oil(optimize=True, verbose=1, plot=True, N=200, Q=7, num_inducing=40, max_iters=1000, **k): + import GPy + from matplotlib import pyplot as plt + import pods - s1 = s1(x) - s2 = s2(x) - s3 = s3(x) - sS = sS(x) + _np.random.seed(0) + data = pods.datasets.oil() - S1 = _np.hstack([s1, sS]) - S2 = _np.hstack([s2, s3, sS]) - S3 = _np.hstack([s3, sS]) + kernel = GPy.kern.RBF(Q, 1., 1. / _np.random.uniform(0, 1, (Q,)), ARD=True) # + GPy.kern.Bias(Q, _np.exp(-2)) + Y = data['X'][:N] + m = GPy.models.SSGPLVM(Y, Q, kernel=kernel, num_inducing=num_inducing, **k) + m.data_labels = data['Y'][:N].argmax(axis=1) - Y1 = S1.dot(_np.random.randn(S1.shape[1], D1)) - Y2 = S2.dot(_np.random.randn(S2.shape[1], D2)) - Y3 = S3.dot(_np.random.randn(S3.shape[1], D3)) + if optimize: + m.optimize('bfgs', messages=verbose, max_iters=max_iters, gtol=.05) - Y1 += .3 * _np.random.randn(*Y1.shape) - Y2 += .2 * _np.random.randn(*Y2.shape) - Y3 += .25 * _np.random.randn(*Y3.shape) + if plot: + fig, (latent_axes, sense_axes) = plt.subplots(1, 2) + m.plot_latent(ax=latent_axes, labels=m.data_labels) + data_show = GPy.plotting.matplot_dep.visualize.vector_show((m.Y[0, :])) + lvm_visualizer = GPy.plotting.matplot_dep.visualize.lvm_dimselect(m.X.mean.values[0:1, :], # @UnusedVariable + m, data_show, latent_axes=latent_axes, sense_axes=sense_axes, labels=m.data_labels) + raw_input('Press enter to finish') + plt.close(fig) + return m - Y1 -= Y1.mean(0) - Y2 -= Y2.mean(0) - Y3 -= Y3.mean(0) - Y1 /= Y1.std(0) - Y2 /= Y2.std(0) - Y3 /= Y3.std(0) +def _simulate_matern(D1, D2, D3, N, num_inducing, plot_sim=False): + Q_signal = 4 + import GPy + import numpy as np + np.random.seed(3000) + + k = GPy.kern.Matern32(Q_signal, 1., lengthscale=(np.random.uniform(1, 6, Q_signal)), ARD=1) + for i in range(Q_signal): + k += GPy.kern.PeriodicExponential(1, variance=1., active_dims=[i], period=3., lower=-2, upper=6) + t = np.c_[[np.linspace(-1, 5, N) for _ in range(Q_signal)]].T + K = k.K(t) + s2, s1, s3, sS = np.random.multivariate_normal(np.zeros(K.shape[0]), K, size=(4))[:, :, None] + + Y1, Y2, Y3, S1, S2, S3 = _generate_high_dimensional_output(D1, D2, D3, s1, s2, s3, sS) slist = [sS, s1, s2, s3] slist_names = ["sS", "s1", "s2", "s3"] Ylist = [Y1, Y2, Y3] if plot_sim: - import pylab + from matplotlib import pyplot as plt import matplotlib.cm as cm import itertools - fig = pylab.figure("MRD Simulation Data", figsize=(8, 6)) + fig = plt.figure("MRD Simulation Data", figsize=(8, 6)) fig.clf() ax = fig.add_subplot(2, 1, 1) labls = slist_names @@ -229,30 +245,75 @@ def _simulate_sincos(D1, D2, D3, N, num_inducing, Q, plot_sim=False): ax.legend() for i, Y in enumerate(Ylist): ax = fig.add_subplot(2, len(Ylist), len(Ylist) + 1 + i) - ax.imshow(Y, aspect='auto', cmap=cm.gray) # @UndefinedVariable + ax.imshow(Y, aspect='auto', cmap=cm.gray) # @UndefinedVariable ax.set_title("Y{}".format(i + 1)) - pylab.draw() - pylab.tight_layout() + plt.draw() + plt.tight_layout() return slist, [S1, S2, S3], Ylist -# def bgplvm_simulation_matlab_compare(): -# from GPy.util.datasets import simulation_BGPLVM -# from GPy import kern -# from GPy.models import BayesianGPLVM -# -# sim_data = simulation_BGPLVM() -# Y = sim_data['Y'] -# mu = sim_data['mu'] -# num_inducing, [_, Q] = 3, mu.shape -# -# k = kern.linear(Q, ARD=True) + kern.bias(Q, _np.exp(-2)) + kern.white(Q, _np.exp(-2)) -# m = BayesianGPLVM(Y, Q, init="PCA", num_inducing=num_inducing, kernel=k, -# _debug=False) -# m.auto_scale_factor = True -# m['noise'] = Y.var() / 100. -# m['linear_variance'] = .01 -# return m +def _simulate_sincos(D1, D2, D3, N, num_inducing, plot_sim=False): + _np.random.seed(1234) + + x = _np.linspace(0, 4 * _np.pi, N)[:, None] + s1 = _np.vectorize(lambda x: _np.sin(x)) + s2 = _np.vectorize(lambda x: _np.cos(x) ** 2) + s3 = _np.vectorize(lambda x:-_np.exp(-_np.cos(2 * x))) + sS = _np.vectorize(lambda x: _np.cos(x)) + + s1 = s1(x) + s2 = s2(x) + s3 = s3(x) + sS = sS(x) + + s1 -= s1.mean(); s1 /= s1.std(0) + s2 -= s2.mean(); s2 /= s2.std(0) + s3 -= s3.mean(); s3 /= s3.std(0) + sS -= sS.mean(); sS /= sS.std(0) + + Y1, Y2, Y3, S1, S2, S3 = _generate_high_dimensional_output(D1, D2, D3, s1, s2, s3, sS) + + slist = [sS, s1, s2, s3] + slist_names = ["sS", "s1", "s2", "s3"] + Ylist = [Y1, Y2, Y3] + + if plot_sim: + from matplotlib import pyplot as plt + import matplotlib.cm as cm + import itertools + fig = plt.figure("MRD Simulation Data", figsize=(8, 6)) + fig.clf() + ax = fig.add_subplot(2, 1, 1) + labls = slist_names + for S, lab in itertools.izip(slist, labls): + ax.plot(S, label=lab) + ax.legend() + for i, Y in enumerate(Ylist): + ax = fig.add_subplot(2, len(Ylist), len(Ylist) + 1 + i) + ax.imshow(Y, aspect='auto', cmap=cm.gray) # @UndefinedVariable + ax.set_title("Y{}".format(i + 1)) + plt.draw() + plt.tight_layout() + + return slist, [S1, S2, S3], Ylist + +def _generate_high_dimensional_output(D1, D2, D3, s1, s2, s3, sS): + S1 = _np.hstack([s1, sS]) + S2 = _np.hstack([s2, s3, sS]) + S3 = _np.hstack([s3, sS]) + Y1 = S1.dot(_np.random.randn(S1.shape[1], D1)) + Y2 = S2.dot(_np.random.randn(S2.shape[1], D2)) + Y3 = S3.dot(_np.random.randn(S3.shape[1], D3)) + Y1 += .3 * _np.random.randn(*Y1.shape) + Y2 += .2 * _np.random.randn(*Y2.shape) + Y3 += .25 * _np.random.randn(*Y3.shape) + Y1 -= Y1.mean(0) + Y2 -= Y2.mean(0) + Y3 -= Y3.mean(0) + Y1 /= Y1.std(0) + Y2 /= Y2.std(0) + Y3 /= Y3.std(0) + return Y1, Y2, Y3, S1, S2, S3 def bgplvm_simulation(optimize=True, verbose=1, plot=True, plot_sim=False, @@ -261,95 +322,181 @@ def bgplvm_simulation(optimize=True, verbose=1, from GPy import kern from GPy.models import BayesianGPLVM - D1, D2, D3, N, num_inducing, Q = 49, 30, 10, 12, 3, 10 - _, _, Ylist = _simulate_sincos(D1, D2, D3, N, num_inducing, Q, plot_sim) + D1, D2, D3, N, num_inducing, Q = 13, 5, 8, 45, 3, 9 + _, _, Ylist = _simulate_matern(D1, D2, D3, N, num_inducing, plot_sim) Y = Ylist[0] - k = kern.linear(Q, ARD=True) + k = kern.Linear(Q, ARD=True) # + kern.white(Q, _np.exp(-2)) # + kern.bias(Q) + # k = kern.RBF(Q, ARD=True, lengthscale=10.) m = BayesianGPLVM(Y, Q, init="PCA", num_inducing=num_inducing, kernel=k) - m.X_variance = m.X_variance * .7 - m['noise'] = Y.var() / 100. + m.X.variance[:] = _np.random.uniform(0, .01, m.X.shape) + m.likelihood.variance = .1 + + if optimize: + print "Optimizing model:" + m.optimize('bfgs', messages=verbose, max_iters=max_iters, + gtol=.05) + if plot: + m.X.plot("BGPLVM Latent Space 1D") + m.kern.plot_ARD('BGPLVM Simulation ARD Parameters') + return m + +def ssgplvm_simulation(optimize=True, verbose=1, + plot=True, plot_sim=False, + max_iters=2e4, useGPU=False + ): + from GPy import kern + from GPy.models import SSGPLVM + + D1, D2, D3, N, num_inducing, Q = 13, 5, 8, 45, 3, 9 + _, _, Ylist = _simulate_matern(D1, D2, D3, N, num_inducing, plot_sim) + Y = Ylist[0] + k = kern.Linear(Q, ARD=True) # + kern.white(Q, _np.exp(-2)) # + kern.bias(Q) + # k = kern.RBF(Q, ARD=True, lengthscale=10.) + m = SSGPLVM(Y, Q, init="pca", num_inducing=num_inducing, kernel=k) + m.X.variance[:] = _np.random.uniform(0, .01, m.X.shape) + m.likelihood.variance = .1 if optimize: print "Optimizing model:" m.optimize('scg', messages=verbose, max_iters=max_iters, gtol=.05) if plot: - m.plot_X_1d("BGPLVM Latent Space 1D") + m.X.plot("SSGPLVM Latent Space 1D") + m.kern.plot_ARD('SSGPLVM Simulation ARD Parameters') + return m + +def bgplvm_simulation_missing_data(optimize=True, verbose=1, + plot=True, plot_sim=False, + max_iters=2e4, percent_missing=.1, + ): + from GPy import kern + from GPy.models.bayesian_gplvm_minibatch import BayesianGPLVMMiniBatch + + D1, D2, D3, N, num_inducing, Q = 13, 5, 8, 400, 3, 4 + _, _, Ylist = _simulate_matern(D1, D2, D3, N, num_inducing, plot_sim) + Y = Ylist[0] + k = kern.Linear(Q, ARD=True) # + kern.white(Q, _np.exp(-2)) # + kern.bias(Q) + + inan = _np.random.binomial(1, percent_missing, size=Y.shape).astype(bool) # 80% missing data + Ymissing = Y.copy() + Ymissing[inan] = _np.nan + + m = BayesianGPLVMMiniBatch(Ymissing, Q, init="random", num_inducing=num_inducing, + kernel=k, missing_data=True) + + m.Yreal = Y + + if optimize: + print "Optimizing model:" + m.optimize('bfgs', messages=verbose, max_iters=max_iters, + gtol=.05) + if plot: + m.X.plot("BGPLVM Latent Space 1D") m.kern.plot_ARD('BGPLVM Simulation ARD Parameters') return m + def mrd_simulation(optimize=True, verbose=True, plot=True, plot_sim=True, **kw): from GPy import kern from GPy.models import MRD - from GPy.likelihoods import Gaussian D1, D2, D3, N, num_inducing, Q = 60, 20, 36, 60, 6, 5 - _, _, Ylist = _simulate_sincos(D1, D2, D3, N, num_inducing, Q, plot_sim) - likelihood_list = [Gaussian(x, normalize=True) for x in Ylist] + _, _, Ylist = _simulate_matern(D1, D2, D3, N, num_inducing, plot_sim) - k = kern.linear(Q, ARD=True)# + kern.bias(Q, _np.exp(-2)) + kern.white(Q, _np.exp(-2)) - m = MRD(likelihood_list, input_dim=Q, num_inducing=num_inducing, kernels=k, initx="", initz='permute', **kw) - m.ensure_default_constraints() + # Ylist = [Ylist[0]] + k = kern.Linear(Q, ARD=True) + m = MRD(Ylist, input_dim=Q, num_inducing=num_inducing, kernel=k, initx="PCA_concat", initz='permute', **kw) + + m['.*noise'] = [Y.var() / 40. for Y in Ylist] - for i, bgplvm in enumerate(m.bgplvms): - m['{}_noise'.format(i)] = 1 #bgplvm.likelihood.Y.var() / 500. - bgplvm.X_variance = bgplvm.X_variance #* .1 if optimize: print "Optimizing Model:" - m.optimize(messages=verbose, max_iters=8e3, gtol=.1) + m.optimize(messages=verbose, max_iters=8e3) if plot: - m.plot_X_1d("MRD Latent Space 1D") + m.X.plot("MRD Latent Space 1D") + m.plot_scales("MRD Scales") + return m + +def mrd_simulation_missing_data(optimize=True, verbose=True, plot=True, plot_sim=True, **kw): + from GPy import kern + from GPy.models import MRD + + D1, D2, D3, N, num_inducing, Q = 60, 20, 36, 60, 6, 5 + _, _, Ylist = _simulate_matern(D1, D2, D3, N, num_inducing, plot_sim) + + # Ylist = [Ylist[0]] + k = kern.Linear(Q, ARD=True) + inanlist = [] + + for Y in Ylist: + inan = _np.random.binomial(1, .6, size=Y.shape).astype(bool) + inanlist.append(inan) + Y[inan] = _np.nan + + m = MRD(Ylist, input_dim=Q, num_inducing=num_inducing, + kernel=k, inference_method=None, + initx="random", initz='permute', **kw) + + if optimize: + print "Optimizing Model:" + m.optimize('bfgs', messages=verbose, max_iters=8e3, gtol=.1) + if plot: + m.X.plot("MRD Latent Space 1D") m.plot_scales("MRD Scales") return m def brendan_faces(optimize=True, verbose=True, plot=True): import GPy + import pods - data = GPy.util.datasets.brendan_faces() + data = pods.datasets.brendan_faces() Q = 2 Y = data['Y'] Yn = Y - Y.mean() Yn /= Yn.std() - m = GPy.models.GPLVM(Yn, Q) + m = GPy.models.BayesianGPLVM(Yn, Q, num_inducing=20) # optimize - m.constrain('rbf|noise|white', GPy.core.transformations.logexp_clipped()) - if optimize: m.optimize('scg', messages=verbose, max_iters=1000) + if optimize: m.optimize('bfgs', messages=verbose, max_iters=1000) if plot: ax = m.plot_latent(which_indices=(0, 1)) - y = m.likelihood.Y[0, :] - data_show = GPy.util.visualize.image_show(y[None, :], dimensions=(20, 28), transpose=True, order='F', invert=False, scale=False) - GPy.util.visualize.lvm(m.X[0, :].copy(), m, data_show, ax) + y = m.Y[0, :] + data_show = GPy.plotting.matplot_dep.visualize.image_show(y[None, :], dimensions=(20, 28), transpose=True, order='F', invert=False, scale=False) + lvm = GPy.plotting.matplot_dep.visualize.lvm(m.X.mean[0, :].copy(), m, data_show, ax) raw_input('Press enter to finish') return m def olivetti_faces(optimize=True, verbose=True, plot=True): import GPy + import pods - data = GPy.util.datasets.olivetti_faces() + data = pods.datasets.olivetti_faces() Q = 2 Y = data['Y'] Yn = Y - Y.mean() Yn /= Yn.std() - m = GPy.models.GPLVM(Yn, Q) - if optimize: m.optimize('scg', messages=verbose, max_iters=1000) + m = GPy.models.BayesianGPLVM(Yn, Q, num_inducing=20) + + if optimize: m.optimize('bfgs', messages=verbose, max_iters=1000) if plot: ax = m.plot_latent(which_indices=(0, 1)) - y = m.likelihood.Y[0, :] - data_show = GPy.util.visualize.image_show(y[None, :], dimensions=(112, 92), transpose=False, invert=False, scale=False) - GPy.util.visualize.lvm(m.X[0, :].copy(), m, data_show, ax) + y = m.Y[0, :] + data_show = GPy.plotting.matplot_dep.visualize.image_show(y[None, :], dimensions=(112, 92), transpose=False, invert=False, scale=False) + lvm = GPy.plotting.matplot_dep.visualize.lvm(m.X.mean[0, :].copy(), m, data_show, ax) raw_input('Press enter to finish') return m def stick_play(range=None, frame_rate=15, optimize=False, verbose=True, plot=True): import GPy - data = GPy.util.datasets.osu_run1() + import pods + + data = pods.datasets.osu_run1() # optimize if range == None: Y = data['Y'].copy() @@ -357,43 +504,46 @@ def stick_play(range=None, frame_rate=15, optimize=False, verbose=True, plot=Tru Y = data['Y'][range[0]:range[1], :].copy() if plot: y = Y[0, :] - data_show = GPy.util.visualize.stick_show(y[None, :], connect=data['connect']) - GPy.util.visualize.data_play(Y, data_show, frame_rate) + data_show = GPy.plotting.matplot_dep.visualize.stick_show(y[None, :], connect=data['connect']) + GPy.plotting.matplot_dep.visualize.data_play(Y, data_show, frame_rate) return Y def stick(kernel=None, optimize=True, verbose=True, plot=True): from matplotlib import pyplot as plt import GPy + import pods - data = GPy.util.datasets.osu_run1() + data = pods.datasets.osu_run1() # optimize m = GPy.models.GPLVM(data['Y'], 2, kernel=kernel) - if optimize: m.optimize(messages=verbose, max_f_eval=10000) - if plot and GPy.util.visualize.visual_available: + if optimize: m.optimize('bfgs', messages=verbose, max_f_eval=10000) + if plot: plt.clf ax = m.plot_latent() - y = m.likelihood.Y[0, :] - data_show = GPy.util.visualize.stick_show(y[None, :], connect=data['connect']) - GPy.util.visualize.lvm(m.X[0, :].copy(), m, data_show, ax) + y = m.Y[0, :] + data_show = GPy.plotting.matplot_dep.visualize.stick_show(y[None, :], connect=data['connect']) + lvm_visualizer = GPy.plotting.matplot_dep.visualize.lvm(m.X[:1, :].copy(), m, data_show, latent_axes=ax) raw_input('Press enter to finish') - + lvm_visualizer.close() + data_show.close() return m def bcgplvm_linear_stick(kernel=None, optimize=True, verbose=True, plot=True): from matplotlib import pyplot as plt import GPy + import pods - data = GPy.util.datasets.osu_run1() + data = pods.datasets.osu_run1() # optimize mapping = GPy.mappings.Linear(data['Y'].shape[1], 2) m = GPy.models.BCGPLVM(data['Y'], 2, kernel=kernel, mapping=mapping) if optimize: m.optimize(messages=verbose, max_f_eval=10000) - if plot and GPy.util.visualize.visual_available: + if plot and GPy.plotting.matplot_dep.visualize.visual_available: plt.clf ax = m.plot_latent() y = m.likelihood.Y[0, :] - data_show = GPy.util.visualize.stick_show(y[None, :], connect=data['connect']) - GPy.util.visualize.lvm(m.X[0, :].copy(), m, data_show, ax) + data_show = GPy.plotting.matplot_dep.visualize.stick_show(y[None, :], connect=data['connect']) + GPy.plotting.matplot_dep.visualize.lvm(m.X[0, :].copy(), m, data_show, ax) raw_input('Press enter to finish') return m @@ -401,32 +551,33 @@ def bcgplvm_linear_stick(kernel=None, optimize=True, verbose=True, plot=True): def bcgplvm_stick(kernel=None, optimize=True, verbose=True, plot=True): from matplotlib import pyplot as plt import GPy + import pods - data = GPy.util.datasets.osu_run1() + data = pods.datasets.osu_run1() # optimize - back_kernel=GPy.kern.rbf(data['Y'].shape[1], lengthscale=5.) + back_kernel = GPy.kern.RBF(data['Y'].shape[1], lengthscale=5.) mapping = GPy.mappings.Kernel(X=data['Y'], output_dim=2, kernel=back_kernel) m = GPy.models.BCGPLVM(data['Y'], 2, kernel=kernel, mapping=mapping) if optimize: m.optimize(messages=verbose, max_f_eval=10000) - if plot and GPy.util.visualize.visual_available: + if plot and GPy.plotting.matplot_dep.visualize.visual_available: plt.clf ax = m.plot_latent() y = m.likelihood.Y[0, :] - data_show = GPy.util.visualize.stick_show(y[None, :], connect=data['connect']) - GPy.util.visualize.lvm(m.X[0, :].copy(), m, data_show, ax) - raw_input('Press enter to finish') + data_show = GPy.plotting.matplot_dep.visualize.stick_show(y[None, :], connect=data['connect']) + GPy.plotting.matplot_dep.visualize.lvm(m.X[0, :].copy(), m, data_show, ax) + # raw_input('Press enter to finish') return m def robot_wireless(optimize=True, verbose=True, plot=True): from matplotlib import pyplot as plt import GPy + import pods - data = GPy.util.datasets.robot_wireless() + data = pods.datasets.robot_wireless() # optimize - m = GPy.models.GPLVM(data['Y'], 2) + m = GPy.models.BayesianGPLVM(data['Y'], 4, num_inducing=25) if optimize: m.optimize(messages=verbose, max_f_eval=10000) - m._set_params(m._get_params()) if plot: m.plot_latent() @@ -435,23 +586,33 @@ def robot_wireless(optimize=True, verbose=True, plot=True): def stick_bgplvm(model=None, optimize=True, verbose=True, plot=True): from GPy.models import BayesianGPLVM from matplotlib import pyplot as plt + import numpy as np import GPy + import pods - data = GPy.util.datasets.osu_run1() + data = pods.datasets.osu_run1() Q = 6 - kernel = GPy.kern.rbf(Q, ARD=True) + GPy.kern.bias(Q, _np.exp(-2)) + GPy.kern.white(Q, _np.exp(-2)) + kernel = GPy.kern.RBF(Q, lengthscale=np.repeat(.5, Q), ARD=True) m = BayesianGPLVM(data['Y'], Q, init="PCA", num_inducing=20, kernel=kernel) + + m.data = data + m.likelihood.variance = 0.001 + # optimize - m.ensure_default_constraints() - if optimize: m.optimize('scg', messages=verbose, max_iters=200, xtol=1e-300, ftol=1e-300) - m._set_params(m._get_params()) + try: + if optimize: m.optimize('bfgs', messages=verbose, max_iters=5e3, bfgs_factor=10) + except KeyboardInterrupt: + print "Keyboard interrupt, continuing to plot and return" + if plot: - plt.clf, (latent_axes, sense_axes) = plt.subplots(1, 2) + fig, (latent_axes, sense_axes) = plt.subplots(1, 2) plt.sca(latent_axes) - m.plot_latent() - y = m.likelihood.Y[0, :].copy() - data_show = GPy.util.visualize.stick_show(y[None, :], connect=data['connect']) - GPy.util.visualize.lvm_dimselect(m.X[0, :].copy(), m, data_show, latent_axes=latent_axes, sense_axes=sense_axes) + m.plot_latent(ax=latent_axes) + y = m.Y[:1, :].copy() + data_show = GPy.plotting.matplot_dep.visualize.stick_show(y, connect=data['connect']) + dim_select = GPy.plotting.matplot_dep.visualize.lvm_dimselect(m.X.mean[:1, :].copy(), m, data_show, latent_axes=latent_axes, sense_axes=sense_axes) + fig.canvas.draw() + fig.canvas.show() raw_input('Press enter to finish') return m @@ -459,20 +620,50 @@ def stick_bgplvm(model=None, optimize=True, verbose=True, plot=True): def cmu_mocap(subject='35', motion=['01'], in_place=True, optimize=True, verbose=True, plot=True): import GPy + import pods - data = GPy.util.datasets.cmu_mocap(subject, motion) + data = pods.datasets.cmu_mocap(subject, motion) if in_place: # Make figure move in place. data['Y'][:, 0:3] = 0.0 - m = GPy.models.GPLVM(data['Y'], 2, normalize_Y=True) + Y = data['Y'] + Y_mean = Y.mean(0) + Y_std = Y.std(0) + m = GPy.models.GPLVM((Y - Y_mean) / Y_std, 2) if optimize: m.optimize(messages=verbose, max_f_eval=10000) if plot: ax = m.plot_latent() - y = m.likelihood.Y[0, :] - data_show = GPy.util.visualize.skeleton_show(y[None, :], data['skel']) - lvm_visualizer = GPy.util.visualize.lvm(m.X[0, :].copy(), m, data_show, ax) + y = m.Y[0, :] + data_show = GPy.plotting.matplot_dep.visualize.skeleton_show(y[None, :], data['skel']) + lvm_visualizer = GPy.plotting.matplot_dep.visualize.lvm(m.X[0].copy(), m, data_show, latent_axes=ax) raw_input('Press enter to finish') lvm_visualizer.close() + data_show.close() return m + +def ssgplvm_simulation_linear(): + import numpy as np + import GPy + N, D, Q = 1000, 20, 5 + pi = 0.2 + + def sample_X(Q, pi): + x = np.empty(Q) + dies = np.random.rand(Q) + for q in xrange(Q): + if dies[q] < pi: + x[q] = np.random.randn() + else: + x[q] = 0. + return x + + Y = np.empty((N, D)) + X = np.empty((N, Q)) + # Generate data from random sampled weight matrices + for n in xrange(N): + X[n] = sample_X(Q, pi) + w = np.random.randn(D, Q) + Y[n] = np.dot(w, X[n]) + diff --git a/GPy/examples/non_gaussian.py b/GPy/examples/non_gaussian.py index bda80137..ddac8813 100644 --- a/GPy/examples/non_gaussian.py +++ b/GPy/examples/non_gaussian.py @@ -1,7 +1,13 @@ +# Copyright (c) 2014, Alan Saul +# Licensed under the BSD 3-clause license (see LICENSE.txt) + import GPy import numpy as np -import matplotlib.pyplot as plt from GPy.util import datasets +try: + import matplotlib.pyplot as plt +except: + pass def student_t_approx(optimize=True, plot=True): """ @@ -30,47 +36,53 @@ def student_t_approx(optimize=True, plot=True): #Yc = Yc/Yc.max() #Add student t random noise to datapoints - deg_free = 5 + deg_free = 1 print "Real noise: ", real_std initial_var_guess = 0.5 edited_real_sd = initial_var_guess # Kernel object - kernel1 = GPy.kern.rbf(X.shape[1]) + GPy.kern.white(X.shape[1]) - kernel2 = kernel1.copy() - kernel3 = kernel1.copy() - kernel4 = kernel1.copy() + kernel1 = GPy.kern.RBF(X.shape[1]) + GPy.kern.White(X.shape[1]) + kernel2 = GPy.kern.RBF(X.shape[1]) + GPy.kern.White(X.shape[1]) + kernel3 = GPy.kern.RBF(X.shape[1]) + GPy.kern.White(X.shape[1]) + kernel4 = GPy.kern.RBF(X.shape[1]) + GPy.kern.White(X.shape[1]) #Gaussian GP model on clean data m1 = GPy.models.GPRegression(X, Y.copy(), kernel=kernel1) # optimize - m1.ensure_default_constraints() - m1.constrain_fixed('white', 1e-5) + m1['.*white'].constrain_fixed(1e-5) m1.randomize() #Gaussian GP model on corrupt data m2 = GPy.models.GPRegression(X, Yc.copy(), kernel=kernel2) - m2.ensure_default_constraints() - m2.constrain_fixed('white', 1e-5) + m2['.*white'].constrain_fixed(1e-5) m2.randomize() #Student t GP model on clean data - t_distribution = GPy.likelihoods.noise_model_constructors.student_t(deg_free=deg_free, sigma2=edited_real_sd) - stu_t_likelihood = GPy.likelihoods.Laplace(Y.copy(), t_distribution) - m3 = GPy.models.GPRegression(X, Y.copy(), kernel3, likelihood=stu_t_likelihood) - m3.ensure_default_constraints() - m3.constrain_bounded('t_noise', 1e-6, 10.) - m3.constrain_fixed('white', 1e-5) + t_distribution = GPy.likelihoods.StudentT(deg_free=deg_free, sigma2=edited_real_sd) + laplace_inf = GPy.inference.latent_function_inference.Laplace() + m3 = GPy.core.GP(X, Y.copy(), kernel3, likelihood=t_distribution, inference_method=laplace_inf) + m3['.*t_scale2'].constrain_bounded(1e-6, 10.) + m3['.*white'].constrain_fixed(1e-5) m3.randomize() #Student t GP model on corrupt data - t_distribution = GPy.likelihoods.noise_model_constructors.student_t(deg_free=deg_free, sigma2=edited_real_sd) - corrupt_stu_t_likelihood = GPy.likelihoods.Laplace(Yc.copy(), t_distribution) - m4 = GPy.models.GPRegression(X, Yc.copy(), kernel4, likelihood=corrupt_stu_t_likelihood) - m4.ensure_default_constraints() - m4.constrain_bounded('t_noise', 1e-6, 10.) - m4.constrain_fixed('white', 1e-5) + t_distribution = GPy.likelihoods.StudentT(deg_free=deg_free, sigma2=edited_real_sd) + laplace_inf = GPy.inference.latent_function_inference.Laplace() + m4 = GPy.core.GP(X, Yc.copy(), kernel4, likelihood=t_distribution, inference_method=laplace_inf) + m4['.*t_scale2'].constrain_bounded(1e-6, 10.) + m4['.*white'].constrain_fixed(1e-5) m4.randomize() + print m4 + debug=True + if debug: + m4.optimize(messages=1) + import pylab as pb + pb.plot(m4.X, m4.inference_method.f_hat) + pb.plot(m4.X, m4.Y, 'rx') + m4.plot() + print m4 + return m4 if optimize: optimizer='scg' @@ -115,6 +127,7 @@ def student_t_approx(optimize=True, plot=True): return m1, m2, m3, m4 def boston_example(optimize=True, plot=True): + raise NotImplementedError("Needs updating") import sklearn from sklearn.cross_validation import KFold optimizer='bfgs' @@ -143,8 +156,8 @@ def boston_example(optimize=True, plot=True): noise = 1e-1 #np.exp(-2) rbf_len = 0.5 data_axis_plot = 4 - kernelstu = GPy.kern.rbf(X.shape[1]) + GPy.kern.white(X.shape[1]) + GPy.kern.bias(X.shape[1]) - kernelgp = GPy.kern.rbf(X.shape[1]) + GPy.kern.white(X.shape[1]) + GPy.kern.bias(X.shape[1]) + kernelstu = GPy.kern.RBF(X.shape[1]) + GPy.kern.white(X.shape[1]) + GPy.kern.bias(X.shape[1]) + kernelgp = GPy.kern.RBF(X.shape[1]) + GPy.kern.white(X.shape[1]) + GPy.kern.bias(X.shape[1]) #Baseline score_folds[0, n] = rmse(Y_test, np.mean(Y_train)) @@ -152,10 +165,9 @@ def boston_example(optimize=True, plot=True): #Gaussian GP print "Gauss GP" mgp = GPy.models.GPRegression(X_train.copy(), Y_train.copy(), kernel=kernelgp.copy()) - mgp.ensure_default_constraints() - mgp.constrain_fixed('white', 1e-5) - mgp['rbf_len'] = rbf_len - mgp['noise'] = noise + mgp.constrain_fixed('.*white', 1e-5) + mgp['.*len'] = rbf_len + mgp['.*noise'] = noise print mgp if optimize: mgp.optimize(optimizer=optimizer, messages=messages) @@ -170,9 +182,8 @@ def boston_example(optimize=True, plot=True): g_distribution = GPy.likelihoods.noise_model_constructors.gaussian(variance=noise, N=N, D=D) g_likelihood = GPy.likelihoods.Laplace(Y_train.copy(), g_distribution) mg = GPy.models.GPRegression(X_train.copy(), Y_train.copy(), kernel=kernelstu.copy(), likelihood=g_likelihood) - mg.ensure_default_constraints() mg.constrain_positive('noise_variance') - mg.constrain_fixed('white', 1e-5) + mg.constrain_fixed('.*white', 1e-5) mg['rbf_len'] = rbf_len mg['noise'] = noise print mg @@ -190,11 +201,10 @@ def boston_example(optimize=True, plot=True): t_distribution = GPy.likelihoods.noise_model_constructors.student_t(deg_free=df, sigma2=noise) stu_t_likelihood = GPy.likelihoods.Laplace(Y_train.copy(), t_distribution) mstu_t = GPy.models.GPRegression(X_train.copy(), Y_train.copy(), kernel=kernelstu.copy(), likelihood=stu_t_likelihood) - mstu_t.ensure_default_constraints() - mstu_t.constrain_fixed('white', 1e-5) - mstu_t.constrain_bounded('t_noise', 0.0001, 1000) + mstu_t.constrain_fixed('.*white', 1e-5) + mstu_t.constrain_bounded('.*t_scale2', 0.0001, 1000) mstu_t['rbf_len'] = rbf_len - mstu_t['t_noise'] = noise + mstu_t['.*t_scale2'] = noise print mstu_t if optimize: mstu_t.optimize(optimizer=optimizer, messages=messages) diff --git a/GPy/examples/regression.py b/GPy/examples/regression.py index 65a50f0e..37a18f63 100644 --- a/GPy/examples/regression.py +++ b/GPy/examples/regression.py @@ -1,22 +1,29 @@ -# Copyright (c) 2012, GPy authors (see AUTHORS.txt). +# Copyright (c) 2012-2014, GPy authors (see AUTHORS.txt). # Licensed under the BSD 3-clause license (see LICENSE.txt) """ Gaussian Processes regression examples """ -import pylab as pb +try: + import pylab as pb +except: + pass import numpy as np import GPy def olympic_marathon_men(optimize=True, plot=True): """Run a standard Gaussian process regression on the Olympic marathon data.""" - data = GPy.util.datasets.olympic_marathon_men() + try:import pods + except ImportError: + print 'pods unavailable, see https://github.com/sods/ods for example datasets' + return + data = pods.datasets.olympic_marathon_men() # create simple GP Model m = GPy.models.GPRegression(data['X'], data['Y']) # set the lengthscale to be something sensible (defaults to 1) - m['rbf_lengthscale'] = 10 + m.kern.lengthscale = 10. if optimize: m.optimize('bfgs', max_iters=200) @@ -25,79 +32,51 @@ def olympic_marathon_men(optimize=True, plot=True): return m -def coregionalization_toy2(optimize=True, plot=True): +def coregionalization_toy(optimize=True, plot=True): """ A simple demonstration of coregionalization on two sinusoidal functions. """ #build a design matrix with a column of integers indicating the output X1 = np.random.rand(50, 1) * 8 X2 = np.random.rand(30, 1) * 5 - index = np.vstack((np.zeros_like(X1), np.ones_like(X2))) - X = np.hstack((np.vstack((X1, X2)), index)) #build a suitable set of observed variables Y1 = np.sin(X1) + np.random.randn(*X1.shape) * 0.05 Y2 = np.sin(X2) + np.random.randn(*X2.shape) * 0.05 + 2. - Y = np.vstack((Y1, Y2)) - #build the kernel - k1 = GPy.kern.rbf(1) + GPy.kern.bias(1) - k2 = GPy.kern.coregionalize(2,1) - k = k1**k2 - m = GPy.models.GPRegression(X, Y, kernel=k) - m.constrain_fixed('.*rbf_var', 1.) + m = GPy.models.GPCoregionalizedRegression(X_list=[X1,X2], Y_list=[Y1,Y2]) if optimize: m.optimize('bfgs', max_iters=100) if plot: - m.plot(fixed_inputs=[(1,0)]) - m.plot(fixed_inputs=[(1,1)], ax=pb.gca()) - + slices = GPy.util.multioutput.get_slices([X1,X2]) + m.plot(fixed_inputs=[(1,0)],which_data_rows=slices[0],Y_metadata={'output_index':0}) + m.plot(fixed_inputs=[(1,1)],which_data_rows=slices[1],Y_metadata={'output_index':1},ax=pb.gca()) return m -#FIXME: Needs recovering once likelihoods are consolidated -#def coregionalization_toy(optimize=True, plot=True): -# """ -# A simple demonstration of coregionalization on two sinusoidal functions. -# """ -# X1 = np.random.rand(50, 1) * 8 -# X2 = np.random.rand(30, 1) * 5 -# X = np.vstack((X1, X2)) -# Y1 = np.sin(X1) + np.random.randn(*X1.shape) * 0.05 -# Y2 = -np.sin(X2) + np.random.randn(*X2.shape) * 0.05 -# Y = np.vstack((Y1, Y2)) -# -# k1 = GPy.kern.rbf(1) -# m = GPy.models.GPMultioutputRegression(X_list=[X1,X2],Y_list=[Y1,Y2],kernel_list=[k1]) -# m.constrain_fixed('.*rbf_var', 1.) -# m.optimize(max_iters=100) -# -# fig, axes = pb.subplots(2,1) -# m.plot(fixed_inputs=[(1,0)],ax=axes[0]) -# m.plot(fixed_inputs=[(1,1)],ax=axes[1]) -# axes[0].set_title('Output 0') -# axes[1].set_title('Output 1') -# return m - def coregionalization_sparse(optimize=True, plot=True): """ A simple demonstration of coregionalization on two sinusoidal functions using sparse approximations. """ - #fetch the data from the non sparse examples - m = coregionalization_toy2(optimize=False, plot=False) - X, Y = m.X, m.likelihood.Y + #build a design matrix with a column of integers indicating the output + X1 = np.random.rand(50, 1) * 8 + X2 = np.random.rand(30, 1) * 5 - #construct a model - m = GPy.models.SparseGPRegression(X,Y) - m.constrain_fixed('iip_\d+_1') # don't optimize the inducing input indexes + #build a suitable set of observed variables + Y1 = np.sin(X1) + np.random.randn(*X1.shape) * 0.05 + Y2 = np.sin(X2) + np.random.randn(*X2.shape) * 0.05 + 2. + + m = GPy.models.SparseGPCoregionalizedRegression(X_list=[X1,X2], Y_list=[Y1,Y2]) if optimize: - m.optimize('bfgs', max_iters=100, messages=1) + m.optimize('bfgs', max_iters=100) if plot: - m.plot(fixed_inputs=[(1,0)]) - m.plot(fixed_inputs=[(1,1)], ax=pb.gca()) + slices = GPy.util.multioutput.get_slices([X1,X2]) + m.plot(fixed_inputs=[(1,0)],which_data_rows=slices[0],Y_metadata={'output_index':0}) + m.plot(fixed_inputs=[(1,1)],which_data_rows=slices[1],Y_metadata={'output_index':1},ax=pb.gca()) + pb.ylim(-3,) return m @@ -107,7 +86,11 @@ def epomeo_gpx(max_iters=200, optimize=True, plot=True): from the Mount Epomeo runs. Requires gpxpy to be installed on your system to load in the data. """ - data = GPy.util.datasets.epomeo_gpx() + try:import pods + except ImportError: + print 'pods unavailable, see https://github.com/sods/ods for example datasets' + return + data = pods.datasets.epomeo_gpx() num_data_list = [] for Xpart in data['X']: num_data_list.append(Xpart.shape[0]) @@ -127,14 +110,14 @@ def epomeo_gpx(max_iters=200, optimize=True, plot=True): Z = np.hstack((np.linspace(t[:,0].min(), t[:, 0].max(), num_inducing)[:, None], np.random.randint(0, 4, num_inducing)[:, None])) - k1 = GPy.kern.rbf(1) - k2 = GPy.kern.coregionalize(output_dim=5, rank=5) + k1 = GPy.kern.RBF(1) + k2 = GPy.kern.Coregionalize(output_dim=5, rank=5) k = k1**k2 m = GPy.models.SparseGPRegression(t, Y, kernel=k, Z=Z, normalize_Y=True) - m.constrain_fixed('.*rbf_var', 1.) - m.constrain_fixed('iip') - m.constrain_bounded('noise_variance', 1e-3, 1e-1) + m.constrain_fixed('.*variance', 1.) + m.inducing_inputs.constrain_fixed() + m.Gaussian_noise.variance.constrain_bounded(1e-3, 1e-1) m.optimize(max_iters=max_iters,messages=True) return m @@ -150,13 +133,17 @@ def multiple_optima(gene_number=937, resolution=80, model_restarts=10, seed=1000 length_scales = np.linspace(0.1, 60., resolution) log_SNRs = np.linspace(-3., 4., resolution) - data = GPy.util.datasets.della_gatta_TRP63_gene_expression(data_set='della_gatta',gene_number=gene_number) + try:import pods + except ImportError: + print 'pods unavailable, see https://github.com/sods/ods for example datasets' + return + data = pods.datasets.della_gatta_TRP63_gene_expression(data_set='della_gatta',gene_number=gene_number) # data['Y'] = data['Y'][0::2, :] # data['X'] = data['X'][0::2, :] data['Y'] = data['Y'] - np.mean(data['Y']) - lls = GPy.examples.regression._contour_data(data, length_scales, log_SNRs, GPy.kern.rbf) + lls = GPy.examples.regression._contour_data(data, length_scales, log_SNRs, GPy.kern.RBF) if plot: pb.contour(length_scales, log_SNRs, np.exp(lls), 20, cmap=pb.cm.jet) ax = pb.gca() @@ -172,20 +159,20 @@ def multiple_optima(gene_number=937, resolution=80, model_restarts=10, seed=1000 optim_point_y = np.empty(2) np.random.seed(seed=seed) for i in range(0, model_restarts): - # kern = GPy.kern.rbf(1, variance=np.random.exponential(1.), lengthscale=np.random.exponential(50.)) - kern = GPy.kern.rbf(1, variance=np.random.uniform(1e-3, 1), lengthscale=np.random.uniform(5, 50)) + # kern = GPy.kern.RBF(1, variance=np.random.exponential(1.), lengthscale=np.random.exponential(50.)) + kern = GPy.kern.RBF(1, variance=np.random.uniform(1e-3, 1), lengthscale=np.random.uniform(5, 50)) m = GPy.models.GPRegression(data['X'], data['Y'], kernel=kern) - m['noise_variance'] = np.random.uniform(1e-3, 1) - optim_point_x[0] = m['rbf_lengthscale'] - optim_point_y[0] = np.log10(m['rbf_variance']) - np.log10(m['noise_variance']); + m.likelihood.variance = np.random.uniform(1e-3, 1) + optim_point_x[0] = m.rbf.lengthscale + optim_point_y[0] = np.log10(m.rbf.variance) - np.log10(m.likelihood.variance); # optimize if optimize: m.optimize('scg', xtol=1e-6, ftol=1e-6, max_iters=max_iters) - optim_point_x[1] = m['rbf_lengthscale'] - optim_point_y[1] = np.log10(m['rbf_variance']) - np.log10(m['noise_variance']); + optim_point_x[1] = m.rbf.lengthscale + optim_point_y[1] = np.log10(m.rbf.variance) - np.log10(m.likelihood.variance); if plot: pb.arrow(optim_point_x[0], optim_point_y[0], optim_point_x[1] - optim_point_x[0], optim_point_y[1] - optim_point_y[0], label=str(i), head_length=1, head_width=0.5, fc='k', ec='k') @@ -196,7 +183,7 @@ def multiple_optima(gene_number=937, resolution=80, model_restarts=10, seed=1000 ax.set_ylim(ylim) return m # (models, lls) -def _contour_data(data, length_scales, log_SNRs, kernel_call=GPy.kern.rbf): +def _contour_data(data, length_scales, log_SNRs, kernel_call=GPy.kern.RBF): """ Evaluate the GP objective function for a given data set for a range of signal to noise ratios and a range of lengthscales. @@ -216,7 +203,7 @@ def _contour_data(data, length_scales, log_SNRs, kernel_call=GPy.kern.rbf): noise_var = total_var / (1. + SNR) signal_var = total_var - noise_var model.kern['.*variance'] = signal_var - model['noise_variance'] = noise_var + model.likelihood.variance = noise_var length_scale_lls = [] for length_scale in length_scales: @@ -230,13 +217,17 @@ def _contour_data(data, length_scales, log_SNRs, kernel_call=GPy.kern.rbf): def olympic_100m_men(optimize=True, plot=True): """Run a standard Gaussian process regression on the Rogers and Girolami olympics data.""" - data = GPy.util.datasets.olympic_100m_men() + try:import pods + except ImportError: + print 'pods unavailable, see https://github.com/sods/ods for example datasets' + return + data = pods.datasets.olympic_100m_men() # create simple GP Model m = GPy.models.GPRegression(data['X'], data['Y']) # set the lengthscale to be something sensible (defaults to 1) - m['rbf_lengthscale'] = 10 + m.rbf.lengthscale = 10 if optimize: m.optimize('bfgs', max_iters=200) @@ -247,7 +238,11 @@ def olympic_100m_men(optimize=True, plot=True): def toy_rbf_1d(optimize=True, plot=True): """Run a simple demonstration of a standard Gaussian process fitting it to data sampled from an RBF covariance.""" - data = GPy.util.datasets.toy_rbf_1d() + try:import pods + except ImportError: + print 'pods unavailable, see https://github.com/sods/ods for example datasets' + return + data = pods.datasets.toy_rbf_1d() # create simple GP Model m = GPy.models.GPRegression(data['X'], data['Y']) @@ -261,7 +256,11 @@ def toy_rbf_1d(optimize=True, plot=True): def toy_rbf_1d_50(optimize=True, plot=True): """Run a simple demonstration of a standard Gaussian process fitting it to data sampled from an RBF covariance.""" - data = GPy.util.datasets.toy_rbf_1d_50() + try:import pods + except ImportError: + print 'pods unavailable, see https://github.com/sods/ods for example datasets' + return + data = pods.datasets.toy_rbf_1d_50() # create simple GP Model m = GPy.models.GPRegression(data['X'], data['Y']) @@ -278,14 +277,15 @@ def toy_poisson_rbf_1d_laplace(optimize=True, plot=True): optimizer='scg' x_len = 30 X = np.linspace(0, 10, x_len)[:, None] - f_true = np.random.multivariate_normal(np.zeros(x_len), GPy.kern.rbf(1).K(X)) + f_true = np.random.multivariate_normal(np.zeros(x_len), GPy.kern.RBF(1).K(X)) Y = np.array([np.random.poisson(np.exp(f)) for f in f_true])[:,None] - noise_model = GPy.likelihoods.poisson() - likelihood = GPy.likelihoods.Laplace(Y,noise_model) + kern = GPy.kern.RBF(1) + poisson_lik = GPy.likelihoods.Poisson() + laplace_inf = GPy.inference.latent_function_inference.Laplace() # create simple GP Model - m = GPy.models.GPRegression(X, Y, likelihood=likelihood) + m = GPy.core.GP(X, Y, kernel=kern, likelihood=poisson_lik, inference_method=laplace_inf) if optimize: m.optimize(optimizer) @@ -316,23 +316,22 @@ def toy_ARD(max_iters=1000, kernel_type='linear', num_samples=300, D=4, optimize Y /= Y.std() if kernel_type == 'linear': - kernel = GPy.kern.linear(X.shape[1], ARD=1) + kernel = GPy.kern.Linear(X.shape[1], ARD=1) elif kernel_type == 'rbf_inv': - kernel = GPy.kern.rbf_inv(X.shape[1], ARD=1) + kernel = GPy.kern.RBF_inv(X.shape[1], ARD=1) else: - kernel = GPy.kern.rbf(X.shape[1], ARD=1) - kernel += GPy.kern.white(X.shape[1]) + GPy.kern.bias(X.shape[1]) + kernel = GPy.kern.RBF(X.shape[1], ARD=1) + kernel += GPy.kern.White(X.shape[1]) + GPy.kern.Bias(X.shape[1]) m = GPy.models.GPRegression(X, Y, kernel) # len_prior = GPy.priors.inverse_gamma(1,18) # 1, 25 # m.set_prior('.*lengthscale',len_prior) if optimize: - m.optimize(optimizer='scg', max_iters=max_iters, messages=1) + m.optimize(optimizer='scg', max_iters=max_iters) if plot: m.kern.plot_ARD() - print m return m def toy_ARD_sparse(max_iters=1000, kernel_type='linear', num_samples=300, D=4, optimize=True, plot=True): @@ -355,36 +354,39 @@ def toy_ARD_sparse(max_iters=1000, kernel_type='linear', num_samples=300, D=4, o Y /= Y.std() if kernel_type == 'linear': - kernel = GPy.kern.linear(X.shape[1], ARD=1) + kernel = GPy.kern.Linear(X.shape[1], ARD=1) elif kernel_type == 'rbf_inv': - kernel = GPy.kern.rbf_inv(X.shape[1], ARD=1) + kernel = GPy.kern.RBF_inv(X.shape[1], ARD=1) else: - kernel = GPy.kern.rbf(X.shape[1], ARD=1) - kernel += GPy.kern.bias(X.shape[1]) + kernel = GPy.kern.RBF(X.shape[1], ARD=1) + #kernel += GPy.kern.Bias(X.shape[1]) X_variance = np.ones(X.shape) * 0.5 m = GPy.models.SparseGPRegression(X, Y, kernel, X_variance=X_variance) # len_prior = GPy.priors.inverse_gamma(1,18) # 1, 25 # m.set_prior('.*lengthscale',len_prior) if optimize: - m.optimize(optimizer='scg', max_iters=max_iters, messages=1) + m.optimize(optimizer='scg', max_iters=max_iters) if plot: m.kern.plot_ARD() - print m return m def robot_wireless(max_iters=100, kernel=None, optimize=True, plot=True): """Predict the location of a robot given wirelss signal strength readings.""" - data = GPy.util.datasets.robot_wireless() + try:import pods + except ImportError: + print 'pods unavailable, see https://github.com/sods/ods for example datasets' + return + data = pods.datasets.robot_wireless() # create simple GP Model m = GPy.models.GPRegression(data['Y'], data['X'], kernel=kernel) # optimize if optimize: - m.optimize(messages=True, max_iters=max_iters) + m.optimize(max_iters=max_iters) Xpredict = m.predict(data['Ytest'])[0] if plot: @@ -396,13 +398,16 @@ def robot_wireless(max_iters=100, kernel=None, optimize=True, plot=True): sse = ((data['Xtest'] - Xpredict)**2).sum() - print m print('Sum of squares error on test data: ' + str(sse)) return m def silhouette(max_iters=100, optimize=True, plot=True): """Predict the pose of a figure given a silhouette. This is a task from Agarwal and Triggs 2004 ICML paper.""" - data = GPy.util.datasets.silhouette() + try:import pods + except ImportError: + print 'pods unavailable, see https://github.com/sods/ods for example datasets' + return + data = pods.datasets.silhouette() # create simple GP Model m = GPy.models.GPRegression(data['X'], data['Y']) @@ -414,32 +419,38 @@ def silhouette(max_iters=100, optimize=True, plot=True): print m return m -def sparse_GP_regression_1D(num_samples=400, num_inducing=5, max_iters=100, optimize=True, plot=True): +def sparse_GP_regression_1D(num_samples=400, num_inducing=5, max_iters=100, optimize=True, plot=True, checkgrad=False): """Run a 1D example of a sparse GP regression.""" # sample inputs and outputs X = np.random.uniform(-3., 3., (num_samples, 1)) Y = np.sin(X) + np.random.randn(num_samples, 1) * 0.05 # construct kernel - rbf = GPy.kern.rbf(1) + rbf = GPy.kern.RBF(1) # create simple GP Model m = GPy.models.SparseGPRegression(X, Y, kernel=rbf, num_inducing=num_inducing) - m.checkgrad(verbose=1) + + if checkgrad: + m.checkgrad() if optimize: - m.optimize('tnc', messages=1, max_iters=max_iters) + m.optimize('tnc', max_iters=max_iters) if plot: m.plot() return m -def sparse_GP_regression_2D(num_samples=400, num_inducing=50, max_iters=100, optimize=True, plot=True): +def sparse_GP_regression_2D(num_samples=400, num_inducing=50, max_iters=100, optimize=True, plot=True, nan=False): """Run a 2D example of a sparse GP regression.""" + np.random.seed(1234) X = np.random.uniform(-3., 3., (num_samples, 2)) Y = np.sin(X[:, 0:1]) * np.sin(X[:, 1:2]) + np.random.randn(num_samples, 1) * 0.05 + if nan: + inan = np.random.binomial(1,.2,size=Y.shape) + Y[inan] = np.nan # construct kernel - rbf = GPy.kern.rbf(2) + rbf = GPy.kern.RBF(2) # create simple GP Model m = GPy.models.SparseGPRegression(X, Y, kernel=rbf, num_inducing=num_inducing) @@ -462,7 +473,7 @@ def sparse_GP_regression_2D(num_samples=400, num_inducing=50, max_iters=100, opt def uncertain_inputs_sparse_regression(max_iters=200, optimize=True, plot=True): """Run a 1D example of a sparse GP regression with uncertain inputs.""" - fig, axes = pb.subplots(1, 2, figsize=(12, 5)) + fig, axes = pb.subplots(1, 2, figsize=(12, 5), sharex=True, sharey=True) # sample inputs and outputs S = np.ones((20, 1)) @@ -471,8 +482,7 @@ def uncertain_inputs_sparse_regression(max_iters=200, optimize=True, plot=True): # likelihood = GPy.likelihoods.Gaussian(Y) Z = np.random.uniform(-3., 3., (7, 1)) - k = GPy.kern.rbf(1) - + k = GPy.kern.RBF(1) # create simple GP Model - no input uncertainty on this one m = GPy.models.SparseGPRegression(X, Y, kernel=k, Z=Z) @@ -485,7 +495,7 @@ def uncertain_inputs_sparse_regression(max_iters=200, optimize=True, plot=True): print m # the same Model with uncertainty - m = GPy.models.SparseGPRegression(X, Y, kernel=k, Z=Z, X_variance=S) + m = GPy.models.SparseGPRegression(X, Y, kernel=GPy.kern.RBF(1), Z=Z, X_variance=S) if optimize: m.optimize('scg', messages=1, max_iters=max_iters) if plot: diff --git a/GPy/examples/stochastic.py b/GPy/examples/stochastic.py deleted file mode 100644 index c302ec7d..00000000 --- a/GPy/examples/stochastic.py +++ /dev/null @@ -1,37 +0,0 @@ -# Copyright (c) 2012, GPy authors (see AUTHORS.txt). -# Licensed under the BSD 3-clause license (see LICENSE.txt) - -import pylab as pb -import numpy as np -import GPy - -def toy_1d(optimize=True, plot=True): - N = 2000 - M = 20 - - #create data - X = np.linspace(0,32,N)[:,None] - Z = np.linspace(0,32,M)[:,None] - Y = np.sin(X) + np.cos(0.3*X) + np.random.randn(*X.shape)/np.sqrt(50.) - - m = GPy.models.SVIGPRegression(X,Y, batchsize=10, Z=Z) - m.constrain_bounded('noise_variance',1e-3,1e-1) - m.constrain_bounded('white_variance',1e-3,1e-1) - - m.param_steplength = 1e-4 - - if plot: - fig = pb.figure() - ax = fig.add_subplot(111) - def cb(foo): - ax.cla() - m.plot(ax=ax,Z_height=-3) - ax.set_ylim(-3,3) - fig.canvas.draw() - - if optimize: - m.optimize(500, callback=cb, callback_interval=1) - - if plot: - m.plot_traces() - return m diff --git a/GPy/examples/tutorials.py b/GPy/examples/tutorials.py deleted file mode 100644 index 7825992d..00000000 --- a/GPy/examples/tutorials.py +++ /dev/null @@ -1,153 +0,0 @@ -# Copyright (c) 2012, GPy authors (see AUTHORS.txt). -# Licensed under the BSD 3-clause license (see LICENSE.txt) - - -""" -Code of Tutorials -""" - -import pylab as pb -pb.ion() -import numpy as np -import GPy - -def tuto_GP_regression(optimize=True, plot=True): - """The detailed explanations of the commands used in this file can be found in the tutorial section""" - - X = np.random.uniform(-3.,3.,(20,1)) - Y = np.sin(X) + np.random.randn(20,1)*0.05 - - kernel = GPy.kern.rbf(input_dim=1, variance=1., lengthscale=1.) - - m = GPy.models.GPRegression(X, Y, kernel) - - print m - if plot: - m.plot() - - m.constrain_positive('') - - m.unconstrain('') # may be used to remove the previous constrains - m.constrain_positive('.*rbf_variance') - m.constrain_bounded('.*lengthscale',1.,10. ) - m.constrain_fixed('.*noise',0.0025) - - if optimize: - m.optimize() - m.optimize_restarts(num_restarts = 10) - - ####################################################### - ####################################################### - # sample inputs and outputs - X = np.random.uniform(-3.,3.,(50,2)) - Y = np.sin(X[:,0:1]) * np.sin(X[:,1:2])+np.random.randn(50,1)*0.05 - - # define kernel - ker = GPy.kern.Matern52(2,ARD=True) + GPy.kern.white(2) - - # create simple GP model - m = GPy.models.GPRegression(X, Y, ker) - - # contrain all parameters to be positive - m.constrain_positive('') - - # optimize and plot - if optimize: - m.optimize('tnc', max_f_eval = 1000) - if plot: - m.plot() - - print m - return(m) - -def tuto_kernel_overview(optimize=True, plot=True): - """The detailed explanations of the commands used in this file can be found in the tutorial section""" - ker1 = GPy.kern.rbf(1) # Equivalent to ker1 = GPy.kern.rbf(input_dim=1, variance=1., lengthscale=1.) - ker2 = GPy.kern.rbf(input_dim=1, variance = .75, lengthscale=2.) - ker3 = GPy.kern.rbf(1, .5, .5) - - print ker2 - - if plot: - ker1.plot() - ker2.plot() - ker3.plot() - - k1 = GPy.kern.rbf(1,1.,2.) - k2 = GPy.kern.Matern32(1, 0.5, 0.2) - - # Product of kernels - k_prod = k1.prod(k2) # By default, tensor=False - k_prodtens = k1.prod(k2,tensor=True) - - # Sum of kernels - k_add = k1.add(k2) # By default, tensor=False - k_addtens = k1.add(k2,tensor=True) - - k1 = GPy.kern.rbf(1,1.,2) - k2 = GPy.kern.periodic_Matern52(1,variance=1e3, lengthscale=1, period = 1.5, lower=-5., upper = 5) - - k = k1 * k2 # equivalent to k = k1.prod(k2) - print k - - # Simulate sample paths - X = np.linspace(-5,5,501)[:,None] - Y = np.random.multivariate_normal(np.zeros(501),k.K(X),1) - - k1 = GPy.kern.rbf(1) - k2 = GPy.kern.Matern32(1) - k3 = GPy.kern.white(1) - - k = k1 + k2 + k3 - print k - - k.constrain_positive('.*var') - k.constrain_fixed(np.array([1]),1.75) - k.tie_params('.*len') - k.unconstrain('white') - k.constrain_bounded('white',lower=1e-5,upper=.5) - print k - - k_cst = GPy.kern.bias(1,variance=1.) - k_mat = GPy.kern.Matern52(1,variance=1., lengthscale=3) - Kanova = (k_cst + k_mat).prod(k_cst + k_mat,tensor=True) - print Kanova - - # sample inputs and outputs - X = np.random.uniform(-3.,3.,(40,2)) - Y = 0.5*X[:,:1] + 0.5*X[:,1:] + 2*np.sin(X[:,:1]) * np.sin(X[:,1:]) - - # Create GP regression model - m = GPy.models.GPRegression(X, Y, Kanova) - - if plot: - fig = pb.figure(figsize=(5,5)) - ax = fig.add_subplot(111) - m.plot(ax=ax) - - pb.figure(figsize=(20,3)) - pb.subplots_adjust(wspace=0.5) - axs = pb.subplot(1,5,1) - m.plot(ax=axs) - pb.subplot(1,5,2) - pb.ylabel("= ",rotation='horizontal',fontsize='30') - axs = pb.subplot(1,5,3) - m.plot(ax=axs, which_parts=[False,True,False,False]) - pb.ylabel("cst +",rotation='horizontal',fontsize='30') - axs = pb.subplot(1,5,4) - m.plot(ax=axs, which_parts=[False,False,True,False]) - pb.ylabel("+ ",rotation='horizontal',fontsize='30') - axs = pb.subplot(1,5,5) - pb.ylabel("+ ",rotation='horizontal',fontsize='30') - m.plot(ax=axs, which_parts=[False,False,False,True]) - - return(m) - - -def model_interaction(optimize=True, plot=True): - X = np.random.randn(20,1) - Y = np.sin(X) + np.random.randn(*X.shape)*0.01 + 5. - k = GPy.kern.rbf(1) + GPy.kern.bias(1) - m = GPy.models.GPRegression(X, Y, kernel=k) - return m - diff --git a/GPy/inference/__init__.py b/GPy/inference/__init__.py index e69de29b..f1ffd595 100644 --- a/GPy/inference/__init__.py +++ b/GPy/inference/__init__.py @@ -0,0 +1,2 @@ +import latent_function_inference +import optimization \ No newline at end of file diff --git a/GPy/inference/latent_function_inference/__init__.py b/GPy/inference/latent_function_inference/__init__.py new file mode 100644 index 00000000..c507f7e1 --- /dev/null +++ b/GPy/inference/latent_function_inference/__init__.py @@ -0,0 +1,98 @@ +# Copyright (c) 2012, James Hensman +# Licensed under the BSD 3-clause license (see LICENSE.txt) + +__doc__ = """ +Inference over Gaussian process latent functions + +In all our GP models, the consistency propery means that we have a Gaussian +prior over a finite set of points f. This prior is + + math:: N(f | 0, K) + +where K is the kernel matrix. + +We also have a likelihood (see GPy.likelihoods) which defines how the data are +related to the latent function: p(y | f). If the likelihood is also a Gaussian, +the inference over f is tractable (see exact_gaussian_inference.py). + +If the likelihood object is something other than Gaussian, then exact inference +is not tractable. We then resort to a Laplace approximation (laplace.py) or +expectation propagation (ep.py). + +The inference methods return a +:class:`~GPy.inference.latent_function_inference.posterior.Posterior` +instance, which is a simple +structure which contains a summary of the posterior. The model classes can then +use this posterior object for making predictions, optimizing hyper-parameters, +etc. + +""" + +class LatentFunctionInference(object): + def on_optimization_start(self): + """ + This function gets called, just before the optimization loop to start. + """ + pass + + def on_optimization_end(self): + """ + This function gets called, just after the optimization loop ended. + """ + pass + +class InferenceMethodList(LatentFunctionInference, list): + + def on_optimization_start(self): + for inf in self: + inf.on_optimization_start() + + def on_optimization_end(self): + for inf in self: + inf.on_optimization_end() + + def __getstate__(self): + state = [] + for inf in self: + state.append(inf) + return state + + def __setstate__(self, state): + for inf in state: + self.append(inf) + +from exact_gaussian_inference import ExactGaussianInference +from laplace import Laplace +from GPy.inference.latent_function_inference.var_dtc import VarDTC +from expectation_propagation import EP +from expectation_propagation_dtc import EPDTC +from dtc import DTC +from fitc import FITC +from var_dtc_parallel import VarDTC_minibatch + +# class FullLatentFunctionData(object): +# +# + +# class EMLikeLatentFunctionInference(LatentFunctionInference): +# def update_approximation(self): +# """ +# This function gets called when the +# """ +# +# def inference(self, kern, X, Z, likelihood, Y, Y_metadata=None): +# """ +# Do inference on the latent functions given a covariance function `kern`, +# inputs and outputs `X` and `Y`, inducing_inputs `Z`, and a likelihood `likelihood`. +# Additional metadata for the outputs `Y` can be given in `Y_metadata`. +# """ +# raise NotImplementedError, "Abstract base class for full inference" +# +# class VariationalLatentFunctionInference(LatentFunctionInference): +# def inference(self, kern, X, Z, likelihood, Y, Y_metadata=None): +# """ +# Do inference on the latent functions given a covariance function `kern`, +# inputs and outputs `X` and `Y`, inducing_inputs `Z`, and a likelihood `likelihood`. +# Additional metadata for the outputs `Y` can be given in `Y_metadata`. +# """ +# raise NotImplementedError, "Abstract base class for full inference" diff --git a/GPy/inference/latent_function_inference/dtc.py b/GPy/inference/latent_function_inference/dtc.py new file mode 100644 index 00000000..5590a079 --- /dev/null +++ b/GPy/inference/latent_function_inference/dtc.py @@ -0,0 +1,162 @@ +# Copyright (c) 2012-2014, James Hensman +# Licensed under the BSD 3-clause license (see LICENSE.txt) + +from posterior import Posterior +from ...util.linalg import jitchol, tdot, dtrtrs, dpotri, pdinv +import numpy as np +from . import LatentFunctionInference +log_2_pi = np.log(2*np.pi) + +class DTC(LatentFunctionInference): + """ + An object for inference when the likelihood is Gaussian, but we want to do sparse inference. + + The function self.inference returns a Posterior object, which summarizes + the posterior. + + NB. It's not recommended to use this function! It's here for historical purposes. + + """ + def __init__(self): + self.const_jitter = 1e-6 + + def inference(self, kern, X, Z, likelihood, Y, Y_metadata=None): + assert X_variance is None, "cannot use X_variance with DTC. Try varDTC." + + num_inducing, _ = Z.shape + num_data, output_dim = Y.shape + + #make sure the noise is not hetero + beta = 1./likelihood.gaussian_variance(Y_metadata) + if beta.size > 1: + raise NotImplementedError, "no hetero noise with this implementation of DTC" + + Kmm = kern.K(Z) + Knn = kern.Kdiag(X) + Knm = kern.K(X, Z) + U = Knm + Uy = np.dot(U.T,Y) + + #factor Kmm + Kmmi, L, Li, _ = pdinv(Kmm) + + # Compute A + LiUTbeta = np.dot(Li, U.T)*np.sqrt(beta) + A = tdot(LiUTbeta) + np.eye(num_inducing) + + # factor A + LA = jitchol(A) + + # back substutue to get b, P, v + tmp, _ = dtrtrs(L, Uy, lower=1) + b, _ = dtrtrs(LA, tmp*beta, lower=1) + tmp, _ = dtrtrs(LA, b, lower=1, trans=1) + v, _ = dtrtrs(L, tmp, lower=1, trans=1) + tmp, _ = dtrtrs(LA, Li, lower=1, trans=0) + P = tdot(tmp.T) + + #compute log marginal + log_marginal = -0.5*num_data*output_dim*np.log(2*np.pi) + \ + -np.sum(np.log(np.diag(LA)))*output_dim + \ + 0.5*num_data*output_dim*np.log(beta) + \ + -0.5*beta*np.sum(np.square(Y)) + \ + 0.5*np.sum(np.square(b)) + + # Compute dL_dKmm + vvT_P = tdot(v.reshape(-1,1)) + P + dL_dK = 0.5*(Kmmi - vvT_P) + + # Compute dL_dU + vY = np.dot(v.reshape(-1,1),Y.T) + dL_dU = vY - np.dot(vvT_P, U.T) + dL_dU *= beta + + #compute dL_dR + Uv = np.dot(U, v) + dL_dR = 0.5*(np.sum(U*np.dot(U,P), 1) - 1./beta + np.sum(np.square(Y), 1) - 2.*np.sum(Uv*Y, 1) + np.sum(np.square(Uv), 1))*beta**2 + + dL_dthetaL = likelihood.exact_inference_gradients(dL_dR) + + grad_dict = {'dL_dKmm': dL_dK, 'dL_dKdiag':np.zeros_like(Knn), 'dL_dKnm':dL_dU.T, 'dL_dthetaL':dL_dthetaL} + + #construct a posterior object + post = Posterior(woodbury_inv=Kmmi-P, woodbury_vector=v, K=Kmm, mean=None, cov=None, K_chol=L) + + return post, log_marginal, grad_dict + +class vDTC(object): + def __init__(self): + self.const_jitter = 1e-6 + + def inference(self, kern, X, X_variance, Z, likelihood, Y, Y_metadata): + assert X_variance is None, "cannot use X_variance with DTC. Try varDTC." + + num_inducing, _ = Z.shape + num_data, output_dim = Y.shape + + #make sure the noise is not hetero + beta = 1./likelihood.gaussian_variance(Y_metadata) + if beta.size > 1: + raise NotImplementedError, "no hetero noise with this implementation of DTC" + + Kmm = kern.K(Z) + Knn = kern.Kdiag(X) + Knm = kern.K(X, Z) + U = Knm + Uy = np.dot(U.T,Y) + + #factor Kmm + Kmmi, L, Li, _ = pdinv(Kmm) + + # Compute A + LiUTbeta = np.dot(Li, U.T)*np.sqrt(beta) + A_ = tdot(LiUTbeta) + trace_term = -0.5*(np.sum(Knn)*beta - np.trace(A_)) + A = A_ + np.eye(num_inducing) + + # factor A + LA = jitchol(A) + + # back substutue to get b, P, v + tmp, _ = dtrtrs(L, Uy, lower=1) + b, _ = dtrtrs(LA, tmp*beta, lower=1) + tmp, _ = dtrtrs(LA, b, lower=1, trans=1) + v, _ = dtrtrs(L, tmp, lower=1, trans=1) + tmp, _ = dtrtrs(LA, Li, lower=1, trans=0) + P = tdot(tmp.T) + stop + + #compute log marginal + log_marginal = -0.5*num_data*output_dim*np.log(2*np.pi) + \ + -np.sum(np.log(np.diag(LA)))*output_dim + \ + 0.5*num_data*output_dim*np.log(beta) + \ + -0.5*beta*np.sum(np.square(Y)) + \ + 0.5*np.sum(np.square(b)) + \ + trace_term + + # Compute dL_dKmm + vvT_P = tdot(v.reshape(-1,1)) + P + LAL = Li.T.dot(A).dot(Li) + dL_dK = Kmmi - 0.5*(vvT_P + LAL) + + # Compute dL_dU + vY = np.dot(v.reshape(-1,1),Y.T) + #dL_dU = vY - np.dot(vvT_P, U.T) + dL_dU = vY - np.dot(vvT_P - Kmmi, U.T) + dL_dU *= beta + + #compute dL_dR + Uv = np.dot(U, v) + dL_dR = 0.5*(np.sum(U*np.dot(U,P), 1) - 1./beta + np.sum(np.square(Y), 1) - 2.*np.sum(Uv*Y, 1) + np.sum(np.square(Uv), 1) )*beta**2 + dL_dR -=beta*trace_term/num_data + + dL_dthetaL = likelihood.exact_inference_gradients(dL_dR) + grad_dict = {'dL_dKmm': dL_dK, 'dL_dKdiag':np.zeros_like(Knn) + -0.5*beta, 'dL_dKnm':dL_dU.T, 'dL_dthetaL':dL_dthetaL} + + #construct a posterior object + post = Posterior(woodbury_inv=Kmmi-P, woodbury_vector=v, K=Kmm, mean=None, cov=None, K_chol=L) + + + return post, log_marginal, grad_dict + + diff --git a/GPy/inference/latent_function_inference/exact_gaussian_inference.py b/GPy/inference/latent_function_inference/exact_gaussian_inference.py new file mode 100644 index 00000000..1312d36a --- /dev/null +++ b/GPy/inference/latent_function_inference/exact_gaussian_inference.py @@ -0,0 +1,59 @@ +# Copyright (c) 2012-2014, GPy authors (see AUTHORS.txt). +# Licensed under the BSD 3-clause license (see LICENSE.txt) + +from posterior import Posterior +from ...util.linalg import pdinv, dpotrs, tdot +from ...util import diag +import numpy as np +from . import LatentFunctionInference +log_2_pi = np.log(2*np.pi) + + +class ExactGaussianInference(LatentFunctionInference): + """ + An object for inference when the likelihood is Gaussian. + + The function self.inference returns a Posterior object, which summarizes + the posterior. + + For efficiency, we sometimes work with the cholesky of Y*Y.T. To save repeatedly recomputing this, we cache it. + + """ + def __init__(self): + pass#self._YYTfactor_cache = caching.cache() + + def get_YYTfactor(self, Y): + """ + find a matrix L which satisfies LL^T = YY^T. + + Note that L may have fewer columns than Y, else L=Y. + """ + N, D = Y.shape + if (N>D): + return Y + else: + #if Y in self.cache, return self.Cache[Y], else store Y in cache and return L. + #print "WARNING: N>D of Y, we need caching of L, such that L*L^T = Y, returning Y still!" + return Y + + def inference(self, kern, X, likelihood, Y, Y_metadata=None): + """ + Returns a Posterior class containing essential quantities of the posterior + """ + YYT_factor = self.get_YYTfactor(Y) + + K = kern.K(X) + + Ky = K.copy() + diag.add(Ky, likelihood.gaussian_variance(Y_metadata)) + Wi, LW, LWi, W_logdet = pdinv(Ky) + + alpha, _ = dpotrs(LW, YYT_factor, lower=1) + + log_marginal = 0.5*(-Y.size * log_2_pi - Y.shape[1] * W_logdet - np.sum(alpha * YYT_factor)) + + dL_dK = 0.5 * (tdot(alpha) - Y.shape[1] * Wi) + + dL_dthetaL = likelihood.exact_inference_gradients(np.diag(dL_dK),Y_metadata) + + return Posterior(woodbury_chol=LW, woodbury_vector=alpha, K=K), log_marginal, {'dL_dK':dL_dK, 'dL_dthetaL':dL_dthetaL} diff --git a/GPy/inference/latent_function_inference/expectation_propagation.py b/GPy/inference/latent_function_inference/expectation_propagation.py new file mode 100644 index 00000000..26144974 --- /dev/null +++ b/GPy/inference/latent_function_inference/expectation_propagation.py @@ -0,0 +1,122 @@ +# Copyright (c) 2012-2014, GPy authors (see AUTHORS.txt). +# Licensed under the BSD 3-clause license (see LICENSE.txt) +import numpy as np +from ...util.linalg import pdinv,jitchol,DSYR,tdot,dtrtrs, dpotrs +from posterior import Posterior +from . import LatentFunctionInference +log_2_pi = np.log(2*np.pi) + +class EP(LatentFunctionInference): + def __init__(self, epsilon=1e-6, eta=1., delta=1.): + """ + The expectation-propagation algorithm. + For nomenclature see Rasmussen & Williams 2006. + + :param epsilon: Convergence criterion, maximum squared difference allowed between mean updates to stop iterations (float) + :type epsilon: float + :param eta: parameter for fractional EP updates. + :type eta: float64 + :param delta: damping EP updates factor. + :type delta: float64 + """ + self.epsilon, self.eta, self.delta = epsilon, eta, delta + self.reset() + + def reset(self): + self.old_mutilde, self.old_vtilde = None, None + self._ep_approximation = None + + def on_optimization_start(self): + self._ep_approximation = None + + def on_optimization_end(self): + # TODO: update approximation in the end as well? Maybe even with a switch? + pass + + def inference(self, kern, X, likelihood, Y, Y_metadata=None, Z=None): + num_data, output_dim = Y.shape + assert output_dim ==1, "ep in 1D only (for now!)" + + K = kern.K(X) + + if self._ep_approximation is None: + mu, Sigma, mu_tilde, tau_tilde, Z_hat = self._ep_approximation = self.expectation_propagation(K, Y, likelihood, Y_metadata) + else: + mu, Sigma, mu_tilde, tau_tilde, Z_hat = self._ep_approximation + + Wi, LW, LWi, W_logdet = pdinv(K + np.diag(1./tau_tilde)) + + alpha, _ = dpotrs(LW, mu_tilde, lower=1) + + log_marginal = 0.5*(-num_data * log_2_pi - W_logdet - np.sum(alpha * mu_tilde)) # TODO: add log Z_hat?? + + dL_dK = 0.5 * (tdot(alpha[:,None]) - Wi) + + dL_dthetaL = np.zeros(likelihood.size)#TODO: derivatives of the likelihood parameters + + return Posterior(woodbury_inv=Wi, woodbury_vector=alpha, K=K), log_marginal, {'dL_dK':dL_dK, 'dL_dthetaL':dL_dthetaL} + + def expectation_propagation(self, K, Y, likelihood, Y_metadata): + + num_data, data_dim = Y.shape + assert data_dim == 1, "This EP methods only works for 1D outputs" + + + #Initial values - Posterior distribution parameters: q(f|X,Y) = N(f|mu,Sigma) + mu = np.zeros(num_data) + Sigma = K.copy() + + #Initial values - Marginal moments + Z_hat = np.empty(num_data,dtype=np.float64) + mu_hat = np.empty(num_data,dtype=np.float64) + sigma2_hat = np.empty(num_data,dtype=np.float64) + + #initial values - Gaussian factors + if self.old_mutilde is None: + tau_tilde, mu_tilde, v_tilde = np.zeros((3, num_data)) + else: + assert old_mutilde.size == num_data, "data size mis-match: did you change the data? try resetting!" + mu_tilde, v_tilde = self.old_mutilde, self.old_vtilde + tau_tilde = v_tilde/mu_tilde + + #Approximation + tau_diff = self.epsilon + 1. + v_diff = self.epsilon + 1. + iterations = 0 + while (tau_diff > self.epsilon) or (v_diff > self.epsilon): + update_order = np.random.permutation(num_data) + for i in update_order: + #Cavity distribution parameters + tau_cav = 1./Sigma[i,i] - self.eta*tau_tilde[i] + v_cav = mu[i]/Sigma[i,i] - self.eta*v_tilde[i] + #Marginal moments + Z_hat[i], mu_hat[i], sigma2_hat[i] = likelihood.moments_match_ep(Y[i], tau_cav, v_cav)#, Y_metadata=None)#=(None if Y_metadata is None else Y_metadata[i])) + #Site parameters update + delta_tau = self.delta/self.eta*(1./sigma2_hat[i] - 1./Sigma[i,i]) + delta_v = self.delta/self.eta*(mu_hat[i]/sigma2_hat[i] - mu[i]/Sigma[i,i]) + tau_tilde[i] += delta_tau + v_tilde[i] += delta_v + #Posterior distribution parameters update + DSYR(Sigma, Sigma[:,i].copy(), -delta_tau/(1.+ delta_tau*Sigma[i,i])) + mu = np.dot(Sigma, v_tilde) + + #(re) compute Sigma and mu using full Cholesky decompy + tau_tilde_root = np.sqrt(tau_tilde) + Sroot_tilde_K = tau_tilde_root[:,None] * K + B = np.eye(num_data) + Sroot_tilde_K * tau_tilde_root[None,:] + L = jitchol(B) + V, _ = dtrtrs(L, Sroot_tilde_K, lower=1) + Sigma = K - np.dot(V.T,V) + mu = np.dot(Sigma,v_tilde) + + #monitor convergence + if iterations>0: + tau_diff = np.mean(np.square(tau_tilde-tau_tilde_old)) + v_diff = np.mean(np.square(v_tilde-v_tilde_old)) + tau_tilde_old = tau_tilde.copy() + v_tilde_old = v_tilde.copy() + + iterations += 1 + + mu_tilde = v_tilde/tau_tilde + return mu, Sigma, mu_tilde, tau_tilde, Z_hat diff --git a/GPy/inference/latent_function_inference/expectation_propagation_dtc.py b/GPy/inference/latent_function_inference/expectation_propagation_dtc.py new file mode 100644 index 00000000..35b1b7dc --- /dev/null +++ b/GPy/inference/latent_function_inference/expectation_propagation_dtc.py @@ -0,0 +1,351 @@ +# Copyright (c) 2012-2014, GPy authors (see AUTHORS.txt). +# Licensed under the BSD 3-clause license (see LICENSE.txt) + +import numpy as np +from ...util import diag +from ...util.linalg import mdot, jitchol, backsub_both_sides, tdot, dtrtrs, dtrtri, dpotri, dpotrs, symmetrify, DSYR +from ...core.parameterization.variational import VariationalPosterior +from . import LatentFunctionInference +from posterior import Posterior +log_2_pi = np.log(2*np.pi) + +class EPDTC(LatentFunctionInference): + const_jitter = 1e-6 + def __init__(self, epsilon=1e-6, eta=1., delta=1., limit=1): + from ...util.caching import Cacher + self.limit = limit + self.get_trYYT = Cacher(self._get_trYYT, limit) + self.get_YYTfactor = Cacher(self._get_YYTfactor, limit) + + self.epsilon, self.eta, self.delta = epsilon, eta, delta + self.reset() + + def set_limit(self, limit): + self.get_trYYT.limit = limit + self.get_YYTfactor.limit = limit + + def on_optimization_start(self): + self._ep_approximation = None + + def on_optimization_end(self): + # TODO: update approximation in the end as well? Maybe even with a switch? + pass + + def _get_trYYT(self, Y): + return np.sum(np.square(Y)) + + def __getstate__(self): + # has to be overridden, as Cacher objects cannot be pickled. + return self.limit + + def __setstate__(self, state): + # has to be overridden, as Cacher objects cannot be pickled. + self.limit = state + from ...util.caching import Cacher + self.get_trYYT = Cacher(self._get_trYYT, self.limit) + self.get_YYTfactor = Cacher(self._get_YYTfactor, self.limit) + + def _get_YYTfactor(self, Y): + """ + find a matrix L which satisfies LLT = YYT. + + Note that L may have fewer columns than Y. + """ + N, D = Y.shape + if (N>=D): + return Y + else: + return jitchol(tdot(Y)) + + def get_VVTfactor(self, Y, prec): + return Y * prec # TODO chache this, and make it effective + + def reset(self): + self.old_mutilde, self.old_vtilde = None, None + self._ep_approximation = None + + def inference(self, kern, X, Z, likelihood, Y, Y_metadata=None): + num_data, output_dim = Y.shape + assert output_dim ==1, "ep in 1D only (for now!)" + + Kmm = kern.K(Z) + Kmn = kern.K(Z,X) + + if self._ep_approximation is None: + mu, Sigma, mu_tilde, tau_tilde, Z_hat = self._ep_approximation = self.expectation_propagation(Kmm, Kmn, Y, likelihood, Y_metadata) + else: + mu, Sigma, mu_tilde, tau_tilde, Z_hat = self._ep_approximation + + + if isinstance(X, VariationalPosterior): + uncertain_inputs = True + psi0 = kern.psi0(Z, X) + psi1 = Kmn.T#kern.psi1(Z, X) + psi2 = kern.psi2(Z, X) + else: + uncertain_inputs = False + psi0 = kern.Kdiag(X) + psi1 = Kmn.T#kern.K(X, Z) + psi2 = None + + #see whether we're using variational uncertain inputs + + _, output_dim = Y.shape + + #see whether we've got a different noise variance for each datum + #beta = 1./np.fmax(likelihood.gaussian_variance(Y_metadata), 1e-6) + beta = tau_tilde + VVT_factor = beta[:,None]*mu_tilde[:,None] + trYYT = self.get_trYYT(mu_tilde[:,None]) + + # do the inference: + het_noise = beta.size > 1 + num_inducing = Z.shape[0] + num_data = Y.shape[0] + # kernel computations, using BGPLVM notation + + Kmm = kern.K(Z).copy() + diag.add(Kmm, self.const_jitter) + Lm = jitchol(Kmm) + + # The rather complex computations of A + if uncertain_inputs: + if het_noise: + psi2_beta = psi2 * (beta.flatten().reshape(num_data, 1, 1)).sum(0) + else: + psi2_beta = psi2.sum(0) * beta + LmInv = dtrtri(Lm) + A = LmInv.dot(psi2_beta.dot(LmInv.T)) + else: + if het_noise: + tmp = psi1 * (np.sqrt(beta.reshape(num_data, 1))) + else: + tmp = psi1 * (np.sqrt(beta)) + tmp, _ = dtrtrs(Lm, tmp.T, lower=1) + A = tdot(tmp) #print A.sum() + + # factor B + B = np.eye(num_inducing) + A + LB = jitchol(B) + psi1Vf = np.dot(psi1.T, VVT_factor) + # back substutue C into psi1Vf + tmp, _ = dtrtrs(Lm, psi1Vf, lower=1, trans=0) + _LBi_Lmi_psi1Vf, _ = dtrtrs(LB, tmp, lower=1, trans=0) + tmp, _ = dtrtrs(LB, _LBi_Lmi_psi1Vf, lower=1, trans=1) + Cpsi1Vf, _ = dtrtrs(Lm, tmp, lower=1, trans=1) + + # data fit and derivative of L w.r.t. Kmm + delit = tdot(_LBi_Lmi_psi1Vf) + data_fit = np.trace(delit) + DBi_plus_BiPBi = backsub_both_sides(LB, output_dim * np.eye(num_inducing) + delit) + delit = -0.5 * DBi_plus_BiPBi + delit += -0.5 * B * output_dim + delit += output_dim * np.eye(num_inducing) + # Compute dL_dKmm + dL_dKmm = backsub_both_sides(Lm, delit) + + # derivatives of L w.r.t. psi + dL_dpsi0, dL_dpsi1, dL_dpsi2 = _compute_dL_dpsi(num_inducing, num_data, output_dim, beta, Lm, + VVT_factor, Cpsi1Vf, DBi_plus_BiPBi, + psi1, het_noise, uncertain_inputs) + + # log marginal likelihood + log_marginal = _compute_log_marginal_likelihood(likelihood, num_data, output_dim, beta, het_noise, + psi0, A, LB, trYYT, data_fit, VVT_factor) + + #put the gradients in the right places + dL_dR = _compute_dL_dR(likelihood, + het_noise, uncertain_inputs, LB, + _LBi_Lmi_psi1Vf, DBi_plus_BiPBi, Lm, A, + psi0, psi1, beta, + data_fit, num_data, output_dim, trYYT, mu_tilde[:,None]) + + dL_dthetaL = 0#likelihood.exact_inference_gradients(dL_dR,Y_metadata) + + if uncertain_inputs: + grad_dict = {'dL_dKmm': dL_dKmm, + 'dL_dpsi0':dL_dpsi0, + 'dL_dpsi1':dL_dpsi1, + 'dL_dpsi2':dL_dpsi2, + 'dL_dthetaL':dL_dthetaL} + else: + grad_dict = {'dL_dKmm': dL_dKmm, + 'dL_dKdiag':dL_dpsi0, + 'dL_dKnm':dL_dpsi1, + 'dL_dthetaL':dL_dthetaL} + + #get sufficient things for posterior prediction + #TODO: do we really want to do this in the loop? + if VVT_factor.shape[1] == Y.shape[1]: + woodbury_vector = Cpsi1Vf # == Cpsi1V + else: + print 'foobar' + psi1V = np.dot(mu_tilde[:,None].T*beta, psi1).T + tmp, _ = dtrtrs(Lm, psi1V, lower=1, trans=0) + tmp, _ = dpotrs(LB, tmp, lower=1) + woodbury_vector, _ = dtrtrs(Lm, tmp, lower=1, trans=1) + Bi, _ = dpotri(LB, lower=1) + symmetrify(Bi) + Bi = -dpotri(LB, lower=1)[0] + diag.add(Bi, 1) + + woodbury_inv = backsub_both_sides(Lm, Bi) + + #construct a posterior object + post = Posterior(woodbury_inv=woodbury_inv, woodbury_vector=woodbury_vector, K=Kmm, mean=None, cov=None, K_chol=Lm) + return post, log_marginal, grad_dict + + + + + + def expectation_propagation(self, Kmm, Kmn, Y, likelihood, Y_metadata): + + num_data, data_dim = Y.shape + assert data_dim == 1, "This EP methods only works for 1D outputs" + + KmnKnm = np.dot(Kmn,Kmn.T) + Lm = jitchol(Kmm) + Lmi = dtrtrs(Lm,np.eye(Lm.shape[0]))[0] #chol_inv(Lm) + Kmmi = np.dot(Lmi.T,Lmi) + KmmiKmn = np.dot(Kmmi,Kmn) + Qnn_diag = np.sum(Kmn*KmmiKmn,-2) + LLT0 = Kmm.copy() + + #Initial values - Posterior distribution parameters: q(f|X,Y) = N(f|mu,Sigma) + mu = np.zeros(num_data) + LLT = Kmm.copy() #Sigma = K.copy() + Sigma_diag = Qnn_diag.copy() + + #Initial values - Marginal moments + Z_hat = np.empty(num_data,dtype=np.float64) + mu_hat = np.empty(num_data,dtype=np.float64) + sigma2_hat = np.empty(num_data,dtype=np.float64) + + #initial values - Gaussian factors + if self.old_mutilde is None: + tau_tilde, mu_tilde, v_tilde = np.zeros((3, num_data)) + else: + assert old_mutilde.size == num_data, "data size mis-match: did you change the data? try resetting!" + mu_tilde, v_tilde = self.old_mutilde, self.old_vtilde + tau_tilde = v_tilde/mu_tilde + + #Approximation + tau_diff = self.epsilon + 1. + v_diff = self.epsilon + 1. + iterations = 0 + while (tau_diff > self.epsilon) or (v_diff > self.epsilon): + update_order = np.random.permutation(num_data) + for i in update_order: + #Cavity distribution parameters + tau_cav = 1./Sigma_diag[i] - self.eta*tau_tilde[i] + v_cav = mu[i]/Sigma_diag[i] - self.eta*v_tilde[i] + #Marginal moments + Z_hat[i], mu_hat[i], sigma2_hat[i] = likelihood.moments_match_ep(Y[i], tau_cav, v_cav)#, Y_metadata=None)#=(None if Y_metadata is None else Y_metadata[i])) + #Site parameters update + delta_tau = self.delta/self.eta*(1./sigma2_hat[i] - 1./Sigma_diag[i]) + delta_v = self.delta/self.eta*(mu_hat[i]/sigma2_hat[i] - mu[i]/Sigma_diag[i]) + tau_tilde[i] += delta_tau + v_tilde[i] += delta_v + #Posterior distribution parameters update + + #DSYR(Sigma, Sigma[:,i].copy(), -delta_tau/(1.+ delta_tau*Sigma[i,i])) + DSYR(LLT,Kmn[:,i].copy(),delta_tau) + L = jitchol(LLT) + + V,info = dtrtrs(L,Kmn,lower=1) + Sigma_diag = np.sum(V*V,-2) + si = np.sum(V.T*V[:,i],-1) + mu += (delta_v-delta_tau*mu[i])*si + #mu = np.dot(Sigma, v_tilde) + + #(re) compute Sigma and mu using full Cholesky decompy + LLT = LLT0 + np.dot(Kmn*tau_tilde[None,:],Kmn.T) + L = jitchol(LLT) + V,info = dtrtrs(L,Kmn,lower=1) + V2,info = dtrtrs(L.T,V,lower=0) + #Sigma_diag = np.sum(V*V,-2) + #Knmv_tilde = np.dot(Kmn,v_tilde) + #mu = np.dot(V2.T,Knmv_tilde) + Sigma = np.dot(V2.T,V2) + mu = np.dot(Sigma,v_tilde) + + #monitor convergence + if iterations>0: + tau_diff = np.mean(np.square(tau_tilde-tau_tilde_old)) + v_diff = np.mean(np.square(v_tilde-v_tilde_old)) + tau_tilde_old = tau_tilde.copy() + v_tilde_old = v_tilde.copy() + + tau_diff = 0 + v_diff = 0 + iterations += 1 + + mu_tilde = v_tilde/tau_tilde + return mu, Sigma, mu_tilde, tau_tilde, Z_hat + +def _compute_dL_dpsi(num_inducing, num_data, output_dim, beta, Lm, VVT_factor, Cpsi1Vf, DBi_plus_BiPBi, psi1, het_noise, uncertain_inputs): + dL_dpsi0 = -0.5 * output_dim * (beta[:,None] * np.ones([num_data, 1])).flatten() + dL_dpsi1 = np.dot(VVT_factor, Cpsi1Vf.T) + dL_dpsi2_beta = 0.5 * backsub_both_sides(Lm, output_dim * np.eye(num_inducing) - DBi_plus_BiPBi) + if het_noise: + if uncertain_inputs: + dL_dpsi2 = beta[:, None, None] * dL_dpsi2_beta[None, :, :] + else: + dL_dpsi1 += 2.*np.dot(dL_dpsi2_beta, (psi1 * beta.reshape(num_data, 1)).T).T + dL_dpsi2 = None + else: + dL_dpsi2 = beta * dL_dpsi2_beta + if uncertain_inputs: + # repeat for each of the N psi_2 matrices + dL_dpsi2 = np.repeat(dL_dpsi2[None, :, :], num_data, axis=0) + else: + # subsume back into psi1 (==Kmn) + dL_dpsi1 += 2.*np.dot(psi1, dL_dpsi2) + dL_dpsi2 = None + + return dL_dpsi0, dL_dpsi1, dL_dpsi2 + + +def _compute_dL_dR(likelihood, het_noise, uncertain_inputs, LB, _LBi_Lmi_psi1Vf, DBi_plus_BiPBi, Lm, A, psi0, psi1, beta, data_fit, num_data, output_dim, trYYT, Y): + # the partial derivative vector for the likelihood + if likelihood.size == 0: + # save computation here. + dL_dR = None + elif het_noise: + if uncertain_inputs: + raise NotImplementedError, "heteroscedatic derivates with uncertain inputs not implemented" + else: + #from ...util.linalg import chol_inv + #LBi = chol_inv(LB) + LBi, _ = dtrtrs(LB,np.eye(LB.shape[0])) + + Lmi_psi1, nil = dtrtrs(Lm, psi1.T, lower=1, trans=0) + _LBi_Lmi_psi1, _ = dtrtrs(LB, Lmi_psi1, lower=1, trans=0) + + dL_dR = -0.5 * beta + 0.5 * (beta*Y)**2 + dL_dR += 0.5 * output_dim * (psi0 - np.sum(Lmi_psi1**2,0))[:,None] * beta**2 + + dL_dR += 0.5*np.sum(mdot(LBi.T,LBi,Lmi_psi1)*Lmi_psi1,0)[:,None]*beta**2 + + dL_dR += -np.dot(_LBi_Lmi_psi1Vf.T,_LBi_Lmi_psi1).T * Y * beta**2 + dL_dR += 0.5*np.dot(_LBi_Lmi_psi1Vf.T,_LBi_Lmi_psi1).T**2 * beta**2 + else: + # likelihood is not heteroscedatic + dL_dR = -0.5 * num_data * output_dim * beta + 0.5 * trYYT * beta ** 2 + dL_dR += 0.5 * output_dim * (psi0.sum() * beta ** 2 - np.trace(A) * beta) + dL_dR += beta * (0.5 * np.sum(A * DBi_plus_BiPBi) - data_fit) + return dL_dR + +def _compute_log_marginal_likelihood(likelihood, num_data, output_dim, beta, het_noise, psi0, A, LB, trYYT, data_fit,Y): + #compute log marginal likelihood + if het_noise: + lik_1 = -0.5 * num_data * output_dim * np.log(2. * np.pi) + 0.5 * np.sum(np.log(beta)) - 0.5 * np.sum(beta * np.square(Y).sum(axis=-1)) + lik_2 = -0.5 * output_dim * (np.sum(beta.flatten() * psi0) - np.trace(A)) + else: + lik_1 = -0.5 * num_data * output_dim * (np.log(2. * np.pi) - np.log(beta)) - 0.5 * beta * trYYT + lik_2 = -0.5 * output_dim * (np.sum(beta * psi0) - np.trace(A)) + lik_3 = -output_dim * (np.sum(np.log(np.diag(LB)))) + lik_4 = 0.5 * data_fit + log_marginal = lik_1 + lik_2 + lik_3 + lik_4 + return log_marginal diff --git a/GPy/inference/latent_function_inference/fitc.py b/GPy/inference/latent_function_inference/fitc.py new file mode 100644 index 00000000..a184c6c4 --- /dev/null +++ b/GPy/inference/latent_function_inference/fitc.py @@ -0,0 +1,89 @@ +# Copyright (c) 2012, James Hensman +# Licensed under the BSD 3-clause license (see LICENSE.txt) + +from posterior import Posterior +from ...util.linalg import jitchol, tdot, dtrtrs, dpotri, pdinv +from ...util import diag +import numpy as np +from . import LatentFunctionInference +log_2_pi = np.log(2*np.pi) + +class FITC(LatentFunctionInference): + """ + An object for inference when the likelihood is Gaussian, but we want to do sparse inference. + + The function self.inference returns a Posterior object, which summarizes + the posterior. + + """ + const_jitter = 1e-6 + + def inference(self, kern, X, Z, likelihood, Y, Y_metadata=None): + + num_inducing, _ = Z.shape + num_data, output_dim = Y.shape + + #make sure the noise is not hetero + sigma_n = likelihood.gaussian_variance(Y_metadata) + if sigma_n.size >1: + raise NotImplementedError, "no hetero noise with this implementation of FITC" + + Kmm = kern.K(Z) + Knn = kern.Kdiag(X) + Knm = kern.K(X, Z) + U = Knm + + #factor Kmm + diag.add(Kmm, self.const_jitter) + Kmmi, L, Li, _ = pdinv(Kmm) + + #compute beta_star, the effective noise precision + LiUT = np.dot(Li, U.T) + sigma_star = Knn + sigma_n - np.sum(np.square(LiUT),0) + beta_star = 1./sigma_star + + # Compute and factor A + A = tdot(LiUT*np.sqrt(beta_star)) + np.eye(num_inducing) + LA = jitchol(A) + + # back substutue to get b, P, v + URiy = np.dot(U.T*beta_star,Y) + tmp, _ = dtrtrs(L, URiy, lower=1) + b, _ = dtrtrs(LA, tmp, lower=1) + tmp, _ = dtrtrs(LA, b, lower=1, trans=1) + v, _ = dtrtrs(L, tmp, lower=1, trans=1) + tmp, _ = dtrtrs(LA, Li, lower=1, trans=0) + P = tdot(tmp.T) + + #compute log marginal + log_marginal = -0.5*num_data*output_dim*np.log(2*np.pi) + \ + -np.sum(np.log(np.diag(LA)))*output_dim + \ + 0.5*output_dim*np.sum(np.log(beta_star)) + \ + -0.5*np.sum(np.square(Y.T*np.sqrt(beta_star))) + \ + 0.5*np.sum(np.square(b)) + #compute dL_dR + Uv = np.dot(U, v) + dL_dR = 0.5*(np.sum(U*np.dot(U,P), 1) - 1./beta_star + np.sum(np.square(Y), 1) - 2.*np.sum(Uv*Y, 1) + np.sum(np.square(Uv), 1))*beta_star**2 + + + # Compute dL_dKmm + vvT_P = tdot(v.reshape(-1,1)) + P + dL_dK = 0.5*(Kmmi - vvT_P) + KiU = np.dot(Kmmi, U.T) + dL_dK += np.dot(KiU*dL_dR, KiU.T) + + # Compute dL_dU + vY = np.dot(v.reshape(-1,1),Y.T) + dL_dU = vY - np.dot(vvT_P, U.T) + dL_dU *= beta_star + dL_dU -= 2.*KiU*dL_dR + + dL_dthetaL = likelihood.exact_inference_gradients(dL_dR) + grad_dict = {'dL_dKmm': dL_dK, 'dL_dKdiag':dL_dR, 'dL_dKnm':dL_dU.T, 'dL_dthetaL':dL_dthetaL} + + #construct a posterior object + post = Posterior(woodbury_inv=Kmmi-P, woodbury_vector=v, K=Kmm, mean=None, cov=None, K_chol=L) + + return post, log_marginal, grad_dict + + diff --git a/GPy/inference/latent_function_inference/inferenceX.py b/GPy/inference/latent_function_inference/inferenceX.py new file mode 100644 index 00000000..f68f17cb --- /dev/null +++ b/GPy/inference/latent_function_inference/inferenceX.py @@ -0,0 +1,162 @@ +# Copyright (c) 2014, Zhenwen Dai +# Licensed under the BSD 3-clause license (see LICENSE.txt) + +import numpy as np +from ...core import Model +from ...core.parameterization import variational + +def infer_newX(model, Y_new, optimize=True, init='L2'): + """ + Infer the distribution of X for the new observed data *Y_new*. + + :param model: the GPy model used in inference + :type model: GPy.core.Model + :param Y_new: the new observed data for inference + :type Y_new: numpy.ndarray + :param optimize: whether to optimize the location of new X (True by default) + :type optimize: boolean + :return: a tuple containing the estimated posterior distribution of X and the model that optimize X + :rtype: (GPy.core.parameterization.variational.VariationalPosterior, GPy.core.Model) + """ + infr_m = InferenceX(model, Y_new, init=init) + + if optimize: + infr_m.optimize() + + return infr_m.X, infr_m + +class InferenceX(Model): + """ + The class for inference of new X with given new Y. (do_test_latent) + + :param model: the GPy model used in inference + :type model: GPy.core.Model + :param Y: the new observed data for inference + :type Y: numpy.ndarray + """ + def __init__(self, model, Y, name='inferenceX', init='L2'): + if np.isnan(Y).any() or getattr(model, 'missing_data', False): + assert Y.shape[0]==1, "The current implementation of inference X only support one data point at a time with missing data!" + self.missing_data = True + self.valid_dim = np.logical_not(np.isnan(Y[0])) + self.ninan = getattr(model, 'ninan', None) + else: + self.missing_data = False + super(InferenceX, self).__init__(name) + self.likelihood = model.likelihood.copy() + self.kern = model.kern.copy() + if model.kern.useGPU: + from ...models import SSGPLVM + if isinstance(model, SSGPLVM): + self.kern.GPU_SSRBF(True) + else: + self.kern.GPU(True) + from copy import deepcopy + self.posterior = deepcopy(model.posterior) + if hasattr(model, 'variational_prior'): + self.uncertain_input = True + self.variational_prior = model.variational_prior.copy() + else: + self.uncertain_input = False + if hasattr(model, 'inducing_inputs'): + self.sparse_gp = True + self.Z = model.Z.copy() + else: + self.sparse_gp = False + self.uncertain_input = False + self.Z = model.X.copy() + self.Y = Y + self.X = self._init_X(model, Y, init=init) + self.compute_dL() + + self.link_parameter(self.X) + + def _init_X(self, model, Y_new, init='L2'): + # Initialize the new X by finding the nearest point in Y space. + + Y = model.Y + if self.missing_data: + Y = Y[:,self.valid_dim] + Y_new = Y_new[:,self.valid_dim] + dist = -2.*Y_new.dot(Y.T) + np.square(Y_new).sum(axis=1)[:,None]+ np.square(Y).sum(axis=1)[None,:] + else: + if init=='L2': + dist = -2.*Y_new.dot(Y.T) + np.square(Y_new).sum(axis=1)[:,None]+ np.square(Y).sum(axis=1)[None,:] + elif init=='NCC': + dist = Y_new.dot(Y.T) + elif init=='rand': + dist = np.random.rand(Y_new.shape[0],Y.shape[0]) + idx = dist.argmin(axis=1) + + from ...models import SSGPLVM + from ...util.misc import param_to_array + if isinstance(model, SSGPLVM): + X = variational.SpikeAndSlabPosterior(param_to_array(model.X.mean[idx]), param_to_array(model.X.variance[idx]), param_to_array(model.X.gamma[idx])) + if model.group_spike: + X.gamma.fix() + else: + if self.uncertain_input and self.sparse_gp: + X = variational.NormalPosterior(param_to_array(model.X.mean[idx]), param_to_array(model.X.variance[idx])) + else: + from ...core import Param + X = Param('latent mean',param_to_array(model.X[idx]).copy()) + + return X + + def compute_dL(self): + # Common computation + beta = 1./np.fmax(self.likelihood.variance, 1e-6) + output_dim = self.Y.shape[-1] + wv = self.posterior.woodbury_vector + if self.missing_data: + wv = wv[:,self.valid_dim] + output_dim = self.valid_dim.sum() + if self.ninan is not None: + self.dL_dpsi2 = beta/2.*(self.posterior.woodbury_inv[:,:,self.valid_dim] - np.einsum('md,od->mo',wv, wv)[:, :, None]).sum(-1) + else: + self.dL_dpsi2 = beta/2.*(output_dim*self.posterior.woodbury_inv - np.einsum('md,od->mo',wv, wv)) + self.dL_dpsi1 = beta*np.dot(self.Y[:,self.valid_dim], wv.T) + self.dL_dpsi0 = - beta/2.* np.ones(self.Y.shape[0]) + else: + self.dL_dpsi2 = beta*(output_dim*self.posterior.woodbury_inv - np.einsum('md,od->mo',wv, wv))/2. + self.dL_dpsi1 = beta*np.dot(self.Y, wv.T) + self.dL_dpsi0 = -beta/2.*output_dim* np.ones(self.Y.shape[0]) + + def parameters_changed(self): + if self.uncertain_input: + psi0 = self.kern.psi0(self.Z, self.X) + psi1 = self.kern.psi1(self.Z, self.X) + psi2 = self.kern.psi2(self.Z, self.X) + else: + psi0 = self.kern.Kdiag(self.X) + psi1 = self.kern.K(self.X, self.Z) + psi2 = np.dot(psi1.T,psi1) + + self._log_marginal_likelihood = (self.dL_dpsi2*psi2).sum()+(self.dL_dpsi1*psi1).sum()+(self.dL_dpsi0*psi0).sum() + + if self.uncertain_input: + X_grad = self.kern.gradients_qX_expectations(variational_posterior=self.X, Z=self.Z, dL_dpsi0=self.dL_dpsi0, dL_dpsi1=self.dL_dpsi1, dL_dpsi2=self.dL_dpsi2) + self.X.set_gradients(X_grad) + else: + dL_dpsi1 = self.dL_dpsi1 + 2.*np.dot(psi1,self.dL_dpsi2) + X_grad = self.kern.gradients_X_diag(self.dL_dpsi0, self.X) + X_grad += self.kern.gradients_X(dL_dpsi1, self.X, self.Z) + self.X.gradient = X_grad + + if self.uncertain_input: + from ...core.parameterization.variational import SpikeAndSlabPrior + if isinstance(self.variational_prior, SpikeAndSlabPrior): + # Update Log-likelihood + KL_div = self.variational_prior.KL_divergence(self.X, N=self.Y.shape[0]) + # update for the KL divergence + self.variational_prior.update_gradients_KL(self.X, N=self.Y.shape[0]) + else: + # Update Log-likelihood + KL_div = self.variational_prior.KL_divergence(self.X) + # update for the KL divergence + self.variational_prior.update_gradients_KL(self.X) + self._log_marginal_likelihood += -KL_div + + def log_likelihood(self): + return self._log_marginal_likelihood + diff --git a/GPy/inference/latent_function_inference/laplace.py b/GPy/inference/latent_function_inference/laplace.py new file mode 100644 index 00000000..05711b0b --- /dev/null +++ b/GPy/inference/latent_function_inference/laplace.py @@ -0,0 +1,251 @@ +# Copyright (c) 2013, 2014 Alan Saul +# Licensed under the BSD 3-clause license (see LICENSE.txt) +# +#Parts of this file were influenced by the Matlab GPML framework written by +#Carl Edward Rasmussen & Hannes Nickisch, however all bugs are our own. +# +#The GPML code is released under the FreeBSD License. +#Copyright (c) 2005-2013 Carl Edward Rasmussen & Hannes Nickisch. All rights reserved. +# +#The code and associated documentation is available from +#http://gaussianprocess.org/gpml/code. + +import numpy as np +from ...util.linalg import mdot, jitchol, dpotrs, dtrtrs, dpotri, symmetrify, pdinv +from posterior import Posterior +import warnings +def warning_on_one_line(message, category, filename, lineno, file=None, line=None): + return ' %s:%s: %s:%s\n' % (filename, lineno, category.__name__, message) +warnings.formatwarning = warning_on_one_line +from scipy import optimize +from . import LatentFunctionInference + +class Laplace(LatentFunctionInference): + + def __init__(self): + """ + Laplace Approximation + + Find the moments \hat{f} and the hessian at this point + (using Newton-Raphson) of the unnormalised posterior + + """ + + self._mode_finding_tolerance = 1e-7 + self._mode_finding_max_iter = 60 + self.bad_fhat = False + #Store whether it is the first run of the inference so that we can choose whether we need + #to calculate things or reuse old variables + self.first_run = True + self._previous_Ki_fhat = None + + def inference(self, kern, X, likelihood, Y, Y_metadata=None): + """ + Returns a Posterior class containing essential quantities of the posterior + """ + + # Compute K + K = kern.K(X) + + #Find mode + if self.bad_fhat or self.first_run: + Ki_f_init = np.zeros_like(Y) + first_run = False + else: + Ki_f_init = self._previous_Ki_fhat + + f_hat, Ki_fhat = self.rasm_mode(K, Y, likelihood, Ki_f_init, Y_metadata=Y_metadata) + self.f_hat = f_hat + self.Ki_fhat = Ki_fhat + self.K = K.copy() + #Compute hessian and other variables at mode + log_marginal, woodbury_inv, dL_dK, dL_dthetaL = self.mode_computations(f_hat, Ki_fhat, K, Y, likelihood, kern, Y_metadata) + + self._previous_Ki_fhat = Ki_fhat.copy() + return Posterior(woodbury_vector=Ki_fhat, woodbury_inv=woodbury_inv, K=K), log_marginal, {'dL_dK':dL_dK, 'dL_dthetaL':dL_dthetaL} + + def rasm_mode(self, K, Y, likelihood, Ki_f_init, Y_metadata=None): + """ + Rasmussen's numerically stable mode finding + For nomenclature see Rasmussen & Williams 2006 + Influenced by GPML (BSD) code, all errors are our own + + :param K: Covariance matrix evaluated at locations X + :type K: NxD matrix + :param Y: The data + :type Y: np.ndarray + :param likelihood: the likelihood of the latent function value for the given data + :type likelihood: a GPy.likelihood object + :param Ki_f_init: the initial guess at the mode + :type Ki_f_init: np.ndarray + :param Y_metadata: information about the data, e.g. which likelihood to take from a multi-likelihood object + :type Y_metadata: np.ndarray | None + :returns: f_hat, mode on which to make laplace approxmiation + :rtype: np.ndarray + """ + + Ki_f = Ki_f_init.copy() + f = np.dot(K, Ki_f) + + #define the objective function (to be maximised) + def obj(Ki_f, f): + return -0.5*np.dot(Ki_f.flatten(), f.flatten()) + np.sum(likelihood.logpdf(f, Y, Y_metadata=Y_metadata)) + + difference = np.inf + iteration = 0 + while difference > self._mode_finding_tolerance and iteration < self._mode_finding_max_iter: + W = -likelihood.d2logpdf_df2(f, Y, Y_metadata=Y_metadata) + if np.any(np.isnan(W)): + raise ValueError('One or more element(s) of W is NaN') + grad = likelihood.dlogpdf_df(f, Y, Y_metadata=Y_metadata) + if np.any(np.isnan(grad)): + raise ValueError('One or more element(s) of grad is NaN') + + W_f = W*f + + b = W_f + grad # R+W p46 line 6. + W12BiW12, _, _ = self._compute_B_statistics(K, W, likelihood.log_concave) + W12BiW12Kb = np.dot(W12BiW12, np.dot(K, b)) + + #Work out the DIRECTION that we want to move in, but don't choose the stepsize yet + full_step_Ki_f = b - W12BiW12Kb # full_step_Ki_f = a in R&W p46 line 6. + dKi_f = full_step_Ki_f - Ki_f + + #define an objective for the line search (minimize this one) + def inner_obj(step_size): + Ki_f_trial = Ki_f + step_size*dKi_f + f_trial = np.dot(K, Ki_f_trial) + return -obj(Ki_f_trial, f_trial) + + #use scipy for the line search, the compute new values of f, Ki_f + step = optimize.brent(inner_obj, tol=1e-4, maxiter=12) + Ki_f_new = Ki_f + step*dKi_f + f_new = np.dot(K, Ki_f_new) + + difference = np.abs(np.sum(f_new - f)) + np.abs(np.sum(Ki_f_new - Ki_f)) + Ki_f = Ki_f_new + f = f_new + iteration += 1 + + #Warn of bad fits + if difference > self._mode_finding_tolerance: + if not self.bad_fhat: + warnings.warn("Not perfect mode found (f_hat). difference: {}, iteration: {} out of max {}".format(difference, iteration, self._mode_finding_max_iter)) + self.bad_fhat = True + elif self.bad_fhat: + self.bad_fhat = False + warnings.warn("f_hat now fine again. difference: {}, iteration: {} out of max {}".format(difference, iteration, self._mode_finding_max_iter)) + + return f, Ki_f + + def mode_computations(self, f_hat, Ki_f, K, Y, likelihood, kern, Y_metadata): + """ + At the mode, compute the hessian and effective covariance matrix. + + returns: logZ : approximation to the marginal likelihood + woodbury_inv : variable required for calculating the approximation to the covariance matrix + dL_dthetaL : array of derivatives (1 x num_kernel_params) + dL_dthetaL : array of derivatives (1 x num_likelihood_params) + """ + #At this point get the hessian matrix (or vector as W is diagonal) + W = -likelihood.d2logpdf_df2(f_hat, Y, Y_metadata=Y_metadata) + if np.any(np.isnan(W)): + raise ValueError('One or more element(s) of W is NaN') + + K_Wi_i, L, LiW12 = self._compute_B_statistics(K, W, likelihood.log_concave) + + #compute vital matrices + C = np.dot(LiW12, K) + Ki_W_i = K - C.T.dot(C) + + #compute the log marginal + log_marginal = -0.5*np.dot(Ki_f.flatten(), f_hat.flatten()) + np.sum(likelihood.logpdf(f_hat, Y, Y_metadata=Y_metadata)) - np.sum(np.log(np.diag(L))) + + # Compute matrices for derivatives + dW_df = -likelihood.d3logpdf_df3(f_hat, Y, Y_metadata=Y_metadata) # -d3lik_d3fhat + if np.any(np.isnan(dW_df)): + raise ValueError('One or more element(s) of dW_df is NaN') + + dL_dfhat = -0.5*(np.diag(Ki_W_i)[:, None]*dW_df) # s2 in R&W p126 line 9. + #BiK, _ = dpotrs(L, K, lower=1) + #dL_dfhat = 0.5*np.diag(BiK)[:, None]*dW_df + I_KW_i = np.eye(Y.shape[0]) - np.dot(K, K_Wi_i) + + #################### + # compute dL_dK # + #################### + if kern.size > 0 and not kern.is_fixed: + #Explicit + explicit_part = 0.5*(np.dot(Ki_f, Ki_f.T) - K_Wi_i) + + #Implicit + implicit_part = np.dot(Ki_f, dL_dfhat.T).dot(I_KW_i) + + dL_dK = explicit_part + implicit_part + else: + dL_dK = np.zeros(likelihood.size) + + #################### + #compute dL_dthetaL# + #################### + if likelihood.size > 0 and not likelihood.is_fixed: + dlik_dthetaL, dlik_grad_dthetaL, dlik_hess_dthetaL = likelihood._laplace_gradients(f_hat, Y, Y_metadata=Y_metadata) + + num_params = likelihood.size + # make space for one derivative for each likelihood parameter + dL_dthetaL = np.zeros(num_params) + for thetaL_i in range(num_params): + #Explicit + dL_dthetaL_exp = ( np.sum(dlik_dthetaL[thetaL_i]) + # The + comes from the fact that dlik_hess_dthetaL == -dW_dthetaL + + 0.5*np.sum(np.diag(Ki_W_i).flatten()*dlik_hess_dthetaL[:, thetaL_i].flatten()) + ) + + #Implicit + dfhat_dthetaL = mdot(I_KW_i, K, dlik_grad_dthetaL[:, thetaL_i]) + #dfhat_dthetaL = mdot(Ki_W_i, dlik_grad_dthetaL[:, thetaL_i]) + dL_dthetaL_imp = np.dot(dL_dfhat.T, dfhat_dthetaL) + dL_dthetaL[thetaL_i] = dL_dthetaL_exp + dL_dthetaL_imp + + else: + dL_dthetaL = np.zeros(likelihood.size) + + return log_marginal, K_Wi_i, dL_dK, dL_dthetaL + + def _compute_B_statistics(self, K, W, log_concave): + """ + Rasmussen suggests the use of a numerically stable positive definite matrix B + Which has a positive diagonal elements and can be easily inverted + + :param K: Prior Covariance matrix evaluated at locations X + :type K: NxN matrix + :param W: Negative hessian at a point (diagonal matrix) + :type W: Vector of diagonal values of Hessian (1xN) + :returns: (W12BiW12, L_B, Li_W12) + """ + if not log_concave: + #print "Under 1e-10: {}".format(np.sum(W < 1e-6)) + W[W<1e-6] = 1e-6 + # NOTE: when setting a parameter inside parameters_changed it will allways come to closed update circles!!! + #W.__setitem__(W < 1e-6, 1e-6, update=False) # FIXME-HACK: This is a hack since GPy can't handle negative variances which can occur + # If the likelihood is non-log-concave. We wan't to say that there is a negative variance + # To cause the posterior to become less certain than the prior and likelihood, + # This is a property only held by non-log-concave likelihoods + if np.any(np.isnan(W)): + raise ValueError('One or more element(s) of W is NaN') + #W is diagonal so its sqrt is just the sqrt of the diagonal elements + W_12 = np.sqrt(W) + B = np.eye(K.shape[0]) + W_12*K*W_12.T + L = jitchol(B) + + LiW12, _ = dtrtrs(L, np.diagflat(W_12), lower=1, trans=0) + K_Wi_i = np.dot(LiW12.T, LiW12) # R = W12BiW12, in R&W p 126, eq 5.25 + + #here's a better way to compute the required matrix. + # you could do the model finding witha backsub, instead of a dot... + #L2 = L/W_12 + #K_Wi_i_2 , _= dpotri(L2) + #symmetrify(K_Wi_i_2) + + return K_Wi_i, L, LiW12 + diff --git a/GPy/inference/latent_function_inference/posterior.py b/GPy/inference/latent_function_inference/posterior.py new file mode 100644 index 00000000..66c68261 --- /dev/null +++ b/GPy/inference/latent_function_inference/posterior.py @@ -0,0 +1,186 @@ +# Copyright (c) 2012, GPy authors (see AUTHORS.txt). +# Licensed under the BSD 3-clause license (see LICENSE.txt) + +import numpy as np +from ...util.linalg import pdinv, dpotrs, dpotri, symmetrify, jitchol + +class Posterior(object): + """ + An object to represent a Gaussian posterior over latent function values, p(f|D). + This may be computed exactly for Gaussian likelihoods, or approximated for + non-Gaussian likelihoods. + + The purpose of this class is to serve as an interface between the inference + schemes and the model classes. the model class can make predictions for + the function at any new point x_* by integrating over this posterior. + + """ + def __init__(self, woodbury_chol=None, woodbury_vector=None, K=None, mean=None, cov=None, K_chol=None, woodbury_inv=None): + """ + woodbury_chol : a lower triangular matrix L that satisfies posterior_covariance = K - K L^{-T} L^{-1} K + woodbury_vector : a matrix (or vector, as Nx1 matrix) M which satisfies posterior_mean = K M + K : the proir covariance (required for lazy computation of various quantities) + mean : the posterior mean + cov : the posterior covariance + + Not all of the above need to be supplied! You *must* supply: + + K (for lazy computation) + or + K_chol (for lazy computation) + + You may supply either: + + woodbury_chol + woodbury_vector + + Or: + + mean + cov + + Of course, you can supply more than that, but this class will lazily + compute all other quantites on demand. + + """ + #obligatory + self._K = K + + if ((woodbury_chol is not None) and (woodbury_vector is not None))\ + or ((woodbury_inv is not None) and (woodbury_vector is not None))\ + or ((woodbury_inv is not None) and (mean is not None))\ + or ((mean is not None) and (cov is not None)): + pass # we have sufficient to compute the posterior + else: + raise ValueError, "insufficient information to compute the posterior" + + self._K_chol = K_chol + self._K = K + #option 1: + self._woodbury_chol = woodbury_chol + self._woodbury_vector = woodbury_vector + + #option 2. + self._woodbury_inv = woodbury_inv + #and woodbury vector + + #option 2: + self._mean = mean + self._covariance = cov + + #compute this lazily + self._precision = None + + @property + def mean(self): + """ + Posterior mean + $$ + K_{xx}v + v := \texttt{Woodbury vector} + $$ + """ + if self._mean is None: + self._mean = np.dot(self._K, self.woodbury_vector) + return self._mean + + @property + def covariance(self): + """ + Posterior covariance + $$ + K_{xx} - K_{xx}W_{xx}^{-1}K_{xx} + W_{xx} := \texttt{Woodbury inv} + $$ + """ + if self._covariance is None: + #LiK, _ = dtrtrs(self.woodbury_chol, self._K, lower=1) + self._covariance = (np.atleast_3d(self._K) - np.tensordot(np.dot(np.atleast_3d(self.woodbury_inv).T, self._K), self._K, [1,0]).T).squeeze() + #self._covariance = self._K - self._K.dot(self.woodbury_inv).dot(self._K) + return self._covariance + + @property + def precision(self): + """ + Inverse of posterior covariance + """ + if self._precision is None: + cov = np.atleast_3d(self.covariance) + self._precision = np.zeros(cov.shape) # if one covariance per dimension + for p in xrange(cov.shape[-1]): + self._precision[:,:,p] = pdinv(cov[:,:,p])[0] + return self._precision + + @property + def woodbury_chol(self): + """ + return $L_{W}$ where L is the lower triangular Cholesky decomposition of the Woodbury matrix + $$ + L_{W}L_{W}^{\top} = W^{-1} + W^{-1} := \texttt{Woodbury inv} + $$ + """ + if self._woodbury_chol is None: + #compute woodbury chol from + if self._woodbury_inv is not None: + winv = np.atleast_3d(self._woodbury_inv) + self._woodbury_chol = np.zeros(winv.shape) + for p in xrange(winv.shape[-1]): + self._woodbury_chol[:,:,p] = pdinv(winv[:,:,p])[2] + #Li = jitchol(self._woodbury_inv) + #self._woodbury_chol, _ = dtrtri(Li) + #W, _, _, _, = pdinv(self._woodbury_inv) + #symmetrify(W) + #self._woodbury_chol = jitchol(W) + #try computing woodbury chol from cov + elif self._covariance is not None: + raise NotImplementedError, "TODO: check code here" + B = self._K - self._covariance + tmp, _ = dpotrs(self.K_chol, B) + self._woodbury_inv, _ = dpotrs(self.K_chol, tmp.T) + _, _, self._woodbury_chol, _ = pdinv(self._woodbury_inv) + else: + raise ValueError, "insufficient information to compute posterior" + return self._woodbury_chol + + @property + def woodbury_inv(self): + """ + The inverse of the woodbury matrix, in the gaussian likelihood case it is defined as + $$ + (K_{xx} + \Sigma_{xx})^{-1} + \Sigma_{xx} := \texttt{Likelihood.variance / Approximate likelihood covariance} + $$ + """ + if self._woodbury_inv is None: + if self._woodbury_chol is not None: + self._woodbury_inv, _ = dpotri(self._woodbury_chol, lower=1) + #self._woodbury_inv, _ = dpotrs(self.woodbury_chol, np.eye(self.woodbury_chol.shape[0]), lower=1) + symmetrify(self._woodbury_inv) + elif self._covariance is not None: + B = self._K - self._covariance + tmp, _ = dpotrs(self.K_chol, B) + self._woodbury_inv, _ = dpotrs(self.K_chol, tmp.T) + return self._woodbury_inv + + @property + def woodbury_vector(self): + """ + Woodbury vector in the gaussian likelihood case only is defined as + $$ + (K_{xx} + \Sigma)^{-1}Y + \Sigma := \texttt{Likelihood.variance / Approximate likelihood covariance} + $$ + """ + if self._woodbury_vector is None: + self._woodbury_vector, _ = dpotrs(self.K_chol, self.mean) + return self._woodbury_vector + + @property + def K_chol(self): + """ + Cholesky of the prior covariance K + """ + if self._K_chol is None: + self._K_chol = jitchol(self._K) + return self._K_chol diff --git a/GPy/inference/latent_function_inference/var_dtc.py b/GPy/inference/latent_function_inference/var_dtc.py new file mode 100644 index 00000000..d61e7f0f --- /dev/null +++ b/GPy/inference/latent_function_inference/var_dtc.py @@ -0,0 +1,249 @@ +# Copyright (c) 2012, GPy authors (see AUTHORS.txt). +# Licensed under the BSD 3-clause license (see LICENSE.txt) + +from posterior import Posterior +from ...util.linalg import mdot, jitchol, backsub_both_sides, tdot, dtrtrs, dtrtri, dpotri, dpotrs, symmetrify +from ...util import diag +from ...core.parameterization.variational import VariationalPosterior +import numpy as np +from . import LatentFunctionInference +log_2_pi = np.log(2*np.pi) +import logging, itertools +logger = logging.getLogger('vardtc') + +class VarDTC(LatentFunctionInference): + """ + An object for inference when the likelihood is Gaussian, but we want to do sparse inference. + + The function self.inference returns a Posterior object, which summarizes + the posterior. + + For efficiency, we sometimes work with the cholesky of Y*Y.T. To save repeatedly recomputing this, we cache it. + + """ + const_jitter = 1e-6 + def __init__(self, limit=1): + #self._YYTfactor_cache = caching.cache() + from ...util.caching import Cacher + self.limit = limit + self.get_trYYT = Cacher(self._get_trYYT, limit) + self.get_YYTfactor = Cacher(self._get_YYTfactor, limit) + + def set_limit(self, limit): + self.get_trYYT.limit = limit + self.get_YYTfactor.limit = limit + + def _get_trYYT(self, Y): + return np.einsum("ij,ij->", Y, Y) + # faster than, but same as: + # return np.sum(np.square(Y)) + + def __getstate__(self): + # has to be overridden, as Cacher objects cannot be pickled. + return self.limit + + def __setstate__(self, state): + # has to be overridden, as Cacher objects cannot be pickled. + self.limit = state + from ...util.caching import Cacher + self.get_trYYT = Cacher(self._get_trYYT, self.limit) + self.get_YYTfactor = Cacher(self._get_YYTfactor, self.limit) + + def _get_YYTfactor(self, Y): + """ + find a matrix L which satisfies LLT = YYT. + + Note that L may have fewer columns than Y. + """ + N, D = Y.shape + if (N>=D): + return Y.view(np.ndarray) + else: + return jitchol(tdot(Y)) + + def get_VVTfactor(self, Y, prec): + return Y * prec # TODO chache this, and make it effective + + + + def inference(self, kern, X, Z, likelihood, Y, Y_metadata=None, Lm=None, dL_dKmm=None): + + _, output_dim = Y.shape + uncertain_inputs = isinstance(X, VariationalPosterior) + + #see whether we've got a different noise variance for each datum + beta = 1./np.fmax(likelihood.gaussian_variance(Y_metadata), 1e-6) + # VVT_factor is a matrix such that tdot(VVT_factor) = VVT...this is for efficiency! + #self.YYTfactor = self.get_YYTfactor(Y) + #VVT_factor = self.get_VVTfactor(self.YYTfactor, beta) + het_noise = beta.size > 1 + if beta.ndim == 1: + beta = beta[:, None] + VVT_factor = beta*Y + #VVT_factor = beta*Y + trYYT = self.get_trYYT(Y) + + # do the inference: + num_inducing = Z.shape[0] + num_data = Y.shape[0] + # kernel computations, using BGPLVM notation + + Kmm = kern.K(Z).copy() + diag.add(Kmm, self.const_jitter) + if Lm is None: + Lm = jitchol(Kmm) + + # The rather complex computations of A, and the psi stats + if uncertain_inputs: + psi0 = kern.psi0(Z, X) + psi1 = kern.psi1(Z, X) + if het_noise: + psi2_beta = np.sum([kern.psi2(Z,X[i:i+1,:]) * beta_i for i,beta_i in enumerate(beta)],0) + else: + psi2_beta = kern.psi2(Z,X) * beta + LmInv = dtrtri(Lm) + A = LmInv.dot(psi2_beta.dot(LmInv.T)) + else: + psi0 = kern.Kdiag(X) + psi1 = kern.K(X, Z) + if het_noise: + tmp = psi1 * (np.sqrt(beta)) + else: + tmp = psi1 * (np.sqrt(beta)) + tmp, _ = dtrtrs(Lm, tmp.T, lower=1) + A = tdot(tmp) #print A.sum() + + # factor B + B = np.eye(num_inducing) + A + LB = jitchol(B) + psi1Vf = np.dot(psi1.T, VVT_factor) + # back substutue C into psi1Vf + tmp, _ = dtrtrs(Lm, psi1Vf, lower=1, trans=0) + _LBi_Lmi_psi1Vf, _ = dtrtrs(LB, tmp, lower=1, trans=0) + tmp, _ = dtrtrs(LB, _LBi_Lmi_psi1Vf, lower=1, trans=1) + Cpsi1Vf, _ = dtrtrs(Lm, tmp, lower=1, trans=1) + + # data fit and derivative of L w.r.t. Kmm + delit = tdot(_LBi_Lmi_psi1Vf) + data_fit = np.trace(delit) + DBi_plus_BiPBi = backsub_both_sides(LB, output_dim * np.eye(num_inducing) + delit) + if dL_dKmm is None: + delit = -0.5 * DBi_plus_BiPBi + delit += -0.5 * B * output_dim + delit += output_dim * np.eye(num_inducing) + # Compute dL_dKmm + dL_dKmm = backsub_both_sides(Lm, delit) + + # derivatives of L w.r.t. psi + dL_dpsi0, dL_dpsi1, dL_dpsi2 = _compute_dL_dpsi(num_inducing, num_data, output_dim, beta, Lm, + VVT_factor, Cpsi1Vf, DBi_plus_BiPBi, + psi1, het_noise, uncertain_inputs) + + # log marginal likelihood + log_marginal = _compute_log_marginal_likelihood(likelihood, num_data, output_dim, beta, het_noise, + psi0, A, LB, trYYT, data_fit, Y) + + #noise derivatives + dL_dR = _compute_dL_dR(likelihood, + het_noise, uncertain_inputs, LB, + _LBi_Lmi_psi1Vf, DBi_plus_BiPBi, Lm, A, + psi0, psi1, beta, + data_fit, num_data, output_dim, trYYT, Y, VVT_factor) + + dL_dthetaL = likelihood.exact_inference_gradients(dL_dR,Y_metadata) + + #put the gradients in the right places + if uncertain_inputs: + grad_dict = {'dL_dKmm': dL_dKmm, + 'dL_dpsi0':dL_dpsi0, + 'dL_dpsi1':dL_dpsi1, + 'dL_dpsi2':dL_dpsi2, + 'dL_dthetaL':dL_dthetaL} + else: + grad_dict = {'dL_dKmm': dL_dKmm, + 'dL_dKdiag':dL_dpsi0, + 'dL_dKnm':dL_dpsi1, + 'dL_dthetaL':dL_dthetaL} + + #get sufficient things for posterior prediction + #TODO: do we really want to do this in the loop? + if VVT_factor.shape[1] == Y.shape[1]: + woodbury_vector = Cpsi1Vf # == Cpsi1V + else: + print 'foobar' + import ipdb; ipdb.set_trace() + psi1V = np.dot(Y.T*beta, psi1).T + tmp, _ = dtrtrs(Lm, psi1V, lower=1, trans=0) + tmp, _ = dpotrs(LB, tmp, lower=1) + woodbury_vector, _ = dtrtrs(Lm, tmp, lower=1, trans=1) + Bi, _ = dpotri(LB, lower=1) + symmetrify(Bi) + Bi = -dpotri(LB, lower=1)[0] + diag.add(Bi, 1) + + woodbury_inv = backsub_both_sides(Lm, Bi) + + #construct a posterior object + post = Posterior(woodbury_inv=woodbury_inv, woodbury_vector=woodbury_vector, K=Kmm, mean=None, cov=None, K_chol=Lm) + return post, log_marginal, grad_dict + +def _compute_dL_dpsi(num_inducing, num_data, output_dim, beta, Lm, VVT_factor, Cpsi1Vf, DBi_plus_BiPBi, psi1, het_noise, uncertain_inputs): + dL_dpsi0 = -0.5 * output_dim * (beta* np.ones([num_data, 1])).flatten() + dL_dpsi1 = np.dot(VVT_factor, Cpsi1Vf.T) + dL_dpsi2_beta = 0.5 * backsub_both_sides(Lm, output_dim * np.eye(num_inducing) - DBi_plus_BiPBi) + if het_noise: + if uncertain_inputs: + dL_dpsi2 = beta[:, None] * dL_dpsi2_beta[None, :, :] + else: + dL_dpsi1 += 2.*np.dot(dL_dpsi2_beta, (psi1 * beta).T).T + dL_dpsi2 = None + else: + dL_dpsi2 = beta * dL_dpsi2_beta + if not uncertain_inputs: + # subsume back into psi1 (==Kmn) + dL_dpsi1 += 2.*np.dot(psi1, dL_dpsi2) + dL_dpsi2 = None + return dL_dpsi0, dL_dpsi1, dL_dpsi2 + + +def _compute_dL_dR(likelihood, het_noise, uncertain_inputs, LB, _LBi_Lmi_psi1Vf, DBi_plus_BiPBi, Lm, A, psi0, psi1, beta, data_fit, num_data, output_dim, trYYT, Y, VVT_factr=None): + # the partial derivative vector for the likelihood + if likelihood.size == 0: + # save computation here. + dL_dR = None + elif het_noise: + if uncertain_inputs: + raise NotImplementedError, "heteroscedatic derivates with uncertain inputs not implemented" + else: + #from ...util.linalg import chol_inv + #LBi = chol_inv(LB) + LBi, _ = dtrtrs(LB,np.eye(LB.shape[0])) + + Lmi_psi1, nil = dtrtrs(Lm, psi1.T, lower=1, trans=0) + _LBi_Lmi_psi1, _ = dtrtrs(LB, Lmi_psi1, lower=1, trans=0) + dL_dR = -0.5 * beta + 0.5 * VVT_factr**2 + dL_dR += 0.5 * output_dim * (psi0 - np.sum(Lmi_psi1**2,0))[:,None] * beta**2 + + dL_dR += 0.5*np.sum(mdot(LBi.T,LBi,Lmi_psi1)*Lmi_psi1,0)[:,None]*beta**2 + + dL_dR += -np.dot(_LBi_Lmi_psi1Vf.T,_LBi_Lmi_psi1).T * Y * beta**2 + dL_dR += 0.5*np.dot(_LBi_Lmi_psi1Vf.T,_LBi_Lmi_psi1).T**2 * beta**2 + else: + # likelihood is not heteroscedatic + dL_dR = -0.5 * num_data * output_dim * beta + 0.5 * trYYT * beta ** 2 + dL_dR += 0.5 * output_dim * (psi0.sum() * beta ** 2 - np.trace(A) * beta) + dL_dR += beta * (0.5 * np.sum(A * DBi_plus_BiPBi) - data_fit) + return dL_dR + +def _compute_log_marginal_likelihood(likelihood, num_data, output_dim, beta, het_noise, psi0, A, LB, trYYT, data_fit, Y): + #compute log marginal likelihood + if het_noise: + lik_1 = -0.5 * num_data * output_dim * np.log(2. * np.pi) + 0.5 * output_dim * np.sum(np.log(beta)) - 0.5 * np.sum(beta.ravel() * np.square(Y).sum(axis=-1)) + lik_2 = -0.5 * output_dim * (np.sum(beta.flatten() * psi0) - np.trace(A)) + else: + lik_1 = -0.5 * num_data * output_dim * (np.log(2. * np.pi) - np.log(beta)) - 0.5 * beta * trYYT + lik_2 = -0.5 * output_dim * (np.sum(beta * psi0) - np.trace(A)) + lik_3 = -output_dim * (np.sum(np.log(np.diag(LB)))) + lik_4 = 0.5 * data_fit + log_marginal = lik_1 + lik_2 + lik_3 + lik_4 + return log_marginal diff --git a/GPy/inference/latent_function_inference/var_dtc_parallel.py b/GPy/inference/latent_function_inference/var_dtc_parallel.py new file mode 100644 index 00000000..2816d578 --- /dev/null +++ b/GPy/inference/latent_function_inference/var_dtc_parallel.py @@ -0,0 +1,479 @@ +# Copyright (c) 2014, GPy authors (see AUTHORS.txt). +# Licensed under the BSD 3-clause license (see LICENSE.txt) + +from posterior import Posterior +from ...util.linalg import jitchol, backsub_both_sides, tdot, dtrtrs, dtrtri,pdinv +from ...util import diag +from ...core.parameterization.variational import VariationalPosterior +import numpy as np +from . import LatentFunctionInference +log_2_pi = np.log(2*np.pi) + +try: + from mpi4py import MPI +except: + pass + +class VarDTC_minibatch(LatentFunctionInference): + """ + An object for inference when the likelihood is Gaussian, but we want to do sparse inference. + + The function self.inference returns a Posterior object, which summarizes + the posterior. + + For efficiency, we sometimes work with the cholesky of Y*Y.T. To save repeatedly recomputing this, we cache it. + + """ + const_jitter = 1e-6 + def __init__(self, batchsize=None, limit=1, mpi_comm=None): + + self.batchsize = batchsize + self.mpi_comm = mpi_comm + self.limit = limit + + # Cache functions + from ...util.caching import Cacher + self.get_trYYT = Cacher(self._get_trYYT, limit) + self.get_YYTfactor = Cacher(self._get_YYTfactor, limit) + + self.midRes = {} + self.batch_pos = 0 # the starting position of the current mini-batch + self.Y_speedup = False # Replace Y with the cholesky factor of YY.T, but the computation of posterior object will be skipped. + + def __getstate__(self): + # has to be overridden, as Cacher objects cannot be pickled. + return self.batchsize, self.limit, self.Y_speedup + + def __setstate__(self, state): + # has to be overridden, as Cacher objects cannot be pickled. + self.batchsize, self.limit, self.Y_speedup = state + self.mpi_comm = None + self.midRes = {} + self.batch_pos = 0 + from ...util.caching import Cacher + self.get_trYYT = Cacher(self._get_trYYT, self.limit) + self.get_YYTfactor = Cacher(self._get_YYTfactor, self.limit) + + def set_limit(self, limit): + self.get_trYYT.limit = limit + self.get_YYTfactor.limit = limit + + def _get_trYYT(self, Y): + return np.sum(np.square(Y)) + + def _get_YYTfactor(self, Y): + """ + find a matrix L which satisfies LLT = YYT. + + Note that L may have fewer columns than Y. + """ + N, D = Y.shape + if (N>=D): + return Y.view(np.ndarray) + else: + return jitchol(tdot(Y)) + + def gatherPsiStat(self, kern, X, Z, Y, beta, uncertain_inputs): + + het_noise = beta.size > 1 + + assert beta.size == 1 + + trYYT = self.get_trYYT(Y) + if self.Y_speedup and not het_noise: + Y = self.get_YYTfactor(Y) + + num_inducing = Z.shape[0] + num_data, output_dim = Y.shape + batchsize = num_data if self.batchsize is None else self.batchsize + + psi2_full = np.zeros((num_inducing,num_inducing)) # MxM + psi1Y_full = np.zeros((output_dim,num_inducing)) # DxM + psi0_full = 0. + YRY_full = 0. + + for n_start in xrange(0,num_data,batchsize): + n_end = min(batchsize+n_start, num_data) + if batchsize==num_data: + Y_slice = Y + X_slice = X + else: + Y_slice = Y[n_start:n_end] + X_slice = X[n_start:n_end] + + if het_noise: + b = beta[n_start] + YRY_full += np.inner(Y_slice, Y_slice)*b + else: + b = beta + + if uncertain_inputs: + psi0 = kern.psi0(Z, X_slice) + psi1 = kern.psi1(Z, X_slice) + psi2_full += kern.psi2(Z, X_slice)*b + else: + psi0 = kern.Kdiag(X_slice) + psi1 = kern.K(X_slice, Z) + psi2_full += np.dot(psi1.T,psi1)*b + + psi0_full += psi0.sum()*b + psi1Y_full += np.dot(Y_slice.T,psi1)*b # DxM + + if not het_noise: + YRY_full = trYYT*beta + + if self.mpi_comm != None: + psi0_all = np.array(psi0_full) + psi1Y_all = psi1Y_full.copy() + psi2_all = psi2_full.copy() + YRY_all = np.array(YRY_full) + self.mpi_comm.Allreduce([psi0_full, MPI.DOUBLE], [psi0_all, MPI.DOUBLE]) + self.mpi_comm.Allreduce([psi1Y_full, MPI.DOUBLE], [psi1Y_all, MPI.DOUBLE]) + self.mpi_comm.Allreduce([psi2_full, MPI.DOUBLE], [psi2_all, MPI.DOUBLE]) + self.mpi_comm.Allreduce([YRY_full, MPI.DOUBLE], [YRY_all, MPI.DOUBLE]) + return psi0_all, psi1Y_all, psi2_all, YRY_all + + return psi0_full, psi1Y_full, psi2_full, YRY_full + + def inference_likelihood(self, kern, X, Z, likelihood, Y): + """ + The first phase of inference: + Compute: log-likelihood, dL_dKmm + + Cached intermediate results: Kmm, KmmInv, + """ + + num_data, output_dim = Y.shape + input_dim = Z.shape[0] + if self.mpi_comm != None: + num_data_all = np.array(num_data,dtype=np.int32) + self.mpi_comm.Allreduce([np.int32(num_data), MPI.INT], [num_data_all, MPI.INT]) + num_data = num_data_all + + if isinstance(X, VariationalPosterior): + uncertain_inputs = True + else: + uncertain_inputs = False + + #see whether we've got a different noise variance for each datum + beta = 1./np.fmax(likelihood.variance, 1e-6) + het_noise = beta.size > 1 + if het_noise: + self.batchsize = 1 + + psi0_full, psi1Y_full, psi2_full, YRY_full = self.gatherPsiStat(kern, X, Z, Y, beta, uncertain_inputs) + + #====================================================================== + # Compute Common Components + #====================================================================== + + Kmm = kern.K(Z).copy() + diag.add(Kmm, self.const_jitter) + Lm = jitchol(Kmm, maxtries=100) + + LmInvPsi2LmInvT = backsub_both_sides(Lm,psi2_full,transpose='right') + Lambda = np.eye(Kmm.shape[0])+LmInvPsi2LmInvT + LL = jitchol(Lambda, maxtries=100) + logdet_L = 2.*np.sum(np.log(np.diag(LL))) + b = dtrtrs(LL,dtrtrs(Lm,psi1Y_full.T)[0])[0] + bbt = np.square(b).sum() + v = dtrtrs(Lm,dtrtrs(LL,b,trans=1)[0],trans=1)[0] + + tmp = -backsub_both_sides(LL, tdot(b)+output_dim*np.eye(input_dim), transpose='left') + dL_dpsi2R = backsub_both_sides(Lm, tmp+output_dim*np.eye(input_dim), transpose='left')/2. + + # Cache intermediate results + self.midRes['dL_dpsi2R'] = dL_dpsi2R + self.midRes['v'] = v + + #====================================================================== + # Compute log-likelihood + #====================================================================== + if het_noise: + logL_R = -np.log(beta).sum() + else: + logL_R = -num_data*np.log(beta) + logL = -(output_dim*(num_data*log_2_pi+logL_R+psi0_full-np.trace(LmInvPsi2LmInvT))+YRY_full-bbt)/2.-output_dim*logdet_L/2. + + #====================================================================== + # Compute dL_dKmm + #====================================================================== + + dL_dKmm = dL_dpsi2R - output_dim*backsub_both_sides(Lm, LmInvPsi2LmInvT, transpose='left')/2. + + #====================================================================== + # Compute the Posterior distribution of inducing points p(u|Y) + #====================================================================== + + if not self.Y_speedup or het_noise: + wd_inv = backsub_both_sides(Lm, np.eye(input_dim)- backsub_both_sides(LL, np.identity(input_dim), transpose='left'), transpose='left') + post = Posterior(woodbury_inv=wd_inv, woodbury_vector=v, K=Kmm, mean=None, cov=None, K_chol=Lm) + else: + post = None + + #====================================================================== + # Compute dL_dthetaL for uncertian input and non-heter noise + #====================================================================== + + if not het_noise: + dL_dthetaL = (YRY_full*beta + beta*output_dim*psi0_full - num_data*output_dim*beta)/2. - beta*(dL_dpsi2R*psi2_full).sum() - beta*(v.T*psi1Y_full).sum() + self.midRes['dL_dthetaL'] = dL_dthetaL + + return logL, dL_dKmm, post + + def inference_minibatch(self, kern, X, Z, likelihood, Y): + """ + The second phase of inference: Computing the derivatives over a minibatch of Y + Compute: dL_dpsi0, dL_dpsi1, dL_dpsi2, dL_dthetaL + return a flag showing whether it reached the end of Y (isEnd) + """ + + num_data, output_dim = Y.shape + + if isinstance(X, VariationalPosterior): + uncertain_inputs = True + else: + uncertain_inputs = False + + #see whether we've got a different noise variance for each datum + beta = 1./np.fmax(likelihood.variance, 1e-6) + het_noise = beta.size > 1 + # VVT_factor is a matrix such that tdot(VVT_factor) = VVT...this is for efficiency! + #self.YYTfactor = beta*self.get_YYTfactor(Y) + if self.Y_speedup and not het_noise: + YYT_factor = self.get_YYTfactor(Y) + else: + YYT_factor = Y + + n_start = self.batch_pos + batchsize = num_data if self.batchsize is None else self.batchsize + n_end = min(batchsize+n_start, num_data) + if n_end==num_data: + isEnd = True + self.batch_pos = 0 + else: + isEnd = False + self.batch_pos = n_end + + if batchsize==num_data: + Y_slice = YYT_factor + X_slice =X + else: + Y_slice = YYT_factor[n_start:n_end] + X_slice = X[n_start:n_end] + + if not uncertain_inputs: + psi0 = kern.Kdiag(X_slice) + psi1 = kern.K(X_slice, Z) + psi2 = None + betapsi1 = np.einsum('n,nm->nm',beta,psi1) + elif het_noise: + psi0 = kern.psi0(Z, X_slice) + psi1 = kern.psi1(Z, X_slice) + psi2 = kern.psi2(Z, X_slice) + betapsi1 = np.einsum('n,nm->nm',beta,psi1) + + if het_noise: + beta = beta[n_start] # assuming batchsize==1 + + betaY = beta*Y_slice + + #====================================================================== + # Load Intermediate Results + #====================================================================== + + dL_dpsi2R = self.midRes['dL_dpsi2R'] + v = self.midRes['v'] + + #====================================================================== + # Compute dL_dpsi + #====================================================================== + + dL_dpsi0 = -output_dim * (beta * np.ones((n_end-n_start,)))/2. + + dL_dpsi1 = np.dot(betaY,v.T) + + if uncertain_inputs: + dL_dpsi2 = beta* dL_dpsi2R + else: + dL_dpsi1 += np.dot(betapsi1,dL_dpsi2R)*2. + dL_dpsi2 = None + + #====================================================================== + # Compute dL_dthetaL + #====================================================================== + + if het_noise: + if uncertain_inputs: + psiR = np.einsum('mo,mo->',dL_dpsi2R,psi2) + else: + psiR = np.einsum('nm,no,mo->',psi1,psi1,dL_dpsi2R) + + dL_dthetaL = ((np.square(betaY)).sum(axis=-1) + np.square(beta)*(output_dim*psi0)-output_dim*beta)/2. - np.square(beta)*psiR- (betaY*np.dot(betapsi1,v)).sum(axis=-1) + else: + if isEnd: + dL_dthetaL = self.midRes['dL_dthetaL'] + else: + dL_dthetaL = 0. + + if uncertain_inputs: + grad_dict = {'dL_dpsi0':dL_dpsi0, + 'dL_dpsi1':dL_dpsi1, + 'dL_dpsi2':dL_dpsi2, + 'dL_dthetaL':dL_dthetaL} + else: + grad_dict = {'dL_dKdiag':dL_dpsi0, + 'dL_dKnm':dL_dpsi1, + 'dL_dthetaL':dL_dthetaL} + + return isEnd, (n_start,n_end), grad_dict + + +def update_gradients(model, mpi_comm=None): + if mpi_comm == None: + Y = model.Y + X = model.X + else: + Y = model.Y_local + X = model.X[model.N_range[0]:model.N_range[1]] + + model._log_marginal_likelihood, dL_dKmm, model.posterior = model.inference_method.inference_likelihood(model.kern, X, model.Z, model.likelihood, Y) + + het_noise = model.likelihood.variance.size > 1 + + if het_noise: + dL_dthetaL = np.empty((model.Y.shape[0],)) + else: + dL_dthetaL = np.float64(0.) + + kern_grad = model.kern.gradient.copy() + kern_grad[:] = 0. + model.Z.gradient = 0. + + isEnd = False + while not isEnd: + isEnd, n_range, grad_dict = model.inference_method.inference_minibatch(model.kern, X, model.Z, model.likelihood, Y) + if isinstance(model.X, VariationalPosterior): + if (n_range[1]-n_range[0])==X.shape[0]: + X_slice = X + elif mpi_comm ==None: + X_slice = model.X[n_range[0]:n_range[1]] + else: + X_slice = model.X[model.N_range[0]+n_range[0]:model.N_range[0]+n_range[1]] + + #gradients w.r.t. kernel + model.kern.update_gradients_expectations(variational_posterior=X_slice, Z=model.Z, dL_dpsi0=grad_dict['dL_dpsi0'], dL_dpsi1=grad_dict['dL_dpsi1'], dL_dpsi2=grad_dict['dL_dpsi2']) + kern_grad += model.kern.gradient + + #gradients w.r.t. Z + model.Z.gradient += model.kern.gradients_Z_expectations( + dL_dpsi0=grad_dict['dL_dpsi0'], dL_dpsi1=grad_dict['dL_dpsi1'], dL_dpsi2=grad_dict['dL_dpsi2'], Z=model.Z, variational_posterior=X_slice) + + #gradients w.r.t. posterior parameters of X + X_grad = model.kern.gradients_qX_expectations(variational_posterior=X_slice, Z=model.Z, dL_dpsi0=grad_dict['dL_dpsi0'], dL_dpsi1=grad_dict['dL_dpsi1'], dL_dpsi2=grad_dict['dL_dpsi2']) + model.set_X_gradients(X_slice, X_grad) + + if het_noise: + dL_dthetaL[n_range[0]:n_range[1]] = grad_dict['dL_dthetaL'] + else: + dL_dthetaL += grad_dict['dL_dthetaL'] + + # Gather the gradients from multiple MPI nodes + if mpi_comm != None: + if het_noise: + raise "het_noise not implemented!" + kern_grad_all = kern_grad.copy() + Z_grad_all = model.Z.gradient.copy() + mpi_comm.Allreduce([kern_grad, MPI.DOUBLE], [kern_grad_all, MPI.DOUBLE]) + mpi_comm.Allreduce([model.Z.gradient, MPI.DOUBLE], [Z_grad_all, MPI.DOUBLE]) + kern_grad = kern_grad_all + model.Z.gradient = Z_grad_all + + #gradients w.r.t. kernel + model.kern.update_gradients_full(dL_dKmm, model.Z, None) + model.kern.gradient += kern_grad + + #gradients w.r.t. Z + model.Z.gradient += model.kern.gradients_X(dL_dKmm, model.Z) + + # Update Log-likelihood + KL_div = model.variational_prior.KL_divergence(X) + # update for the KL divergence + model.variational_prior.update_gradients_KL(X) + + if mpi_comm != None: + KL_div_all = np.array(KL_div) + mpi_comm.Allreduce([np.float64(KL_div), MPI.DOUBLE], [KL_div_all, MPI.DOUBLE]) + KL_div = KL_div_all + [mpi_comm.Allgatherv([pp.copy(), MPI.DOUBLE], [pa, (model.N_list*pa.shape[-1], None), MPI.DOUBLE]) for pp,pa in zip(model.get_X_gradients(X),model.get_X_gradients(model.X))] +# from ...models import SSGPLVM +# if isinstance(model, SSGPLVM): +# grad_pi = np.array(model.variational_prior.pi.gradient) +# mpi_comm.Allreduce([grad_pi.copy(), MPI.DOUBLE], [model.variational_prior.pi.gradient, MPI.DOUBLE]) + model._log_marginal_likelihood -= KL_div + + # dL_dthetaL + model.likelihood.update_gradients(dL_dthetaL) + +def update_gradients_sparsegp(model, mpi_comm=None): + if mpi_comm == None: + Y = model.Y + X = model.X + else: + Y = model.Y_local + X = model.X[model.N_range[0]:model.N_range[1]] + + model._log_marginal_likelihood, dL_dKmm, model.posterior = model.inference_method.inference_likelihood(model.kern, X, model.Z, model.likelihood, Y) + + het_noise = model.likelihood.variance.size > 1 + + if het_noise: + dL_dthetaL = np.empty((model.Y.shape[0],)) + else: + dL_dthetaL = np.float64(0.) + + kern_grad = model.kern.gradient.copy() + kern_grad[:] = 0. + model.Z.gradient = 0. + + isEnd = False + while not isEnd: + isEnd, n_range, grad_dict = model.inference_method.inference_minibatch(model.kern, X, model.Z, model.likelihood, Y) + + if (n_range[1]-n_range[0])==X.shape[0]: + X_slice = X + elif mpi_comm ==None: + X_slice = model.X[n_range[0]:n_range[1]] + else: + X_slice = model.X[model.N_range[0]+n_range[0]:model.N_range[0]+n_range[1]] + + model.kern.update_gradients_diag(grad_dict['dL_dKdiag'], X_slice) + kern_grad += model.kern.gradient + model.kern.update_gradients_full(grad_dict['dL_dKnm'], X_slice, model.Z) + kern_grad += model.kern.gradient + + model.Z.gradient += model.kern.gradients_X(grad_dict['dL_dKnm'].T, model.Z, X_slice) + + if het_noise: + dL_dthetaL[n_range[0]:n_range[1]] = grad_dict['dL_dthetaL'] + else: + dL_dthetaL += grad_dict['dL_dthetaL'] + + # Gather the gradients from multiple MPI nodes + if mpi_comm != None: + if het_noise: + raise "het_noise not implemented!" + kern_grad_all = kern_grad.copy() + Z_grad_all = model.Z.gradient.copy() + mpi_comm.Allreduce([kern_grad, MPI.DOUBLE], [kern_grad_all, MPI.DOUBLE]) + mpi_comm.Allreduce([model.Z.gradient, MPI.DOUBLE], [Z_grad_all, MPI.DOUBLE]) + kern_grad = kern_grad_all + model.Z.gradient = Z_grad_all + + model.kern.update_gradients_full(dL_dKmm, model.Z, None) + model.kern.gradient += kern_grad + + model.Z.gradient += model.kern.gradients_X(dL_dKmm, model.Z) + + # dL_dthetaL + model.likelihood.update_gradients(dL_dthetaL) diff --git a/GPy/inference/mcmc/__init__.py b/GPy/inference/mcmc/__init__.py new file mode 100644 index 00000000..956448d4 --- /dev/null +++ b/GPy/inference/mcmc/__init__.py @@ -0,0 +1 @@ +from hmc import HMC diff --git a/GPy/inference/mcmc/hmc.py b/GPy/inference/mcmc/hmc.py new file mode 100644 index 00000000..21bc13cc --- /dev/null +++ b/GPy/inference/mcmc/hmc.py @@ -0,0 +1,174 @@ +# ## Copyright (c) 2014, Zhenwen Dai +# Licensed under the BSD 3-clause license (see LICENSE.txt) + +import numpy as np + + +class HMC: + """ + An implementation of Hybrid Monte Carlo (HMC) for GPy models + + Initialize an object for HMC sampling. Note that the status of the model (model parameters) will be changed during sampling. + + :param model: the GPy model that will be sampled + :type model: GPy.core.Model + :param M: the mass matrix (an identity matrix by default) + :type M: numpy.ndarray + :param stepsize: the step size for HMC sampling + :type stepsize: float + """ + def __init__(self, model, M=None,stepsize=1e-1): + self.model = model + self.stepsize = stepsize + self.p = np.empty_like(model.optimizer_array.copy()) + if M is None: + self.M = np.eye(self.p.size) + else: + self.M = M + self.Minv = np.linalg.inv(self.M) + + def sample(self, num_samples=1000, hmc_iters=20): + """ + Sample the (unfixed) model parameters. + + :param num_samples: the number of samples to draw (1000 by default) + :type num_samples: int + :param hmc_iters: the number of leap-frog iterations (20 by default) + :type hmc_iters: int + :return: the list of parameters samples with the size N x P (N - the number of samples, P - the number of parameters to sample) + :rtype: numpy.ndarray + """ + params = np.empty((num_samples,self.p.size)) + for i in xrange(num_samples): + self.p[:] = np.random.multivariate_normal(np.zeros(self.p.size),self.M) + H_old = self._computeH() + theta_old = self.model.optimizer_array.copy() + params[i] = self.model.unfixed_param_array + #Matropolis + self._update(hmc_iters) + H_new = self._computeH() + + if H_old>H_new: + k = 1. + else: + k = np.exp(H_old-H_new) + if np.random.rand()H_new: + k = 1. + else: + k = np.exp(H_old-H_new) + if np.random.rand()pos: + pos = -1 + i += pos + self.model.optimizer_array = theta_buf[hmc_iters] + self.p[:] = -p_buf[hmc_iters] + else: + pos_new = pos-hmc_iters+i + self.model.optimizer_array = theta_buf[hmc_iters+pos_new] + self.p[:] = -p_buf[hmc_iters+pos_new] + break + else: + Hlist = range(hmc_iters+pos,hmc_iters+pos+self.groupsize) + + if self._testH(H_buf[Hlist]): + pos += -1 + else: + # Reverse the trajectory for the 2nd time + r = (hmc_iters - i)%((reversal[0]-pos)*2) + if r>(reversal[0]-pos): + pos_new = 2*reversal[0] - r - pos + else: + pos_new = pos + r + self.model.optimizer_array = theta_buf[hmc_iters+pos_new] + self.p[:] = p_buf[hmc_iters+pos_new] # the sign of momentum might be wrong! + break + + def _testH(self, Hlist): + Hstd = np.std(Hlist) + if Hstdself.Hstd_th[1]: + return False + else: + return True + + def _computeH(self,): + return self.model.objective_function()+self.p.size*np.log(2*np.pi)/2.+np.log(np.linalg.det(self.M))/2.+np.dot(self.p, np.dot(self.Minv,self.p[:,None]))/2. + diff --git a/GPy/inference/samplers.py b/GPy/inference/mcmc/samplers.py similarity index 97% rename from GPy/inference/samplers.py rename to GPy/inference/mcmc/samplers.py index c2b47bce..444d99d7 100644 --- a/GPy/inference/samplers.py +++ b/GPy/inference/mcmc/samplers.py @@ -1,10 +1,9 @@ -# Copyright (c) 2012, GPy authors (see AUTHORS.txt). +# ## Copyright (c) 2014, Zhenwen Dai # Licensed under the BSD 3-clause license (see LICENSE.txt) import numpy as np from scipy import linalg, optimize -import pylab as pb import Tango import sys import re @@ -80,6 +79,3 @@ class Metropolis_Hastings: fs.append(function(*args)) self.model._set_params(param)# reset model to starting state return fs - - - diff --git a/GPy/inference/optimization/__init__.py b/GPy/inference/optimization/__init__.py new file mode 100644 index 00000000..226fb1f5 --- /dev/null +++ b/GPy/inference/optimization/__init__.py @@ -0,0 +1 @@ +from optimization import * diff --git a/GPy/inference/conjugate_gradient_descent.py b/GPy/inference/optimization/conjugate_gradient_descent.py similarity index 98% rename from GPy/inference/conjugate_gradient_descent.py rename to GPy/inference/optimization/conjugate_gradient_descent.py index 9eabf5dd..dfc4a48d 100644 --- a/GPy/inference/conjugate_gradient_descent.py +++ b/GPy/inference/optimization/conjugate_gradient_descent.py @@ -1,9 +1,7 @@ -''' -Created on 24 Apr 2013 +# Copyright (c) 2012-2014, Max Zwiessele +# Licensed under the BSD 3-clause license (see LICENSE.txt) -@author: maxz -''' -from GPy.inference.gradient_descent_update_rules import FletcherReeves, \ +from gradient_descent_update_rules import FletcherReeves, \ PolakRibiere from Queue import Empty from multiprocessing import Value diff --git a/GPy/inference/gradient_descent_update_rules.py b/GPy/inference/optimization/gradient_descent_update_rules.py similarity index 93% rename from GPy/inference/gradient_descent_update_rules.py rename to GPy/inference/optimization/gradient_descent_update_rules.py index 1c14ed63..9536549c 100644 --- a/GPy/inference/gradient_descent_update_rules.py +++ b/GPy/inference/optimization/gradient_descent_update_rules.py @@ -1,8 +1,6 @@ -''' -Created on 24 Apr 2013 +# Copyright (c) 2012-2014, Max Zwiessele +# Licensed under the BSD 3-clause license (see LICENSE.txt) -@author: maxz -''' import numpy class GDUpdateRule(): diff --git a/GPy/inference/optimization.py b/GPy/inference/optimization/optimization.py similarity index 83% rename from GPy/inference/optimization.py rename to GPy/inference/optimization/optimization.py index 0ace8ba9..d537150e 100644 --- a/GPy/inference/optimization.py +++ b/GPy/inference/optimization/optimization.py @@ -1,7 +1,6 @@ -# Copyright (c) 2012, GPy authors (see AUTHORS.txt). +# Copyright (c) 2012-2014, GPy authors (see AUTHORS.txt). # Licensed under the BSD 3-clause license (see LICENSE.txt) -import pylab as pb import datetime as dt from scipy import optimize from warnings import warn @@ -57,13 +56,14 @@ class Optimizer(): raise NotImplementedError, "this needs to be implemented to use the optimizer class" def plot(self): - if self.trace == None: - print "No trace present so I can't plot it. Please check that the optimizer actually supplies a trace." - else: - pb.figure() - pb.plot(self.trace) - pb.xlabel('Iteration') - pb.ylabel('f(x)') + """ + See GPy.plotting.matplot_dep.inference_plots + """ + import sys + assert "matplotlib" in sys.modules, "matplotlib package has not been imported." + from ...plotting.matplot_dep import inference_plots + inference_plots.plot_optimizer(self) + def __str__(self): diagnostics = "Optimizer: \t\t\t\t %s\n" % self.opt_name @@ -118,7 +118,7 @@ class opt_lbfgsb(Optimizer): assert f_fp != None, "BFGS requires f_fp" if self.messages: - iprint = 0 + iprint = 1 else: iprint = -1 @@ -126,29 +126,18 @@ class opt_lbfgsb(Optimizer): if self.xtol is not None: print "WARNING: l-bfgs-b doesn't have an xtol arg, so I'm going to ignore it" if self.ftol is not None: - opt_dict['ftol'] = self.ftol - # print "WARNING: l-bfgs-b doesn't have an ftol arg, so I'm going to ignore it" + print "WARNING: l-bfgs-b doesn't have an ftol arg, so I'm going to ignore it" if self.gtol is not None: - opt_dict['gtol'] = self.gtol + opt_dict['pgtol'] = self.gtol if self.bfgs_factor is not None: opt_dict['factr'] = self.bfgs_factor - opt_dict['iprint'] = iprint - opt_dict['maxiter'] = self.max_iters - opt_dict['disp'] = self.messages - #dict(maxiter=self.max_iters, disp=self.messages, iprint=iprint, ftol=self.ftol, gtol=self.gtol) - - opt_result = optimize.minimize(f_fp, self.x_init, method='L-BFGS-B', jac=True, options=opt_dict) - #opt_result = optimize.fmin_l_bfgs_b(f_fp, self.x_init, iprint=iprint, - # maxfun=self.max_iters, **opt_dict) - #self.x_opt = opt_result[0] - #self.f_opt = f_fp(self.x_opt)[0] - #self.funct_eval = opt_result[2]['funcalls'] - #self.status = rcstrings[opt_result[2]['warnflag']] - self.x_opt = opt_result.x - self.status = opt_result.success - self.funct_eval = opt_result.nfev - self.f_opt = opt_result.fun - self.opt_result = opt_result + + opt_result = optimize.fmin_l_bfgs_b(f_fp, self.x_init, iprint=iprint, + maxfun=self.max_iters, **opt_dict) + self.x_opt = opt_result[0] + self.f_opt = f_fp(self.x_opt)[0] + self.funct_eval = opt_result[2]['funcalls'] + self.status = rcstrings[opt_result[2]['warnflag']] class opt_simplex(Optimizer): def __init__(self, *args, **kwargs): @@ -236,13 +225,11 @@ class opt_SCG(Optimizer): self.status = opt_result[3] def get_optimizer(f_min): - from sgd import opt_SGD - optimizers = {'fmin_tnc': opt_tnc, 'simplex': opt_simplex, 'lbfgsb': opt_lbfgsb, 'scg': opt_SCG, - 'sgd': opt_SGD} + } if rasm_available: optimizers['rasmussen'] = opt_rasm diff --git a/GPy/inference/scg.py b/GPy/inference/optimization/scg.py similarity index 92% rename from GPy/inference/scg.py rename to GPy/inference/optimization/scg.py index 1cd4d6e4..7efeb781 100644 --- a/GPy/inference/scg.py +++ b/GPy/inference/optimization/scg.py @@ -28,11 +28,11 @@ import sys def print_out(len_maxiters, fnow, current_grad, beta, iteration): print '\r', - print '{0:>0{mi}g} {1:> 12e} {2:> 12e} {3:> 12e}'.format(iteration, float(fnow), float(beta), float(current_grad), mi=len_maxiters), # print 'Iteration:', iteration, ' Objective:', fnow, ' Scale:', beta, '\r', + print '{0:>0{mi}g} {1:> 12e} {2:< 12.6e} {3:> 12e}'.format(iteration, float(fnow), float(beta), float(current_grad), mi=len_maxiters), # print 'Iteration:', iteration, ' Objective:', fnow, ' Scale:', beta, '\r', sys.stdout.flush() def exponents(fnow, current_grad): - exps = [np.abs(fnow), current_grad] + exps = [np.abs(np.float(fnow)), current_grad] return np.sign(exps) * np.log10(exps).astype(int) def SCG(f, gradf, x, optargs=(), maxiters=500, max_f_eval=np.inf, display=True, xtol=None, ftol=None, gtol=None): @@ -56,13 +56,13 @@ def SCG(f, gradf, x, optargs=(), maxiters=500, max_f_eval=np.inf, display=True, if gtol is None: gtol = 1e-5 - sigma0 = 1.0e-8 + sigma0 = 1.0e-7 fold = f(x, *optargs) # Initial function value. function_eval = 1 fnow = fold gradnew = gradf(x, *optargs) # Initial gradient. - if any(np.isnan(gradnew)): - raise UnexpectedInfOrNan, "Gradient contribution resulted in a NaN value" + #if any(np.isnan(gradnew)): + # raise UnexpectedInfOrNan, "Gradient contribution resulted in a NaN value" current_grad = np.dot(gradnew, gradnew) gradold = gradnew.copy() d = -gradnew # Initial search direction. @@ -168,13 +168,13 @@ def SCG(f, gradf, x, optargs=(), maxiters=500, max_f_eval=np.inf, display=True, if Delta < 0.25: beta = min(4.0 * beta, betamax) if Delta > 0.75: - beta = max(0.5 * beta, betamin) + beta = max(0.25 * beta, betamin) # Update search direction using Polak-Ribiere formula, or re-start # in direction of negative gradient after nparams steps. if nsuccess == x.size: d = -gradnew -# beta = 1. # TODO: betareset!! + beta = 1. # This is not in the original paper nsuccess = 0 elif success: Gamma = np.dot(gradold - gradnew, gradnew) / (mu) diff --git a/GPy/inference/optimization/stochastics.py b/GPy/inference/optimization/stochastics.py new file mode 100644 index 00000000..dc71d539 --- /dev/null +++ b/GPy/inference/optimization/stochastics.py @@ -0,0 +1,56 @@ +# Copyright (c) 2012-2014, Max Zwiessele +# Licensed under the BSD 3-clause license (see LICENSE.txt) + +class StochasticStorage(object): + ''' + This is a container for holding the stochastic parameters, + such as subset indices or step length and so on. + ''' + def __init__(self, model): + """ + Initialize this stochastic container using the given model + """ + + def do_stochastics(self): + """ + Update the internal state to the next batch of the stochastic + descent algorithm. + """ + pass + + def reset(self): + """ + Reset the state of this stochastics generator. + """ + +class SparseGPMissing(StochasticStorage): + def __init__(self, model, batchsize=1): + """ + Here we want to loop over all dimensions everytime. + Thus, we can just make sure the loop goes over self.d every + time. + """ + self.d = xrange(model.Y_normalized.shape[1]) + +class SparseGPStochastics(StochasticStorage): + """ + For the sparse gp we need to store the dimension we are in, + and the indices corresponding to those + """ + def __init__(self, model, batchsize=1): + self.batchsize = batchsize + self.output_dim = model.Y.shape[1] + self.reset() + self.do_stochastics() + + def do_stochastics(self): + if self.batchsize == 1: + self.current_dim = (self.current_dim+1)%self.output_dim + self.d = [self.current_dim] + else: + import numpy as np + self.d = np.random.choice(self.output_dim, size=self.batchsize, replace=False) + + def reset(self): + self.current_dim = -1 + self.d = None diff --git a/GPy/inference/sgd.py b/GPy/inference/sgd.py deleted file mode 100644 index 5cd144e8..00000000 --- a/GPy/inference/sgd.py +++ /dev/null @@ -1,355 +0,0 @@ -import numpy as np -import scipy as sp -import scipy.sparse -from optimization import Optimizer -from scipy import linalg, optimize -import pylab as plt -import copy, sys, pickle - -class opt_SGD(Optimizer): - """ - Optimize using stochastic gradient descent. - - :param Model: reference to the Model object - :param iterations: number of iterations - :param learning_rate: learning rate - :param momentum: momentum - - """ - - def __init__(self, start, iterations = 10, learning_rate = 1e-4, momentum = 0.9, model = None, messages = False, batch_size = 1, self_paced = False, center = True, iteration_file = None, learning_rate_adaptation=None, actual_iter=None, schedule=None, **kwargs): - self.opt_name = "Stochastic Gradient Descent" - - self.Model = model - self.iterations = iterations - self.momentum = momentum - self.learning_rate = learning_rate - self.x_opt = None - self.f_opt = None - self.messages = messages - self.batch_size = batch_size - self.self_paced = self_paced - self.center = center - self.param_traces = [('noise',[])] - self.iteration_file = iteration_file - self.learning_rate_adaptation = learning_rate_adaptation - self.actual_iter = actual_iter - if self.learning_rate_adaptation != None: - if self.learning_rate_adaptation == 'annealing': - self.learning_rate_0 = self.learning_rate - else: - self.learning_rate_0 = self.learning_rate.mean() - - self.schedule = schedule - # if len([p for p in self.model.kern.parts if p.name == 'bias']) == 1: - # self.param_traces.append(('bias',[])) - # if len([p for p in self.model.kern.parts if p.name == 'linear']) == 1: - # self.param_traces.append(('linear',[])) - # if len([p for p in self.model.kern.parts if p.name == 'rbf']) == 1: - # self.param_traces.append(('rbf_var',[])) - - self.param_traces = dict(self.param_traces) - self.fopt_trace = [] - - num_params = len(self.Model._get_params()) - if isinstance(self.learning_rate, float): - self.learning_rate = np.ones((num_params,)) * self.learning_rate - - assert (len(self.learning_rate) == num_params), "there must be one learning rate per parameter" - - def __str__(self): - status = "\nOptimizer: \t\t\t %s\n" % self.opt_name - status += "f(x_opt): \t\t\t %.4f\n" % self.f_opt - status += "Number of iterations: \t\t %d\n" % self.iterations - status += "Learning rate: \t\t\t max %.3f, min %.3f\n" % (self.learning_rate.max(), self.learning_rate.min()) - status += "Momentum: \t\t\t %.3f\n" % self.momentum - status += "Batch size: \t\t\t %d\n" % self.batch_size - status += "Time elapsed: \t\t\t %s\n" % self.time - return status - - def plot_traces(self): - plt.figure() - plt.subplot(211) - plt.title('Parameters') - for k in self.param_traces.keys(): - plt.plot(self.param_traces[k], label=k) - plt.legend(loc=0) - plt.subplot(212) - plt.title('Objective function') - plt.plot(self.fopt_trace) - - - def non_null_samples(self, data): - return (np.isnan(data).sum(axis=1) == 0) - - def check_for_missing(self, data): - if sp.sparse.issparse(self.Model.likelihood.Y): - return True - else: - return np.isnan(data).sum() > 0 - - def subset_parameter_vector(self, x, samples, param_shapes): - subset = np.array([], dtype = int) - x = np.arange(0, len(x)) - i = 0 - - for s in param_shapes: - N, input_dim = s - X = x[i:i+N*input_dim].reshape(N, input_dim) - X = X[samples] - subset = np.append(subset, X.flatten()) - i += N*input_dim - - subset = np.append(subset, x[i:]) - - return subset - - def shift_constraints(self, j): - - constrained_indices = copy.deepcopy(self.Model.constrained_indices) - - for c, constraint in enumerate(constrained_indices): - mask = (np.ones_like(constrained_indices[c]) == 1) - for i in range(len(constrained_indices[c])): - pos = np.where(j == constrained_indices[c][i])[0] - if len(pos) == 1: - self.Model.constrained_indices[c][i] = pos - else: - mask[i] = False - - self.Model.constrained_indices[c] = self.Model.constrained_indices[c][mask] - return constrained_indices - # back them up - # bounded_i = copy.deepcopy(self.Model.constrained_bounded_indices) - # bounded_l = copy.deepcopy(self.Model.constrained_bounded_lowers) - # bounded_u = copy.deepcopy(self.Model.constrained_bounded_uppers) - - # for b in range(len(bounded_i)): # for each group of constraints - # for bc in range(len(bounded_i[b])): - # pos = np.where(j == bounded_i[b][bc])[0] - # if len(pos) == 1: - # pos2 = np.where(self.Model.constrained_bounded_indices[b] == bounded_i[b][bc])[0][0] - # self.Model.constrained_bounded_indices[b][pos2] = pos[0] - # else: - # if len(self.Model.constrained_bounded_indices[b]) == 1: - # # if it's the last index to be removed - # # the logic here is just a mess. If we remove the last one, then all the - # # b-indices change and we have to iterate through everything to find our - # # current index. Can't deal with this right now. - # raise NotImplementedError - - # else: # just remove it from the indices - # mask = self.Model.constrained_bounded_indices[b] != bc - # self.Model.constrained_bounded_indices[b] = self.Model.constrained_bounded_indices[b][mask] - - - # # here we shif the positive constraints. We cycle through each positive - # # constraint - # positive = self.Model.constrained_positive_indices.copy() - # mask = (np.ones_like(positive) == 1) - # for p in range(len(positive)): - # # we now check whether the constrained index appears in the j vector - # # (the vector of the "active" indices) - # pos = np.where(j == self.Model.constrained_positive_indices[p])[0] - # if len(pos) == 1: - # self.Model.constrained_positive_indices[p] = pos - # else: - # mask[p] = False - # self.Model.constrained_positive_indices = self.Model.constrained_positive_indices[mask] - - # return (bounded_i, bounded_l, bounded_u), positive - - def restore_constraints(self, c):#b, p): - # self.Model.constrained_bounded_indices = b[0] - # self.Model.constrained_bounded_lowers = b[1] - # self.Model.constrained_bounded_uppers = b[2] - # self.Model.constrained_positive_indices = p - self.Model.constrained_indices = c - - def get_param_shapes(self, N = None, input_dim = None): - model_name = self.Model.__class__.__name__ - if model_name == 'GPLVM': - return [(N, input_dim)] - if model_name == 'Bayesian_GPLVM': - return [(N, input_dim), (N, input_dim)] - else: - raise NotImplementedError - - def step_with_missing_data(self, f_fp, X, step, shapes): - N, input_dim = X.shape - - if not sp.sparse.issparse(self.Model.likelihood.Y): - Y = self.Model.likelihood.Y - samples = self.non_null_samples(self.Model.likelihood.Y) - self.Model.N = samples.sum() - Y = Y[samples] - else: - samples = self.Model.likelihood.Y.nonzero()[0] - self.Model.N = len(samples) - Y = np.asarray(self.Model.likelihood.Y[samples].todense(), dtype = np.float64) - - if self.Model.N == 0 or Y.std() == 0.0: - return 0, step, self.Model.N - - self.Model.likelihood._offset = Y.mean() - self.Model.likelihood._scale = Y.std() - self.Model.likelihood.set_data(Y) - # self.Model.likelihood.V = self.Model.likelihood.Y*self.Model.likelihood.precision - - sigma = self.Model.likelihood._variance - self.Model.likelihood._variance = None # invalidate cache - self.Model.likelihood._set_params(sigma) - - - j = self.subset_parameter_vector(self.x_opt, samples, shapes) - self.Model.X = X[samples] - - model_name = self.Model.__class__.__name__ - - if model_name == 'Bayesian_GPLVM': - self.Model.likelihood.YYT = np.dot(self.Model.likelihood.Y, self.Model.likelihood.Y.T) - self.Model.likelihood.trYYT = np.trace(self.Model.likelihood.YYT) - - ci = self.shift_constraints(j) - f, fp = f_fp(self.x_opt[j]) - - step[j] = self.momentum * step[j] + self.learning_rate[j] * fp - self.x_opt[j] -= step[j] - self.restore_constraints(ci) - - self.Model.grads[j] = fp - # restore likelihood _offset and _scale, otherwise when we call set_data(y) on - # the next feature, it will get normalized with the mean and std of this one. - self.Model.likelihood._offset = 0 - self.Model.likelihood._scale = 1 - - return f, step, self.Model.N - - def adapt_learning_rate(self, t, D): - if self.learning_rate_adaptation == 'adagrad': - if t > 0: - g_k = self.Model.grads - self.s_k += np.square(g_k) - t0 = 100.0 - self.learning_rate = 0.1/(t0 + np.sqrt(self.s_k)) - - import pdb; pdb.set_trace() - else: - self.learning_rate = np.zeros_like(self.learning_rate) - self.s_k = np.zeros_like(self.x_opt) - - elif self.learning_rate_adaptation == 'annealing': - #self.learning_rate = self.learning_rate_0/(1+float(t+1)/10) - self.learning_rate = np.ones_like(self.learning_rate) * self.schedule[t] - - - elif self.learning_rate_adaptation == 'semi_pesky': - if self.Model.__class__.__name__ == 'Bayesian_GPLVM': - g_t = self.Model.grads - if t == 0: - self.hbar_t = 0.0 - self.tau_t = 100.0 - self.gbar_t = 0.0 - - self.gbar_t = (1-1/self.tau_t)*self.gbar_t + 1/self.tau_t * g_t - self.hbar_t = (1-1/self.tau_t)*self.hbar_t + 1/self.tau_t * np.dot(g_t.T, g_t) - self.learning_rate = np.ones_like(self.learning_rate)*(np.dot(self.gbar_t.T, self.gbar_t) / self.hbar_t) - tau_t = self.tau_t*(1-self.learning_rate) + 1 - - - def opt(self, f_fp=None, f=None, fp=None): - self.x_opt = self.Model._get_params_transformed() - self.grads = [] - - X, Y = self.Model.X.copy(), self.Model.likelihood.Y.copy() - - self.Model.likelihood.YYT = 0 - self.Model.likelihood.trYYT = 0 - self.Model.likelihood._offset = 0.0 - self.Model.likelihood._scale = 1.0 - - N, input_dim = self.Model.X.shape - D = self.Model.likelihood.Y.shape[1] - num_params = self.Model._get_params() - self.trace = [] - missing_data = self.check_for_missing(self.Model.likelihood.Y) - - step = np.zeros_like(num_params) - for it in range(self.iterations): - if self.actual_iter != None: - it = self.actual_iter - - self.Model.grads = np.zeros_like(self.x_opt) # TODO this is ugly - - if it == 0 or self.self_paced is False: - features = np.random.permutation(Y.shape[1]) - else: - features = np.argsort(NLL) - - b = len(features)/self.batch_size - features = [features[i::b] for i in range(b)] - NLL = [] - import pylab as plt - for count, j in enumerate(features): - self.Model.input_dim = len(j) - self.Model.likelihood.input_dim = len(j) - self.Model.likelihood.set_data(Y[:, j]) - # self.Model.likelihood.V = self.Model.likelihood.Y*self.Model.likelihood.precision - - sigma = self.Model.likelihood._variance - self.Model.likelihood._variance = None # invalidate cache - self.Model.likelihood._set_params(sigma) - - if missing_data: - shapes = self.get_param_shapes(N, input_dim) - f, step, Nj = self.step_with_missing_data(f_fp, X, step, shapes) - else: - self.Model.likelihood.YYT = np.dot(self.Model.likelihood.Y, self.Model.likelihood.Y.T) - self.Model.likelihood.trYYT = np.trace(self.Model.likelihood.YYT) - Nj = N - f, fp = f_fp(self.x_opt) - self.Model.grads = fp.copy() - step = self.momentum * step + self.learning_rate * fp - self.x_opt -= step - - if self.messages == 2: - noise = self.Model.likelihood._variance - status = "evaluating {feature: 5d}/{tot: 5d} \t f: {f: 2.3f} \t non-missing: {nm: 4d}\t noise: {noise: 2.4f}\r".format(feature = count, tot = len(features), f = f, nm = Nj, noise = noise) - sys.stdout.write(status) - sys.stdout.flush() - self.param_traces['noise'].append(noise) - - self.adapt_learning_rate(it+count, D) - NLL.append(f) - self.fopt_trace.append(NLL[-1]) - # fig = plt.figure('traces') - # plt.clf() - # plt.plot(self.param_traces['noise']) - - # for k in self.param_traces.keys(): - # self.param_traces[k].append(self.Model.get(k)[0]) - self.grads.append(self.Model.grads.tolist()) - # should really be a sum(), but earlier samples in the iteration will have a very crappy ll - self.f_opt = np.mean(NLL) - self.Model.N = N - self.Model.X = X - self.Model.input_dim = D - self.Model.likelihood.N = N - self.Model.likelihood.input_dim = D - self.Model.likelihood.Y = Y - sigma = self.Model.likelihood._variance - self.Model.likelihood._variance = None # invalidate cache - self.Model.likelihood._set_params(sigma) - - self.trace.append(self.f_opt) - if self.iteration_file is not None: - f = open(self.iteration_file + "iteration%d.pickle" % it, 'w') - data = [self.x_opt, self.fopt_trace, self.param_traces] - pickle.dump(data, f) - f.close() - - if self.messages != 0: - sys.stdout.write('\r' + ' '*len(status)*2 + ' \r') - status = "SGD Iteration: {0: 3d}/{1: 3d} f: {2: 2.3f} max eta: {3: 1.5f}\n".format(it+1, self.iterations, self.f_opt, self.learning_rate.max()) - sys.stdout.write(status) - sys.stdout.flush() diff --git a/GPy/installation.cfg b/GPy/installation.cfg new file mode 100644 index 00000000..901a7ef5 --- /dev/null +++ b/GPy/installation.cfg @@ -0,0 +1,2 @@ +# This is the local installation configuration file for GPy + diff --git a/GPy/kern/__init__.py b/GPy/kern/__init__.py index eb4076c3..c400277c 100644 --- a/GPy/kern/__init__.py +++ b/GPy/kern/__init__.py @@ -1,9 +1,19 @@ -# Copyright (c) 2012, 2013 GPy authors (see AUTHORS.txt). -# Licensed under the BSD 3-clause license (see LICENSE.txt) +from _src.kern import Kern +from _src.rbf import RBF +from _src.linear import Linear, LinearFull +from _src.static import Bias, White +from _src.brownian import Brownian +from _src.stationary import Exponential, OU, Matern32, Matern52, ExpQuad, RatQuad, Cosine +from _src.mlp import MLP +from _src.periodic import PeriodicExponential, PeriodicMatern32, PeriodicMatern52 +from _src.independent_outputs import IndependentOutputs, Hierarchical +from _src.coregionalize import Coregionalize +from _src.ODE_UY import ODE_UY +from _src.ODE_UYC import ODE_UYC +from _src.ODE_st import ODE_st +from _src.ODE_t import ODE_t +from _src.poly import Poly + +from _src.trunclinear import TruncLinear,TruncLinear_inf +from _src.splitKern import SplitKern,DiffGenomeKern -from constructors import * -try: - from constructors import rbf_sympy, sympykern # these depend on sympy -except: - pass -from kern import * diff --git a/GPy/kern/_src/ODE_UY.py b/GPy/kern/_src/ODE_UY.py new file mode 100644 index 00000000..b4a2b42d --- /dev/null +++ b/GPy/kern/_src/ODE_UY.py @@ -0,0 +1,282 @@ +# Copyright (c) 2013, GPy authors (see AUTHORS.txt). +# Licensed under the BSD 3-clause license (see LICENSE.txt) + +from kern import Kern +from ...core.parameterization import Param +from ...core.parameterization.transformations import Logexp +import numpy as np +from independent_outputs import index_to_slices + +class ODE_UY(Kern): + def __init__(self, input_dim, variance_U=3., variance_Y=1., lengthscale_U=1., lengthscale_Y=1., active_dims=None, name='ode_uy'): + assert input_dim ==2, "only defined for 2 input dims" + super(ODE_UY, self).__init__(input_dim, active_dims, name) + + self.variance_Y = Param('variance_Y', variance_Y, Logexp()) + self.variance_U = Param('variance_U', variance_Y, Logexp()) + self.lengthscale_Y = Param('lengthscale_Y', lengthscale_Y, Logexp()) + self.lengthscale_U = Param('lengthscale_U', lengthscale_Y, Logexp()) + + self.link_parameters(self.variance_Y, self.variance_U, self.lengthscale_Y, self.lengthscale_U) + + def K(self, X, X2=None): + # model : a * dy/dt + b * y = U + #lu=sqrt(3)/theta1 ly=1/theta2 theta2= a/b :thetay sigma2=1/(2ab) :sigmay + + X,slices = X[:,:-1],index_to_slices(X[:,-1]) + if X2 is None: + X2,slices2 = X,slices + K = np.zeros((X.shape[0], X.shape[0])) + else: + X2,slices2 = X2[:,:-1],index_to_slices(X2[:,-1]) + K = np.zeros((X.shape[0], X2.shape[0])) + + + #rdist = X[:,0][:,None] - X2[:,0][:,None].T + rdist = X - X2.T + ly=1/self.lengthscale_Y + lu=np.sqrt(3)/self.lengthscale_U + #iu=self.input_lengthU #dimention of U + Vu=self.variance_U + Vy=self.variance_Y + #Vy=ly/2 + #stop + + + # kernel for kuu matern3/2 + kuu = lambda dist:Vu * (1 + lu* np.abs(dist)) * np.exp(-lu * np.abs(dist)) + + # kernel for kyy + k1 = lambda dist:np.exp(-ly*np.abs(dist))*(2*lu+ly)/(lu+ly)**2 + k2 = lambda dist:(np.exp(-lu*dist)*(ly-2*lu+lu*ly*dist-lu**2*dist) + np.exp(-ly*dist)*(2*lu-ly) ) / (ly-lu)**2 + k3 = lambda dist:np.exp(-lu*dist) * ( (1+lu*dist)/(lu+ly) + (lu)/(lu+ly)**2 ) + kyy = lambda dist:Vu*Vy*(k1(dist) + k2(dist) + k3(dist)) + + + # cross covariance function + kyu3 = lambda dist:np.exp(-lu*dist)/(lu+ly)*(1+lu*(dist+1/(lu+ly))) + #kyu3 = lambda dist: 0 + + k1cros = lambda dist:np.exp(ly*dist)/(lu-ly) * ( 1- np.exp( (lu-ly)*dist) + lu* ( dist*np.exp( (lu-ly)*dist ) + (1- np.exp( (lu-ly)*dist ) ) /(lu-ly) ) ) + #k1cros = lambda dist:0 + + k2cros = lambda dist:np.exp(ly*dist)*( 1/(lu+ly) + lu/(lu+ly)**2 ) + #k2cros = lambda dist:0 + + Vyu=np.sqrt(Vy*ly*2) + + # cross covariance kuy + kuyp = lambda dist:Vu*Vyu*(kyu3(dist)) #t>0 kuy + kuyn = lambda dist:Vu*Vyu*(k1cros(dist)+k2cros(dist)) #t<0 kuy + # cross covariance kyu + kyup = lambda dist:Vu*Vyu*(k1cros(-dist)+k2cros(-dist)) #t>0 kyu + kyun = lambda dist:Vu*Vyu*(kyu3(-dist)) #t<0 kyu + + + for i, s1 in enumerate(slices): + for j, s2 in enumerate(slices2): + for ss1 in s1: + for ss2 in s2: + if i==0 and j==0: + K[ss1,ss2] = kuu(np.abs(rdist[ss1,ss2])) + elif i==0 and j==1: + #K[ss1,ss2]= np.where( rdist[ss1,ss2]>0 , kuyp(np.abs(rdist[ss1,ss2])), kuyn(np.abs(rdist[ss1,ss2]) ) ) + K[ss1,ss2]= np.where( rdist[ss1,ss2]>0 , kuyp(rdist[ss1,ss2]), kuyn(rdist[ss1,ss2] ) ) + elif i==1 and j==1: + K[ss1,ss2] = kyy(np.abs(rdist[ss1,ss2])) + else: + #K[ss1,ss2]= 0 + #K[ss1,ss2]= np.where( rdist[ss1,ss2]>0 , kyup(np.abs(rdist[ss1,ss2])), kyun(np.abs(rdist[ss1,ss2]) ) ) + K[ss1,ss2] = np.where( rdist[ss1,ss2]>0 , kyup(rdist[ss1,ss2]), kyun(rdist[ss1,ss2] ) ) + return K + + + + def Kdiag(self, X): + """Compute the diagonal of the covariance matrix associated to X.""" + Kdiag = np.zeros(X.shape[0]) + ly=1/self.lengthscale_Y + lu=np.sqrt(3)/self.lengthscale_U + + Vu = self.variance_U + Vy=self.variance_Y + + k1 = (2*lu+ly)/(lu+ly)**2 + k2 = (ly-2*lu + 2*lu-ly ) / (ly-lu)**2 + k3 = 1/(lu+ly) + (lu)/(lu+ly)**2 + + slices = index_to_slices(X[:,-1]) + + for i, ss1 in enumerate(slices): + for s1 in ss1: + if i==0: + Kdiag[s1]+= self.variance_U + elif i==1: + Kdiag[s1]+= Vu*Vy*(k1+k2+k3) + else: + raise ValueError, "invalid input/output index" + #Kdiag[slices[0][0]]+= self.variance_U #matern32 diag + #Kdiag[slices[1][0]]+= self.variance_U*self.variance_Y*(k1+k2+k3) # diag + return Kdiag + + + def update_gradients_full(self, dL_dK, X, X2=None): + """derivative of the covariance matrix with respect to the parameters.""" + X,slices = X[:,:-1],index_to_slices(X[:,-1]) + if X2 is None: + X2,slices2 = X,slices + else: + X2,slices2 = X2[:,:-1],index_to_slices(X2[:,-1]) + #rdist = X[:,0][:,None] - X2[:,0][:,None].T + + rdist = X - X2.T + ly=1/self.lengthscale_Y + lu=np.sqrt(3)/self.lengthscale_U + + Vu=self.variance_U + Vy=self.variance_Y + Vyu = np.sqrt(Vy*ly*2) + dVdly = 0.5/np.sqrt(ly)*np.sqrt(2*Vy) + dVdVy = 0.5/np.sqrt(Vy)*np.sqrt(2*ly) + + rd=rdist.shape + dktheta1 = np.zeros(rd) + dktheta2 = np.zeros(rd) + dkUdvar = np.zeros(rd) + dkYdvar = np.zeros(rd) + + # dk dtheta for UU + UUdtheta1 = lambda dist: np.exp(-lu* dist)*dist + (-dist)*np.exp(-lu* dist)*(1+lu*dist) + UUdtheta2 = lambda dist: 0 + #UUdvar = lambda dist: (1 + lu*dist)*np.exp(-lu*dist) + UUdvar = lambda dist: (1 + lu* np.abs(dist)) * np.exp(-lu * np.abs(dist)) + + # dk dtheta for YY + + dk1theta1 = lambda dist: np.exp(-ly*dist)*2*(-lu)/(lu+ly)**3 + + dk2theta1 = lambda dist: (1.0)*( + np.exp(-lu*dist)*dist*(-ly+2*lu-lu*ly*dist+dist*lu**2)*(ly-lu)**(-2) + np.exp(-lu*dist)*(-2+ly*dist-2*dist*lu)*(ly-lu)**(-2) + +np.exp(-dist*lu)*(ly-2*lu+ly*lu*dist-dist*lu**2)*2*(ly-lu)**(-3) + +np.exp(-dist*ly)*2*(ly-lu)**(-2) + +np.exp(-dist*ly)*2*(2*lu-ly)*(ly-lu)**(-3) + ) + + dk3theta1 = lambda dist: np.exp(-dist*lu)*(lu+ly)**(-2)*((2*lu+ly+dist*lu**2+lu*ly*dist)*(-dist-2/(lu+ly))+2+2*lu*dist+ly*dist) + + #dktheta1 = lambda dist: self.variance_U*self.variance_Y*(dk1theta1+dk2theta1+dk3theta1) + + + + + dk1theta2 = lambda dist: np.exp(-ly*dist) * ((lu+ly)**(-2)) * ( (-dist)*(2*lu+ly) + 1 + (-2)*(2*lu+ly)/(lu+ly) ) + + dk2theta2 =lambda dist: 1*( + np.exp(-dist*lu)*(ly-lu)**(-2) * ( 1+lu*dist+(-2)*(ly-2*lu+lu*ly*dist-dist*lu**2)*(ly-lu)**(-1) ) + +np.exp(-dist*ly)*(ly-lu)**(-2) * ( (-dist)*(2*lu-ly) -1+(2*lu-ly)*(-2)*(ly-lu)**(-1) ) + ) + + dk3theta2 = lambda dist: np.exp(-dist*lu) * (-3*lu-ly-dist*lu**2-lu*ly*dist)/(lu+ly)**3 + + #dktheta2 = lambda dist: self.variance_U*self.variance_Y*(dk1theta2 + dk2theta2 +dk3theta2) + + # kyy kernel + + k1 = lambda dist: np.exp(-ly*dist)*(2*lu+ly)/(lu+ly)**2 + k2 = lambda dist: (np.exp(-lu*dist)*(ly-2*lu+lu*ly*dist-lu**2*dist) + np.exp(-ly*dist)*(2*lu-ly) ) / (ly-lu)**2 + k3 = lambda dist: np.exp(-lu*dist) * ( (1+lu*dist)/(lu+ly) + (lu)/(lu+ly)**2 ) + #dkdvar = k1+k2+k3 + + + + # cross covariance function + kyu3 = lambda dist:np.exp(-lu*dist)/(lu+ly)*(1+lu*(dist+1/(lu+ly))) + + k1cros = lambda dist:np.exp(ly*dist)/(lu-ly) * ( 1- np.exp( (lu-ly)*dist) + lu* ( dist*np.exp( (lu-ly)*dist ) + (1- np.exp( (lu-ly)*dist ) ) /(lu-ly) ) ) + + k2cros = lambda dist:np.exp(ly*dist)*( 1/(lu+ly) + lu/(lu+ly)**2 ) + # cross covariance kuy + kuyp = lambda dist:(kyu3(dist)) #t>0 kuy + kuyn = lambda dist:(k1cros(dist)+k2cros(dist)) #t<0 kuy + # cross covariance kyu + kyup = lambda dist:(k1cros(-dist)+k2cros(-dist)) #t>0 kyu + kyun = lambda dist:(kyu3(-dist)) #t<0 kyu + + # dk dtheta for UY + + + dkyu3dtheta2 = lambda dist: np.exp(-lu*dist) * ( (-1)*(lu+ly)**(-2)*(1+lu*dist+lu*(lu+ly)**(-1)) + (lu+ly)**(-1)*(-lu)*(lu+ly)**(-2) ) + dkyu3dtheta1 = lambda dist: np.exp(-lu*dist)*(lu+ly)**(-1)* ( (-dist)*(1+dist*lu+lu*(lu+ly)**(-1)) -\ + (lu+ly)**(-1)*(1+dist*lu+lu*(lu+ly)**(-1)) +dist+(lu+ly)**(-1)-lu*(lu+ly)**(-2) ) + + dkcros2dtheta1 = lambda dist: np.exp(ly*dist)* ( -(ly+lu)**(-2) + (ly+lu)**(-2) + (-2)*lu*(lu+ly)**(-3) ) + dkcros2dtheta2 = lambda dist: np.exp(ly*dist)*dist* ( (ly+lu)**(-1) + lu*(lu+ly)**(-2) ) + \ + np.exp(ly*dist)*( -(lu+ly)**(-2) + lu*(-2)*(lu+ly)**(-3) ) + + dkcros1dtheta1 = lambda dist: np.exp(ly*dist)*( -(lu-ly)**(-2)*( 1-np.exp((lu-ly)*dist) + lu*dist*np.exp((lu-ly)*dist)+ \ + lu*(1-np.exp((lu-ly)*dist))/(lu-ly) ) + (lu-ly)**(-1)*( -np.exp( (lu-ly)*dist )*dist + dist*np.exp( (lu-ly)*dist)+\ + lu*dist**2*np.exp((lu-ly)*dist)+(1-np.exp((lu-ly)*dist))/(lu-ly) - lu*np.exp((lu-ly)*dist)*dist/(lu-ly) -\ + lu*(1-np.exp((lu-ly)*dist))/(lu-ly)**2 ) ) + + dkcros1dtheta2 = lambda t: np.exp(ly*t)*t/(lu-ly)*( 1-np.exp((lu-ly)*t) +lu*t*np.exp((lu-ly)*t)+\ + lu*(1-np.exp((lu-ly)*t))/(lu-ly) )+\ + np.exp(ly*t)/(lu-ly)**2* ( 1-np.exp((lu-ly)*t) +lu*t*np.exp((lu-ly)*t) + lu*( 1-np.exp((lu-ly)*t) )/(lu-ly) )+\ + np.exp(ly*t)/(lu-ly)*( np.exp((lu-ly)*t)*t -lu*t*t*np.exp((lu-ly)*t) +lu*t*np.exp((lu-ly)*t)/(lu-ly)+\ + lu*( 1-np.exp((lu-ly)*t) )/(lu-ly)**2 ) + + dkuypdtheta1 = lambda dist:(dkyu3dtheta1(dist)) #t>0 kuy + dkuyndtheta1 = lambda dist:(dkcros1dtheta1(dist)+dkcros2dtheta1(dist)) #t<0 kuy + # cross covariance kyu + dkyupdtheta1 = lambda dist:(dkcros1dtheta1(-dist)+dkcros2dtheta1(-dist)) #t>0 kyu + dkyundtheta1 = lambda dist:(dkyu3dtheta1(-dist)) #t<0 kyu + + dkuypdtheta2 = lambda dist:(dkyu3dtheta2(dist)) #t>0 kuy + dkuyndtheta2 = lambda dist:(dkcros1dtheta2(dist)+dkcros2dtheta2(dist)) #t<0 kuy + # cross covariance kyu + dkyupdtheta2 = lambda dist:(dkcros1dtheta2(-dist)+dkcros2dtheta2(-dist)) #t>0 kyu + dkyundtheta2 = lambda dist:(dkyu3dtheta2(-dist)) #t<0 kyu + + + for i, s1 in enumerate(slices): + for j, s2 in enumerate(slices2): + for ss1 in s1: + for ss2 in s2: + if i==0 and j==0: + #target[ss1,ss2] = kuu(np.abs(rdist[ss1,ss2])) + dktheta1[ss1,ss2] = Vu*UUdtheta1(np.abs(rdist[ss1,ss2])) + dktheta2[ss1,ss2] = 0 + dkUdvar[ss1,ss2] = UUdvar(np.abs(rdist[ss1,ss2])) + dkYdvar[ss1,ss2] = 0 + elif i==0 and j==1: + ########target[ss1,ss2] = np.where( rdist[ss1,ss2]>0 , kuyp(np.abs(rdist[ss1,ss2])), kuyn(np.abs(rdist[s1[0],s2[0]]) ) ) + #np.where( rdist[ss1,ss2]>0 , kuyp(np.abs(rdist[ss1,ss2])), kuyn(np.abs(rdist[s1[0],s2[0]]) ) ) + #dktheta1[ss1,ss2] = np.where( rdist[ss1,ss2]>0 , self.variance_U*self.variance_Y*dkcrtheta1(np.abs(rdist[ss1,ss2])) ,self.variance_U*self.variance_Y*(dk1theta1(np.abs(rdist[ss1,ss2]))+dk2theta1(np.abs(rdist[ss1,ss2]))) ) + #dktheta2[ss1,ss2] = np.where( rdist[ss1,ss2]>0 , self.variance_U*self.variance_Y*dkcrtheta2(np.abs(rdist[ss1,ss2])) ,self.variance_U*self.variance_Y*(dk1theta2(np.abs(rdist[ss1,ss2]))+dk2theta2(np.abs(rdist[ss1,ss2]))) ) + dktheta1[ss1,ss2] = np.where( rdist[ss1,ss2]>0 , Vu*Vyu*dkuypdtheta1(rdist[ss1,ss2]),Vu*Vyu*dkuyndtheta1(rdist[ss1,ss2]) ) + dkUdvar[ss1,ss2] = np.where( rdist[ss1,ss2]>0 , Vyu*kuyp(rdist[ss1,ss2]), Vyu* kuyn(rdist[ss1,ss2]) ) + dktheta2[ss1,ss2] = np.where( rdist[ss1,ss2]>0 , Vu*Vyu*dkuypdtheta2(rdist[ss1,ss2])+Vu*dVdly*kuyp(rdist[ss1,ss2]),Vu*Vyu*dkuyndtheta2(rdist[ss1,ss2])+Vu*dVdly*kuyn(rdist[ss1,ss2]) ) + dkYdvar[ss1,ss2] = np.where( rdist[ss1,ss2]>0 , Vu*dVdVy*kuyp(rdist[ss1,ss2]), Vu*dVdVy* kuyn(rdist[ss1,ss2]) ) + elif i==1 and j==1: + #target[ss1,ss2] = kyy(np.abs(rdist[ss1,ss2])) + dktheta1[ss1,ss2] = self.variance_U*self.variance_Y*(dk1theta1(np.abs(rdist[ss1,ss2]))+dk2theta1(np.abs(rdist[ss1,ss2]))+dk3theta1(np.abs(rdist[ss1,ss2]))) + dktheta2[ss1,ss2] = self.variance_U*self.variance_Y*(dk1theta2(np.abs(rdist[ss1,ss2])) + dk2theta2(np.abs(rdist[ss1,ss2])) +dk3theta2(np.abs(rdist[ss1,ss2]))) + dkUdvar[ss1,ss2] = self.variance_Y*(k1(np.abs(rdist[ss1,ss2]))+k2(np.abs(rdist[ss1,ss2]))+k3(np.abs(rdist[ss1,ss2])) ) + dkYdvar[ss1,ss2] = self.variance_U*(k1(np.abs(rdist[ss1,ss2]))+k2(np.abs(rdist[ss1,ss2]))+k3(np.abs(rdist[ss1,ss2])) ) + else: + #######target[ss1,ss2] = np.where( rdist[ss1,ss2]>0 , kyup(np.abs(rdist[ss1,ss2])), kyun(np.abs(rdist[s1[0],s2[0]]) ) ) + #dktheta1[ss1,ss2] = np.where( rdist[ss1,ss2]>0 ,self.variance_U*self.variance_Y*(dk1theta1(np.abs(rdist[ss1,ss2]))+dk2theta1(np.abs(rdist[ss1,ss2]))) , self.variance_U*self.variance_Y*dkcrtheta1(np.abs(rdist[ss1,ss2])) ) + #dktheta2[ss1,ss2] = np.where( rdist[ss1,ss2]>0 ,self.variance_U*self.variance_Y*(dk1theta2(np.abs(rdist[ss1,ss2]))+dk2theta2(np.abs(rdist[ss1,ss2]))) , self.variance_U*self.variance_Y*dkcrtheta2(np.abs(rdist[ss1,ss2])) ) + dktheta1[ss1,ss2] = np.where( rdist[ss1,ss2]>0 , Vu*Vyu*dkyupdtheta1(rdist[ss1,ss2]),Vu*Vyu*dkyundtheta1(rdist[ss1,ss2]) ) + dkUdvar[ss1,ss2] = np.where( rdist[ss1,ss2]>0 , Vyu*kyup(rdist[ss1,ss2]),Vyu*kyun(rdist[ss1,ss2])) + dktheta2[ss1,ss2] = np.where( rdist[ss1,ss2]>0 , Vu*Vyu*dkyupdtheta2(rdist[ss1,ss2])+Vu*dVdly*kyup(rdist[ss1,ss2]),Vu*Vyu*dkyundtheta2(rdist[ss1,ss2])+Vu*dVdly*kyun(rdist[ss1,ss2]) ) + dkYdvar[ss1,ss2] = np.where( rdist[ss1,ss2]>0 , Vu*dVdVy*kyup(rdist[ss1,ss2]), Vu*dVdVy*kyun(rdist[ss1,ss2])) + + #stop + self.variance_U.gradient = np.sum(dkUdvar * dL_dK) # Vu + + self.variance_Y.gradient = np.sum(dkYdvar * dL_dK) # Vy + + self.lengthscale_U.gradient = np.sum(dktheta1*(-np.sqrt(3)*self.lengthscale_U**(-2))* dL_dK) #lu + + self.lengthscale_Y.gradient = np.sum(dktheta2*(-self.lengthscale_Y**(-2)) * dL_dK) #ly + diff --git a/GPy/kern/_src/ODE_UYC.py b/GPy/kern/_src/ODE_UYC.py new file mode 100644 index 00000000..1722d2e1 --- /dev/null +++ b/GPy/kern/_src/ODE_UYC.py @@ -0,0 +1,290 @@ +# Copyright (c) 2013, GPy authors (see AUTHORS.txt). +# Licensed under the BSD 3-clause license (see LICENSE.txt) + +from kern import Kern +from ...core.parameterization import Param +from ...core.parameterization.transformations import Logexp +import numpy as np +from independent_outputs import index_to_slices + +class ODE_UYC(Kern): + def __init__(self, input_dim, variance_U=3., variance_Y=1., lengthscale_U=1., lengthscale_Y=1., ubias =1. ,active_dims=None, name='ode_uyc'): + assert input_dim ==2, "only defined for 2 input dims" + super(ODE_UYC, self).__init__(input_dim, active_dims, name) + + self.variance_Y = Param('variance_Y', variance_Y, Logexp()) + self.variance_U = Param('variance_U', variance_U, Logexp()) + self.lengthscale_Y = Param('lengthscale_Y', lengthscale_Y, Logexp()) + self.lengthscale_U = Param('lengthscale_U', lengthscale_U, Logexp()) + self.ubias = Param('ubias', ubias, Logexp()) + + self.add_parameters(self.variance_Y, self.variance_U, self.lengthscale_Y, self.lengthscale_U, self.ubias) + + def K(self, X, X2=None): + # model : a * dy/dt + b * y = U + #lu=sqrt(3)/theta1 ly=1/theta2 theta2= a/b :thetay sigma2=1/(2ab) :sigmay + + X,slices = X[:,:-1],index_to_slices(X[:,-1]) + if X2 is None: + X2,slices2 = X,slices + K = np.zeros((X.shape[0], X.shape[0])) + else: + X2,slices2 = X2[:,:-1],index_to_slices(X2[:,-1]) + K = np.zeros((X.shape[0], X2.shape[0])) + + #stop + #rdist = X[:,0][:,None] - X2[:,0][:,None].T + rdist = X - X2.T + ly=1/self.lengthscale_Y + lu=np.sqrt(3)/self.lengthscale_U + #iu=self.input_lengthU #dimention of U + Vu=self.variance_U + Vy=self.variance_Y + #Vy=ly/2 + #stop + + + # kernel for kuu matern3/2 + kuu = lambda dist:Vu * (1 + lu* np.abs(dist)) * np.exp(-lu * np.abs(dist)) +self.ubias + + # kernel for kyy + k1 = lambda dist:np.exp(-ly*np.abs(dist))*(2*lu+ly)/(lu+ly)**2 + k2 = lambda dist:(np.exp(-lu*dist)*(ly-2*lu+lu*ly*dist-lu**2*dist) + np.exp(-ly*dist)*(2*lu-ly) ) / (ly-lu)**2 + k3 = lambda dist:np.exp(-lu*dist) * ( (1+lu*dist)/(lu+ly) + (lu)/(lu+ly)**2 ) + kyy = lambda dist:Vu*Vy*(k1(dist) + k2(dist) + k3(dist)) + + + # cross covariance function + kyu3 = lambda dist:np.exp(-lu*dist)/(lu+ly)*(1+lu*(dist+1/(lu+ly))) + #kyu3 = lambda dist: 0 + + k1cros = lambda dist:np.exp(ly*dist)/(lu-ly) * ( 1- np.exp( (lu-ly)*dist) + lu* ( dist*np.exp( (lu-ly)*dist ) + (1- np.exp( (lu-ly)*dist ) ) /(lu-ly) ) ) + #k1cros = lambda dist:0 + + k2cros = lambda dist:np.exp(ly*dist)*( 1/(lu+ly) + lu/(lu+ly)**2 ) + #k2cros = lambda dist:0 + + Vyu=np.sqrt(Vy*ly*2) + + # cross covariance kuy + kuyp = lambda dist:Vu*Vyu*(kyu3(dist)) #t>0 kuy + kuyn = lambda dist:Vu*Vyu*(k1cros(dist)+k2cros(dist)) #t<0 kuy + # cross covariance kyu + kyup = lambda dist:Vu*Vyu*(k1cros(-dist)+k2cros(-dist)) #t>0 kyu + kyun = lambda dist:Vu*Vyu*(kyu3(-dist)) #t<0 kyu + + + for i, s1 in enumerate(slices): + for j, s2 in enumerate(slices2): + for ss1 in s1: + for ss2 in s2: + if i==0 and j==0: + K[ss1,ss2] = kuu(np.abs(rdist[ss1,ss2])) + elif i==0 and j==1: + #K[ss1,ss2]= np.where( rdist[ss1,ss2]>0 , kuyp(np.abs(rdist[ss1,ss2])), kuyn(np.abs(rdist[ss1,ss2]) ) ) + K[ss1,ss2]= np.where( rdist[ss1,ss2]>0 , kuyp(rdist[ss1,ss2]), kuyn(rdist[ss1,ss2] ) ) + elif i==1 and j==1: + K[ss1,ss2] = kyy(np.abs(rdist[ss1,ss2])) + else: + #K[ss1,ss2]= 0 + #K[ss1,ss2]= np.where( rdist[ss1,ss2]>0 , kyup(np.abs(rdist[ss1,ss2])), kyun(np.abs(rdist[ss1,ss2]) ) ) + K[ss1,ss2] = np.where( rdist[ss1,ss2]>0 , kyup(rdist[ss1,ss2]), kyun(rdist[ss1,ss2] ) ) + return K + + + + def Kdiag(self, X): + """Compute the diagonal of the covariance matrix associated to X.""" + Kdiag = np.zeros(X.shape[0]) + ly=1/self.lengthscale_Y + lu=np.sqrt(3)/self.lengthscale_U + + Vu = self.variance_U + Vy=self.variance_Y + + k1 = (2*lu+ly)/(lu+ly)**2 + k2 = (ly-2*lu + 2*lu-ly ) / (ly-lu)**2 + k3 = 1/(lu+ly) + (lu)/(lu+ly)**2 + + slices = index_to_slices(X[:,-1]) + + for i, ss1 in enumerate(slices): + for s1 in ss1: + if i==0: + Kdiag[s1]+= self.variance_U + self.ubias + elif i==1: + Kdiag[s1]+= Vu*Vy*(k1+k2+k3) + else: + raise ValueError, "invalid input/output index" + #Kdiag[slices[0][0]]+= self.variance_U #matern32 diag + #Kdiag[slices[1][0]]+= self.variance_U*self.variance_Y*(k1+k2+k3) # diag + return Kdiag + + + def update_gradients_full(self, dL_dK, X, X2=None): + """derivative of the covariance matrix with respect to the parameters.""" + X,slices = X[:,:-1],index_to_slices(X[:,-1]) + if X2 is None: + X2,slices2 = X,slices + else: + X2,slices2 = X2[:,:-1],index_to_slices(X2[:,-1]) + #rdist = X[:,0][:,None] - X2[:,0][:,None].T + + rdist = X - X2.T + ly=1/self.lengthscale_Y + lu=np.sqrt(3)/self.lengthscale_U + + Vu=self.variance_U + Vy=self.variance_Y + Vyu = np.sqrt(Vy*ly*2) + dVdly = 0.5/np.sqrt(ly)*np.sqrt(2*Vy) + dVdVy = 0.5/np.sqrt(Vy)*np.sqrt(2*ly) + + rd=rdist.shape[0] + dktheta1 = np.zeros([rd,rd]) + dktheta2 = np.zeros([rd,rd]) + dkUdvar = np.zeros([rd,rd]) + dkYdvar = np.zeros([rd,rd]) + + dkdubias = np.zeros([rd,rd]) + + # dk dtheta for UU + UUdtheta1 = lambda dist: np.exp(-lu* dist)*dist + (-dist)*np.exp(-lu* dist)*(1+lu*dist) + UUdtheta2 = lambda dist: 0 + #UUdvar = lambda dist: (1 + lu*dist)*np.exp(-lu*dist) + UUdvar = lambda dist: (1 + lu* np.abs(dist)) * np.exp(-lu * np.abs(dist)) + + # dk dtheta for YY + + dk1theta1 = lambda dist: np.exp(-ly*dist)*2*(-lu)/(lu+ly)**3 + + dk2theta1 = lambda dist: (1.0)*( + np.exp(-lu*dist)*dist*(-ly+2*lu-lu*ly*dist+dist*lu**2)*(ly-lu)**(-2) + np.exp(-lu*dist)*(-2+ly*dist-2*dist*lu)*(ly-lu)**(-2) + +np.exp(-dist*lu)*(ly-2*lu+ly*lu*dist-dist*lu**2)*2*(ly-lu)**(-3) + +np.exp(-dist*ly)*2*(ly-lu)**(-2) + +np.exp(-dist*ly)*2*(2*lu-ly)*(ly-lu)**(-3) + ) + + dk3theta1 = lambda dist: np.exp(-dist*lu)*(lu+ly)**(-2)*((2*lu+ly+dist*lu**2+lu*ly*dist)*(-dist-2/(lu+ly))+2+2*lu*dist+ly*dist) + + #dktheta1 = lambda dist: self.variance_U*self.variance_Y*(dk1theta1+dk2theta1+dk3theta1) + + + + + dk1theta2 = lambda dist: np.exp(-ly*dist) * ((lu+ly)**(-2)) * ( (-dist)*(2*lu+ly) + 1 + (-2)*(2*lu+ly)/(lu+ly) ) + + dk2theta2 =lambda dist: 1*( + np.exp(-dist*lu)*(ly-lu)**(-2) * ( 1+lu*dist+(-2)*(ly-2*lu+lu*ly*dist-dist*lu**2)*(ly-lu)**(-1) ) + +np.exp(-dist*ly)*(ly-lu)**(-2) * ( (-dist)*(2*lu-ly) -1+(2*lu-ly)*(-2)*(ly-lu)**(-1) ) + ) + + dk3theta2 = lambda dist: np.exp(-dist*lu) * (-3*lu-ly-dist*lu**2-lu*ly*dist)/(lu+ly)**3 + + #dktheta2 = lambda dist: self.variance_U*self.variance_Y*(dk1theta2 + dk2theta2 +dk3theta2) + + # kyy kernel + + k1 = lambda dist: np.exp(-ly*dist)*(2*lu+ly)/(lu+ly)**2 + k2 = lambda dist: (np.exp(-lu*dist)*(ly-2*lu+lu*ly*dist-lu**2*dist) + np.exp(-ly*dist)*(2*lu-ly) ) / (ly-lu)**2 + k3 = lambda dist: np.exp(-lu*dist) * ( (1+lu*dist)/(lu+ly) + (lu)/(lu+ly)**2 ) + #dkdvar = k1+k2+k3 + + + + # cross covariance function + kyu3 = lambda dist:np.exp(-lu*dist)/(lu+ly)*(1+lu*(dist+1/(lu+ly))) + + k1cros = lambda dist:np.exp(ly*dist)/(lu-ly) * ( 1- np.exp( (lu-ly)*dist) + lu* ( dist*np.exp( (lu-ly)*dist ) + (1- np.exp( (lu-ly)*dist ) ) /(lu-ly) ) ) + + k2cros = lambda dist:np.exp(ly*dist)*( 1/(lu+ly) + lu/(lu+ly)**2 ) + # cross covariance kuy + kuyp = lambda dist:(kyu3(dist)) #t>0 kuy + kuyn = lambda dist:(k1cros(dist)+k2cros(dist)) #t<0 kuy + # cross covariance kyu + kyup = lambda dist:(k1cros(-dist)+k2cros(-dist)) #t>0 kyu + kyun = lambda dist:(kyu3(-dist)) #t<0 kyu + + # dk dtheta for UY + + + dkyu3dtheta2 = lambda dist: np.exp(-lu*dist) * ( (-1)*(lu+ly)**(-2)*(1+lu*dist+lu*(lu+ly)**(-1)) + (lu+ly)**(-1)*(-lu)*(lu+ly)**(-2) ) + dkyu3dtheta1 = lambda dist: np.exp(-lu*dist)*(lu+ly)**(-1)* ( (-dist)*(1+dist*lu+lu*(lu+ly)**(-1)) -\ + (lu+ly)**(-1)*(1+dist*lu+lu*(lu+ly)**(-1)) +dist+(lu+ly)**(-1)-lu*(lu+ly)**(-2) ) + + dkcros2dtheta1 = lambda dist: np.exp(ly*dist)* ( -(ly+lu)**(-2) + (ly+lu)**(-2) + (-2)*lu*(lu+ly)**(-3) ) + dkcros2dtheta2 = lambda dist: np.exp(ly*dist)*dist* ( (ly+lu)**(-1) + lu*(lu+ly)**(-2) ) + \ + np.exp(ly*dist)*( -(lu+ly)**(-2) + lu*(-2)*(lu+ly)**(-3) ) + + dkcros1dtheta1 = lambda dist: np.exp(ly*dist)*( -(lu-ly)**(-2)*( 1-np.exp((lu-ly)*dist) + lu*dist*np.exp((lu-ly)*dist)+ \ + lu*(1-np.exp((lu-ly)*dist))/(lu-ly) ) + (lu-ly)**(-1)*( -np.exp( (lu-ly)*dist )*dist + dist*np.exp( (lu-ly)*dist)+\ + lu*dist**2*np.exp((lu-ly)*dist)+(1-np.exp((lu-ly)*dist))/(lu-ly) - lu*np.exp((lu-ly)*dist)*dist/(lu-ly) -\ + lu*(1-np.exp((lu-ly)*dist))/(lu-ly)**2 ) ) + + dkcros1dtheta2 = lambda t: np.exp(ly*t)*t/(lu-ly)*( 1-np.exp((lu-ly)*t) +lu*t*np.exp((lu-ly)*t)+\ + lu*(1-np.exp((lu-ly)*t))/(lu-ly) )+\ + np.exp(ly*t)/(lu-ly)**2* ( 1-np.exp((lu-ly)*t) +lu*t*np.exp((lu-ly)*t) + lu*( 1-np.exp((lu-ly)*t) )/(lu-ly) )+\ + np.exp(ly*t)/(lu-ly)*( np.exp((lu-ly)*t)*t -lu*t*t*np.exp((lu-ly)*t) +lu*t*np.exp((lu-ly)*t)/(lu-ly)+\ + lu*( 1-np.exp((lu-ly)*t) )/(lu-ly)**2 ) + + dkuypdtheta1 = lambda dist:(dkyu3dtheta1(dist)) #t>0 kuy + dkuyndtheta1 = lambda dist:(dkcros1dtheta1(dist)+dkcros2dtheta1(dist)) #t<0 kuy + # cross covariance kyu + dkyupdtheta1 = lambda dist:(dkcros1dtheta1(-dist)+dkcros2dtheta1(-dist)) #t>0 kyu + dkyundtheta1 = lambda dist:(dkyu3dtheta1(-dist)) #t<0 kyu + + dkuypdtheta2 = lambda dist:(dkyu3dtheta2(dist)) #t>0 kuy + dkuyndtheta2 = lambda dist:(dkcros1dtheta2(dist)+dkcros2dtheta2(dist)) #t<0 kuy + # cross covariance kyu + dkyupdtheta2 = lambda dist:(dkcros1dtheta2(-dist)+dkcros2dtheta2(-dist)) #t>0 kyu + dkyundtheta2 = lambda dist:(dkyu3dtheta2(-dist)) #t<0 kyu + + + for i, s1 in enumerate(slices): + for j, s2 in enumerate(slices2): + for ss1 in s1: + for ss2 in s2: + if i==0 and j==0: + #target[ss1,ss2] = kuu(np.abs(rdist[ss1,ss2])) + dktheta1[ss1,ss2] = Vu*UUdtheta1(np.abs(rdist[ss1,ss2])) + dktheta2[ss1,ss2] = 0 + dkUdvar[ss1,ss2] = UUdvar(np.abs(rdist[ss1,ss2])) + dkYdvar[ss1,ss2] = 0 + dkdubias[ss1,ss2] = 1 + elif i==0 and j==1: + ########target[ss1,ss2] = np.where( rdist[ss1,ss2]>0 , kuyp(np.abs(rdist[ss1,ss2])), kuyn(np.abs(rdist[s1[0],s2[0]]) ) ) + #np.where( rdist[ss1,ss2]>0 , kuyp(np.abs(rdist[ss1,ss2])), kuyn(np.abs(rdist[s1[0],s2[0]]) ) ) + #dktheta1[ss1,ss2] = np.where( rdist[ss1,ss2]>0 , self.variance_U*self.variance_Y*dkcrtheta1(np.abs(rdist[ss1,ss2])) ,self.variance_U*self.variance_Y*(dk1theta1(np.abs(rdist[ss1,ss2]))+dk2theta1(np.abs(rdist[ss1,ss2]))) ) + #dktheta2[ss1,ss2] = np.where( rdist[ss1,ss2]>0 , self.variance_U*self.variance_Y*dkcrtheta2(np.abs(rdist[ss1,ss2])) ,self.variance_U*self.variance_Y*(dk1theta2(np.abs(rdist[ss1,ss2]))+dk2theta2(np.abs(rdist[ss1,ss2]))) ) + dktheta1[ss1,ss2] = np.where( rdist[ss1,ss2]>0 , Vu*Vyu*dkuypdtheta1(rdist[ss1,ss2]),Vu*Vyu*dkuyndtheta1(rdist[ss1,ss2]) ) + dkUdvar[ss1,ss2] = np.where( rdist[ss1,ss2]>0 , Vyu*kuyp(rdist[ss1,ss2]), Vyu* kuyn(rdist[ss1,ss2]) ) + dktheta2[ss1,ss2] = np.where( rdist[ss1,ss2]>0 , Vu*Vyu*dkuypdtheta2(rdist[ss1,ss2])+Vu*dVdly*kuyp(rdist[ss1,ss2]),Vu*Vyu*dkuyndtheta2(rdist[ss1,ss2])+Vu*dVdly*kuyn(rdist[ss1,ss2]) ) + dkYdvar[ss1,ss2] = np.where( rdist[ss1,ss2]>0 , Vu*dVdVy*kuyp(rdist[ss1,ss2]), Vu*dVdVy* kuyn(rdist[ss1,ss2]) ) + dkdubias[ss1,ss2] = 0 + elif i==1 and j==1: + #target[ss1,ss2] = kyy(np.abs(rdist[ss1,ss2])) + dktheta1[ss1,ss2] = self.variance_U*self.variance_Y*(dk1theta1(np.abs(rdist[ss1,ss2]))+dk2theta1(np.abs(rdist[ss1,ss2]))+dk3theta1(np.abs(rdist[ss1,ss2]))) + dktheta2[ss1,ss2] = self.variance_U*self.variance_Y*(dk1theta2(np.abs(rdist[ss1,ss2])) + dk2theta2(np.abs(rdist[ss1,ss2])) +dk3theta2(np.abs(rdist[ss1,ss2]))) + dkUdvar[ss1,ss2] = self.variance_Y*(k1(np.abs(rdist[ss1,ss2]))+k2(np.abs(rdist[ss1,ss2]))+k3(np.abs(rdist[ss1,ss2])) ) + dkYdvar[ss1,ss2] = self.variance_U*(k1(np.abs(rdist[ss1,ss2]))+k2(np.abs(rdist[ss1,ss2]))+k3(np.abs(rdist[ss1,ss2])) ) + dkdubias[ss1,ss2] = 0 + else: + #######target[ss1,ss2] = np.where( rdist[ss1,ss2]>0 , kyup(np.abs(rdist[ss1,ss2])), kyun(np.abs(rdist[s1[0],s2[0]]) ) ) + #dktheta1[ss1,ss2] = np.where( rdist[ss1,ss2]>0 ,self.variance_U*self.variance_Y*(dk1theta1(np.abs(rdist[ss1,ss2]))+dk2theta1(np.abs(rdist[ss1,ss2]))) , self.variance_U*self.variance_Y*dkcrtheta1(np.abs(rdist[ss1,ss2])) ) + #dktheta2[ss1,ss2] = np.where( rdist[ss1,ss2]>0 ,self.variance_U*self.variance_Y*(dk1theta2(np.abs(rdist[ss1,ss2]))+dk2theta2(np.abs(rdist[ss1,ss2]))) , self.variance_U*self.variance_Y*dkcrtheta2(np.abs(rdist[ss1,ss2])) ) + dktheta1[ss1,ss2] = np.where( rdist[ss1,ss2]>0 , Vu*Vyu*dkyupdtheta1(rdist[ss1,ss2]),Vu*Vyu*dkyundtheta1(rdist[ss1,ss2]) ) + dkUdvar[ss1,ss2] = np.where( rdist[ss1,ss2]>0 , Vyu*kyup(rdist[ss1,ss2]),Vyu*kyun(rdist[ss1,ss2])) + dktheta2[ss1,ss2] = np.where( rdist[ss1,ss2]>0 , Vu*Vyu*dkyupdtheta2(rdist[ss1,ss2])+Vu*dVdly*kyup(rdist[ss1,ss2]),Vu*Vyu*dkyundtheta2(rdist[ss1,ss2])+Vu*dVdly*kyun(rdist[ss1,ss2]) ) + dkYdvar[ss1,ss2] = np.where( rdist[ss1,ss2]>0 , Vu*dVdVy*kyup(rdist[ss1,ss2]), Vu*dVdVy*kyun(rdist[ss1,ss2])) + dkdubias[ss1,ss2] = 0 + #stop + self.variance_U.gradient = np.sum(dkUdvar * dL_dK) # Vu + + self.variance_Y.gradient = np.sum(dkYdvar * dL_dK) # Vy + + self.lengthscale_U.gradient = np.sum(dktheta1*(-np.sqrt(3)*self.lengthscale_U**(-2))* dL_dK) #lu + + self.lengthscale_Y.gradient = np.sum(dktheta2*(-self.lengthscale_Y**(-2)) * dL_dK) #ly + + self.ubias.gradient = np.sum(dkdubias * dL_dK) + diff --git a/GPy/kern/_src/ODE_st.py b/GPy/kern/_src/ODE_st.py new file mode 100644 index 00000000..665be230 --- /dev/null +++ b/GPy/kern/_src/ODE_st.py @@ -0,0 +1,267 @@ +# Copyright (c) 2012, GPy authors (see AUTHORS.txt). +# Licensed under the BSD 3-clause license (see LICENSE.txt) +from kern import Kern +from ...core.parameterization import Param +from ...core.parameterization.transformations import Logexp +import numpy as np +from independent_outputs import index_to_slices + + +class ODE_st(Kern): + """ + kernel resultiong from a first order ODE with OU driving GP + + :param input_dim: the number of input dimension, has to be equal to one + :type input_dim: int + :param varianceU: variance of the driving GP + :type varianceU: float + :param lengthscaleU: lengthscale of the driving GP (sqrt(3)/lengthscaleU) + :type lengthscaleU: float + :param varianceY: 'variance' of the transfer function + :type varianceY: float + :param lengthscaleY: 'lengthscale' of the transfer function (1/lengthscaleY) + :type lengthscaleY: float + :rtype: kernel object + + """ + + def __init__(self, input_dim, a=1.,b=1., c=1.,variance_Yx=3.,variance_Yt=1.5, lengthscale_Yx=1.5, lengthscale_Yt=1.5, active_dims=None, name='ode_st'): + assert input_dim ==3, "only defined for 3 input dims" + super(ODE_st, self).__init__(input_dim, active_dims, name) + + self.variance_Yt = Param('variance_Yt', variance_Yt, Logexp()) + self.variance_Yx = Param('variance_Yx', variance_Yx, Logexp()) + self.lengthscale_Yt = Param('lengthscale_Yt', lengthscale_Yt, Logexp()) + self.lengthscale_Yx = Param('lengthscale_Yx', lengthscale_Yx, Logexp()) + + self.a= Param('a', a, Logexp()) + self.b = Param('b', b, Logexp()) + self.c = Param('c', c, Logexp()) + + self.add_parameters(self.a, self.b, self.c, self.variance_Yt, self.variance_Yx, self.lengthscale_Yt,self.lengthscale_Yx) + + + def K(self, X, X2=None): + # model : -a d^2y/dx^2 + b dy/dt + c * y = U + # kernel Kyy rbf spatiol temporal + # vyt Y temporal variance vyx Y spatiol variance lyt Y temporal lengthscale lyx Y spatiol lengthscale + # kernel Kuu doper( doper(Kyy)) + # a b c lyt lyx vyx*vyt + """Compute the covariance matrix between X and X2.""" + X,slices = X[:,:-1],index_to_slices(X[:,-1]) + if X2 is None: + X2,slices2 = X,slices + K = np.zeros((X.shape[0], X.shape[0])) + else: + X2,slices2 = X2[:,:-1],index_to_slices(X2[:,-1]) + K = np.zeros((X.shape[0], X2.shape[0])) + + + tdist = (X[:,0][:,None] - X2[:,0][None,:])**2 + xdist = (X[:,1][:,None] - X2[:,1][None,:])**2 + + ttdist = (X[:,0][:,None] - X2[:,0][None,:]) + #rdist = [tdist,xdist] + #dist = np.abs(X - X2.T) + vyt = self.variance_Yt + vyx = self.variance_Yx + + lyt=1/(2*self.lengthscale_Yt) + lyx=1/(2*self.lengthscale_Yx) + + a = self.a ## -a is used in the model, negtive diffusion + b = self.b + c = self.c + + kyy = lambda tdist,xdist: np.exp(-lyt*(tdist) -lyx*(xdist)) + + k1 = lambda tdist: (2*lyt - 4*lyt**2 * (tdist) ) + + k2 = lambda xdist: ( 4*lyx**2 * (xdist) - 2*lyx ) + + k3 = lambda xdist: ( 3*4*lyx**2 - 6*8*xdist*lyx**3 + 16*xdist**2*lyx**4 ) + + k4 = lambda ttdist: 2*lyt*(ttdist) + + for i, s1 in enumerate(slices): + for j, s2 in enumerate(slices2): + for ss1 in s1: + for ss2 in s2: + if i==0 and j==0: + K[ss1,ss2] = vyt*vyx*kyy(tdist[ss1,ss2],xdist[ss1,ss2]) + elif i==0 and j==1: + K[ss1,ss2] = (-a*k2(xdist[ss1,ss2]) + b*k4(ttdist[ss1,ss2]) + c)*vyt*vyx*kyy(tdist[ss1,ss2],xdist[ss1,ss2]) + #K[ss1,ss2]= np.where( rdist[ss1,ss2]>0 , kuyp(np.abs(rdist[ss1,ss2])), kuyn(np.abs(rdist[ss1,ss2]) ) ) + #K[ss1,ss2]= np.where( rdist[ss1,ss2]>0 , kuyp(rdist[ss1,ss2]), kuyn(rdist[ss1,ss2] ) ) + elif i==1 and j==1: + K[ss1,ss2] = ( b**2*k1(tdist[ss1,ss2]) - 2*a*c*k2(xdist[ss1,ss2]) + a**2*k3(xdist[ss1,ss2]) + c**2 )* vyt*vyx* kyy(tdist[ss1,ss2],xdist[ss1,ss2]) + else: + K[ss1,ss2] = (-a*k2(xdist[ss1,ss2]) - b*k4(ttdist[ss1,ss2]) + c)*vyt*vyx*kyy(tdist[ss1,ss2],xdist[ss1,ss2]) + #K[ss1,ss2]= np.where( rdist[ss1,ss2]>0 , kyup(np.abs(rdist[ss1,ss2])), kyun(np.abs(rdist[ss1,ss2]) ) ) + #K[ss1,ss2] = np.where( rdist[ss1,ss2]>0 , kyup(rdist[ss1,ss2]), kyun(rdist[ss1,ss2] ) ) + + #stop + return K + + def Kdiag(self, X): + """Compute the diagonal of the covariance matrix associated to X.""" + vyt = self.variance_Yt + vyx = self.variance_Yx + + lyt = 1./(2*self.lengthscale_Yt) + lyx = 1./(2*self.lengthscale_Yx) + + a = self.a + b = self.b + c = self.c + + ## dk^2/dtdt' + k1 = (2*lyt )*vyt*vyx + ## dk^2/dx^2 + k2 = ( - 2*lyx )*vyt*vyx + ## dk^4/dx^2dx'^2 + k3 = ( 4*3*lyx**2 )*vyt*vyx + + + Kdiag = np.zeros(X.shape[0]) + slices = index_to_slices(X[:,-1]) + + for i, ss1 in enumerate(slices): + for s1 in ss1: + if i==0: + Kdiag[s1]+= vyt*vyx + elif i==1: + #i=1 + Kdiag[s1]+= b**2*k1 - 2*a*c*k2 + a**2*k3 + c**2*vyt*vyx + #Kdiag[s1]+= Vu*Vy*(k1+k2+k3) + else: + raise ValueError, "invalid input/output index" + + return Kdiag + + + def update_gradients_full(self, dL_dK, X, X2=None): + #def dK_dtheta(self, dL_dK, X, X2, target): + """derivative of the covariance matrix with respect to the parameters.""" + X,slices = X[:,:-1],index_to_slices(X[:,-1]) + if X2 is None: + X2,slices2 = X,slices + K = np.zeros((X.shape[0], X.shape[0])) + else: + X2,slices2 = X2[:,:-1],index_to_slices(X2[:,-1]) + + vyt = self.variance_Yt + vyx = self.variance_Yx + + lyt = 1./(2*self.lengthscale_Yt) + lyx = 1./(2*self.lengthscale_Yx) + + a = self.a + b = self.b + c = self.c + + tdist = (X[:,0][:,None] - X2[:,0][None,:])**2 + xdist = (X[:,1][:,None] - X2[:,1][None,:])**2 + #rdist = [tdist,xdist] + ttdist = (X[:,0][:,None] - X2[:,0][None,:]) + + rd=tdist.shape[0] + + dka = np.zeros([rd,rd]) + dkb = np.zeros([rd,rd]) + dkc = np.zeros([rd,rd]) + dkYdvart = np.zeros([rd,rd]) + dkYdvarx = np.zeros([rd,rd]) + dkYdlent = np.zeros([rd,rd]) + dkYdlenx = np.zeros([rd,rd]) + + + kyy = lambda tdist,xdist: np.exp(-lyt*(tdist) -lyx*(xdist)) + #k1 = lambda tdist: (lyt - lyt**2 * (tdist) ) + #k2 = lambda xdist: ( lyx**2 * (xdist) - lyx ) + #k3 = lambda xdist: ( 3*lyx**2 - 6*xdist*lyx**3 + xdist**2*lyx**4 ) + #k4 = lambda tdist: -lyt*np.sqrt(tdist) + + k1 = lambda tdist: (2*lyt - 4*lyt**2 * (tdist) ) + + k2 = lambda xdist: ( 4*lyx**2 * (xdist) - 2*lyx ) + + k3 = lambda xdist: ( 3*4*lyx**2 - 6*8*xdist*lyx**3 + 16*xdist**2*lyx**4 ) + + k4 = lambda ttdist: 2*lyt*(ttdist) + + dkyydlyx = lambda tdist,xdist: kyy(tdist,xdist)*(-xdist) + dkyydlyt = lambda tdist,xdist: kyy(tdist,xdist)*(-tdist) + + dk1dlyt = lambda tdist: 2. - 4*2.*lyt*tdist + dk2dlyx = lambda xdist: (4.*2.*lyx*xdist -2.) + dk3dlyx = lambda xdist: (6.*4.*lyx - 18.*8*xdist*lyx**2 + 4*16*xdist**2*lyx**3) + + dk4dlyt = lambda ttdist: 2*(ttdist) + + for i, s1 in enumerate(slices): + for j, s2 in enumerate(slices2): + for ss1 in s1: + for ss2 in s2: + if i==0 and j==0: + dka[ss1,ss2] = 0 + dkb[ss1,ss2] = 0 + dkc[ss1,ss2] = 0 + dkYdvart[ss1,ss2] = vyx*kyy(tdist[ss1,ss2],xdist[ss1,ss2]) + dkYdvarx[ss1,ss2] = vyt*kyy(tdist[ss1,ss2],xdist[ss1,ss2]) + dkYdlenx[ss1,ss2] = vyt*vyx*dkyydlyx(tdist[ss1,ss2],xdist[ss1,ss2]) + dkYdlent[ss1,ss2] = vyt*vyx*dkyydlyt(tdist[ss1,ss2],xdist[ss1,ss2]) + elif i==0 and j==1: + dka[ss1,ss2] = -k2(xdist[ss1,ss2])*vyt*vyx*kyy(tdist[ss1,ss2],xdist[ss1,ss2]) + dkb[ss1,ss2] = k4(ttdist[ss1,ss2])*vyt*vyx*kyy(tdist[ss1,ss2],xdist[ss1,ss2]) + dkc[ss1,ss2] = vyt*vyx*kyy(tdist[ss1,ss2],xdist[ss1,ss2]) + #dkYdvart[ss1,ss2] = 0 + #dkYdvarx[ss1,ss2] = 0 + #dkYdlent[ss1,ss2] = 0 + #dkYdlenx[ss1,ss2] = 0 + dkYdvart[ss1,ss2] = (-a*k2(xdist[ss1,ss2])+b*k4(ttdist[ss1,ss2])+c)*vyx*kyy(tdist[ss1,ss2],xdist[ss1,ss2]) + dkYdvarx[ss1,ss2] = (-a*k2(xdist[ss1,ss2])+b*k4(ttdist[ss1,ss2])+c)*vyt*kyy(tdist[ss1,ss2],xdist[ss1,ss2]) + dkYdlent[ss1,ss2] = vyt*vyx*dkyydlyt(tdist[ss1,ss2],xdist[ss1,ss2])* (-a*k2(xdist[ss1,ss2])+b*k4(ttdist[ss1,ss2])+c)+\ + vyt*vyx*kyy(tdist[ss1,ss2],xdist[ss1,ss2])*b*dk4dlyt(ttdist[ss1,ss2]) + dkYdlenx[ss1,ss2] = vyt*vyx*dkyydlyx(tdist[ss1,ss2],xdist[ss1,ss2])*(-a*k2(xdist[ss1,ss2])+b*k4(ttdist[ss1,ss2])+c)+\ + vyt*vyx*kyy(tdist[ss1,ss2],xdist[ss1,ss2])*(-a*dk2dlyx(xdist[ss1,ss2])) + elif i==1 and j==1: + dka[ss1,ss2] = (2*a*k3(xdist[ss1,ss2]) - 2*c*k2(xdist[ss1,ss2]))*vyt*vyx* kyy(tdist[ss1,ss2],xdist[ss1,ss2]) + dkb[ss1,ss2] = 2*b*k1(tdist[ss1,ss2])*vyt*vyx* kyy(tdist[ss1,ss2],xdist[ss1,ss2]) + dkc[ss1,ss2] = (-2*a*k2(xdist[ss1,ss2]) + 2*c )*vyt*vyx* kyy(tdist[ss1,ss2],xdist[ss1,ss2]) + dkYdvart[ss1,ss2] = ( b**2*k1(tdist[ss1,ss2]) - 2*a*c*k2(xdist[ss1,ss2]) + a**2*k3(xdist[ss1,ss2]) + c**2 )*vyx* kyy(tdist[ss1,ss2],xdist[ss1,ss2]) + dkYdvarx[ss1,ss2] = ( b**2*k1(tdist[ss1,ss2]) - 2*a*c*k2(xdist[ss1,ss2]) + a**2*k3(xdist[ss1,ss2]) + c**2 )*vyt* kyy(tdist[ss1,ss2],xdist[ss1,ss2]) + dkYdlent[ss1,ss2] = vyt*vyx*dkyydlyt(tdist[ss1,ss2],xdist[ss1,ss2])*( b**2*k1(tdist[ss1,ss2]) - 2*a*c*k2(xdist[ss1,ss2]) + a**2*k3(xdist[ss1,ss2]) + c**2 ) +\ + vyx*vyt*kyy(tdist[ss1,ss2],xdist[ss1,ss2])*b**2*dk1dlyt(tdist[ss1,ss2]) + dkYdlenx[ss1,ss2] = vyt*vyx*dkyydlyx(tdist[ss1,ss2],xdist[ss1,ss2])*( b**2*k1(tdist[ss1,ss2]) - 2*a*c*k2(xdist[ss1,ss2]) + a**2*k3(xdist[ss1,ss2]) + c**2 ) +\ + vyx*vyt*kyy(tdist[ss1,ss2],xdist[ss1,ss2])* (-2*a*c*dk2dlyx(xdist[ss1,ss2]) + a**2*dk3dlyx(xdist[ss1,ss2]) ) + else: + dka[ss1,ss2] = -k2(xdist[ss1,ss2])*vyt*vyx*kyy(tdist[ss1,ss2],xdist[ss1,ss2]) + dkb[ss1,ss2] = -k4(ttdist[ss1,ss2])*vyt*vyx*kyy(tdist[ss1,ss2],xdist[ss1,ss2]) + dkc[ss1,ss2] = vyt*vyx*kyy(tdist[ss1,ss2],xdist[ss1,ss2]) + #dkYdvart[ss1,ss2] = 0 + #dkYdvarx[ss1,ss2] = 0 + #dkYdlent[ss1,ss2] = 0 + #dkYdlenx[ss1,ss2] = 0 + dkYdvart[ss1,ss2] = (-a*k2(xdist[ss1,ss2])-b*k4(ttdist[ss1,ss2])+c)*vyx*kyy(tdist[ss1,ss2],xdist[ss1,ss2]) + dkYdvarx[ss1,ss2] = (-a*k2(xdist[ss1,ss2])-b*k4(ttdist[ss1,ss2])+c)*vyt*kyy(tdist[ss1,ss2],xdist[ss1,ss2]) + dkYdlent[ss1,ss2] = vyt*vyx*dkyydlyt(tdist[ss1,ss2],xdist[ss1,ss2])* (-a*k2(xdist[ss1,ss2])-b*k4(ttdist[ss1,ss2])+c)+\ + vyt*vyx*kyy(tdist[ss1,ss2],xdist[ss1,ss2])*(-1)*b*dk4dlyt(ttdist[ss1,ss2]) + dkYdlenx[ss1,ss2] = vyt*vyx*dkyydlyx(tdist[ss1,ss2],xdist[ss1,ss2])*(-a*k2(xdist[ss1,ss2])-b*k4(ttdist[ss1,ss2])+c)+\ + vyt*vyx*kyy(tdist[ss1,ss2],xdist[ss1,ss2])*(-a*dk2dlyx(xdist[ss1,ss2])) + + self.a.gradient = np.sum(dka * dL_dK) + + self.b.gradient = np.sum(dkb * dL_dK) + + self.c.gradient = np.sum(dkc * dL_dK) + + + self.variance_Yt.gradient = np.sum(dkYdvart * dL_dK) # Vy + + self.variance_Yx.gradient = np.sum(dkYdvarx * dL_dK) + + self.lengthscale_Yt.gradient = np.sum(dkYdlent*(-0.5*self.lengthscale_Yt**(-2)) * dL_dK) #ly np.sum(dktheta2*(-self.lengthscale_Y**(-2)) * dL_dK) + + self.lengthscale_Yx.gradient = np.sum(dkYdlenx*(-0.5*self.lengthscale_Yx**(-2)) * dL_dK) + diff --git a/GPy/kern/_src/ODE_t.py b/GPy/kern/_src/ODE_t.py new file mode 100644 index 00000000..a470cbec --- /dev/null +++ b/GPy/kern/_src/ODE_t.py @@ -0,0 +1,165 @@ +from kern import Kern +from ...core.parameterization import Param +from ...core.parameterization.transformations import Logexp +import numpy as np +from independent_outputs import index_to_slices + + +class ODE_t(Kern): + + def __init__(self, input_dim, a=1., c=1.,variance_Yt=3., lengthscale_Yt=1.5,ubias =1., active_dims=None, name='ode_st'): + assert input_dim ==2, "only defined for 2 input dims" + super(ODE_t, self).__init__(input_dim, active_dims, name) + + self.variance_Yt = Param('variance_Yt', variance_Yt, Logexp()) + self.lengthscale_Yt = Param('lengthscale_Yt', lengthscale_Yt, Logexp()) + + self.a= Param('a', a, Logexp()) + self.c = Param('c', c, Logexp()) + self.ubias = Param('ubias', ubias, Logexp()) + self.add_parameters(self.a, self.c, self.variance_Yt, self.lengthscale_Yt,self.ubias) + + def K(self, X, X2=None): + """Compute the covariance matrix between X and X2.""" + X,slices = X[:,:-1],index_to_slices(X[:,-1]) + if X2 is None: + X2,slices2 = X,slices + K = np.zeros((X.shape[0], X.shape[0])) + else: + X2,slices2 = X2[:,:-1],index_to_slices(X2[:,-1]) + K = np.zeros((X.shape[0], X2.shape[0])) + + tdist = (X[:,0][:,None] - X2[:,0][None,:])**2 + ttdist = (X[:,0][:,None] - X2[:,0][None,:]) + + vyt = self.variance_Yt + + lyt=1/(2*self.lengthscale_Yt) + + a = -self.a + c = self.c + + kyy = lambda tdist: np.exp(-lyt*(tdist)) + + k1 = lambda tdist: (2*lyt - 4*lyt**2 *(tdist) ) + + k4 = lambda tdist: 2*lyt*(tdist) + + for i, s1 in enumerate(slices): + for j, s2 in enumerate(slices2): + for ss1 in s1: + for ss2 in s2: + if i==0 and j==0: + K[ss1,ss2] = vyt*kyy(tdist[ss1,ss2]) + elif i==0 and j==1: + K[ss1,ss2] = (k4(ttdist[ss1,ss2])+1)*vyt*kyy(tdist[ss1,ss2]) + #K[ss1,ss2] = (2*lyt*(ttdist[ss1,ss2])+1)*vyt*kyy(tdist[ss1,ss2]) + elif i==1 and j==1: + K[ss1,ss2] = ( k1(tdist[ss1,ss2]) + 1. )*vyt* kyy(tdist[ss1,ss2])+self.ubias + else: + K[ss1,ss2] = (-k4(ttdist[ss1,ss2])+1)*vyt*kyy(tdist[ss1,ss2]) + #K[ss1,ss2] = (-2*lyt*(ttdist[ss1,ss2])+1)*vyt*kyy(tdist[ss1,ss2]) + #stop + return K + + + def Kdiag(self, X): + + vyt = self.variance_Yt + lyt = 1./(2*self.lengthscale_Yt) + + a = -self.a + c = self.c + + k1 = (2*lyt )*vyt + + Kdiag = np.zeros(X.shape[0]) + slices = index_to_slices(X[:,-1]) + + for i, ss1 in enumerate(slices): + for s1 in ss1: + if i==0: + Kdiag[s1]+= vyt + elif i==1: + #i=1 + Kdiag[s1]+= k1 + vyt+self.ubias + #Kdiag[s1]+= Vu*Vy*(k1+k2+k3) + else: + raise ValueError, "invalid input/output index" + + return Kdiag + + def update_gradients_full(self, dL_dK, X, X2=None): + """derivative of the covariance matrix with respect to the parameters.""" + X,slices = X[:,:-1],index_to_slices(X[:,-1]) + if X2 is None: + X2,slices2 = X,slices + K = np.zeros((X.shape[0], X.shape[0])) + else: + X2,slices2 = X2[:,:-1],index_to_slices(X2[:,-1]) + + + vyt = self.variance_Yt + + lyt = 1./(2*self.lengthscale_Yt) + + tdist = (X[:,0][:,None] - X2[:,0][None,:])**2 + ttdist = (X[:,0][:,None] - X2[:,0][None,:]) + #rdist = [tdist,xdist] + + rd=tdist.shape[0] + + dka = np.zeros([rd,rd]) + dkc = np.zeros([rd,rd]) + dkYdvart = np.zeros([rd,rd]) + dkYdlent = np.zeros([rd,rd]) + + dkdubias = np.zeros([rd,rd]) + + kyy = lambda tdist: np.exp(-lyt*(tdist)) + dkyydlyt = lambda tdist: kyy(tdist)*(-tdist) + + k1 = lambda tdist: (2*lyt - 4*lyt**2 * (tdist) ) + + k4 = lambda ttdist: 2*lyt*(ttdist) + + dk1dlyt = lambda tdist: 2. - 4*2.*lyt*tdist + + dk4dlyt = lambda ttdist: 2*(ttdist) + + for i, s1 in enumerate(slices): + for j, s2 in enumerate(slices2): + for ss1 in s1: + for ss2 in s2: + if i==0 and j==0: + dkYdvart[ss1,ss2] = kyy(tdist[ss1,ss2]) + dkYdlent[ss1,ss2] = vyt*dkyydlyt(tdist[ss1,ss2]) + dkdubias[ss1,ss2] = 0 + elif i==0 and j==1: + dkYdvart[ss1,ss2] = (k4(ttdist[ss1,ss2])+1)*kyy(tdist[ss1,ss2]) + #dkYdvart[ss1,ss2] = ((2*lyt*ttdist[ss1,ss2])+1)*kyy(tdist[ss1,ss2]) + dkYdlent[ss1,ss2] = vyt*dkyydlyt(tdist[ss1,ss2])* (k4(ttdist[ss1,ss2])+1.)+\ + vyt*kyy(tdist[ss1,ss2])*(dk4dlyt(ttdist[ss1,ss2])) + #dkYdlent[ss1,ss2] = vyt*dkyydlyt(tdist[ss1,ss2])* (2*lyt*(ttdist[ss1,ss2])+1.)+\ + #vyt*kyy(tdist[ss1,ss2])*(2*ttdist[ss1,ss2]) + dkdubias[ss1,ss2] = 0 + elif i==1 and j==1: + dkYdvart[ss1,ss2] = (k1(tdist[ss1,ss2]) + 1. )* kyy(tdist[ss1,ss2]) + dkYdlent[ss1,ss2] = vyt*dkyydlyt(tdist[ss1,ss2])*( k1(tdist[ss1,ss2]) + 1. ) +\ + vyt*kyy(tdist[ss1,ss2])*dk1dlyt(tdist[ss1,ss2]) + dkdubias[ss1,ss2] = 1 + else: + dkYdvart[ss1,ss2] = (-k4(ttdist[ss1,ss2])+1)*kyy(tdist[ss1,ss2]) + #dkYdvart[ss1,ss2] = (-2*lyt*(ttdist[ss1,ss2])+1)*kyy(tdist[ss1,ss2]) + dkYdlent[ss1,ss2] = vyt*dkyydlyt(tdist[ss1,ss2])* (-k4(ttdist[ss1,ss2])+1.)+\ + vyt*kyy(tdist[ss1,ss2])*(-dk4dlyt(ttdist[ss1,ss2]) ) + dkdubias[ss1,ss2] = 0 + #dkYdlent[ss1,ss2] = vyt*dkyydlyt(tdist[ss1,ss2])* (-2*lyt*(ttdist[ss1,ss2])+1.)+\ + #vyt*kyy(tdist[ss1,ss2])*(-2)*(ttdist[ss1,ss2]) + + + self.variance_Yt.gradient = np.sum(dkYdvart * dL_dK) + + self.lengthscale_Yt.gradient = np.sum(dkYdlent*(-0.5*self.lengthscale_Yt**(-2)) * dL_dK) + + self.ubias.gradient = np.sum(dkdubias * dL_dK) \ No newline at end of file diff --git a/GPy/kern/_src/__init__.py b/GPy/kern/_src/__init__.py new file mode 100644 index 00000000..e69de29b diff --git a/GPy/kern/_src/add.py b/GPy/kern/_src/add.py new file mode 100644 index 00000000..4c72a254 --- /dev/null +++ b/GPy/kern/_src/add.py @@ -0,0 +1,188 @@ +# Copyright (c) 2012, GPy authors (see AUTHORS.txt). +# Licensed under the BSD 3-clause license (see LICENSE.txt) + +import numpy as np +import itertools +from ...util.caching import Cache_this +from kern import CombinationKernel + +class Add(CombinationKernel): + """ + Add given list of kernels together. + propagates gradients through. + + This kernel will take over the active dims of it's subkernels passed in. + """ + def __init__(self, subkerns, name='add'): + for i, kern in enumerate(subkerns[:]): + if isinstance(kern, Add): + del subkerns[i] + for part in kern.parts[::-1]: + kern.unlink_parameter(part) + subkerns.insert(i, part) + + super(Add, self).__init__(subkerns, name) + + @Cache_this(limit=2, force_kwargs=['which_parts']) + def K(self, X, X2=None, which_parts=None): + """ + Add all kernels together. + If a list of parts (of this kernel!) `which_parts` is given, only + the parts of the list are taken to compute the covariance. + """ + if which_parts is None: + which_parts = self.parts + elif not isinstance(which_parts, (list, tuple)): + # if only one part is given + which_parts = [which_parts] + return reduce(np.add, (p.K(X, X2) for p in which_parts)) + + @Cache_this(limit=2, force_kwargs=['which_parts']) + def Kdiag(self, X, which_parts=None): + if which_parts is None: + which_parts = self.parts + elif not isinstance(which_parts, (list, tuple)): + # if only one part is given + which_parts = [which_parts] + return reduce(np.add, (p.Kdiag(X) for p in which_parts)) + + def update_gradients_full(self, dL_dK, X, X2=None): + [p.update_gradients_full(dL_dK, X, X2) for p in self.parts if not p.is_fixed] + + def update_gradients_diag(self, dL_dK, X): + [p.update_gradients_diag(dL_dK, X) for p in self.parts] + + def gradients_X(self, dL_dK, X, X2=None): + """Compute the gradient of the objective function with respect to X. + + :param dL_dK: An array of gradients of the objective function with respect to the covariance function. + :type dL_dK: np.ndarray (num_samples x num_inducing) + :param X: Observed data inputs + :type X: np.ndarray (num_samples x input_dim) + :param X2: Observed data inputs (optional, defaults to X) + :type X2: np.ndarray (num_inducing x input_dim)""" + + target = np.zeros(X.shape) + [target.__iadd__(p.gradients_X(dL_dK, X, X2)) for p in self.parts] + return target + + def gradients_X_diag(self, dL_dKdiag, X): + target = np.zeros(X.shape) + [target.__iadd__(p.gradients_X_diag(dL_dKdiag, X)) for p in self.parts] + return target + + @Cache_this(limit=2, force_kwargs=['which_parts']) + def psi0(self, Z, variational_posterior): + return reduce(np.add, (p.psi0(Z, variational_posterior) for p in self.parts)) + + @Cache_this(limit=2, force_kwargs=['which_parts']) + def psi1(self, Z, variational_posterior): + return reduce(np.add, (p.psi1(Z, variational_posterior) for p in self.parts)) + + @Cache_this(limit=2, force_kwargs=['which_parts']) + def psi2(self, Z, variational_posterior): + psi2 = reduce(np.add, (p.psi2(Z, variational_posterior) for p in self.parts)) + #return psi2 + # compute the "cross" terms + from static import White, Bias + from rbf import RBF + #from rbf_inv import RBFInv + from linear import Linear + #ffrom fixed import Fixed + + for p1, p2 in itertools.combinations(self.parts, 2): + # i1, i2 = p1.active_dims, p2.active_dims + # white doesn;t combine with anything + if isinstance(p1, White) or isinstance(p2, White): + pass + # rbf X bias + #elif isinstance(p1, (Bias, Fixed)) and isinstance(p2, (RBF, RBFInv)): + elif isinstance(p1, Bias) and isinstance(p2, (RBF, Linear)): + tmp = p2.psi1(Z, variational_posterior).sum(axis=0) + psi2 += p1.variance * (tmp[:,None]+tmp[None,:]) #(tmp[:, :, None] + tmp[:, None, :]) + #elif isinstance(p2, (Bias, Fixed)) and isinstance(p1, (RBF, RBFInv)): + elif isinstance(p2, Bias) and isinstance(p1, (RBF, Linear)): + tmp = p1.psi1(Z, variational_posterior).sum(axis=0) + psi2 += p2.variance * (tmp[:,None]+tmp[None,:]) #(tmp[:, :, None] + tmp[:, None, :]) + elif isinstance(p2, (RBF, Linear)) and isinstance(p1, (RBF, Linear)): + assert np.intersect1d(p1.active_dims, p2.active_dims).size == 0, "only non overlapping kernel dimensions allowed so far" + tmp1 = p1.psi1(Z, variational_posterior) + tmp2 = p2.psi1(Z, variational_posterior) + psi2 += np.einsum('nm,no->mo',tmp1,tmp2)+np.einsum('nm,no->mo',tmp2,tmp1) + #(tmp1[:, :, None] * tmp2[:, None, :]) + (tmp2[:, :, None] * tmp1[:, None, :]) + else: + raise NotImplementedError, "psi2 cannot be computed for this kernel" + return psi2 + + def update_gradients_expectations(self, dL_dpsi0, dL_dpsi1, dL_dpsi2, Z, variational_posterior): + from static import White, Bias + for p1 in self.parts: + #compute the effective dL_dpsi1. Extra terms appear becaue of the cross terms in psi2! + eff_dL_dpsi1 = dL_dpsi1.copy() + for p2 in self.parts: + if p2 is p1: + continue + if isinstance(p2, White): + continue + elif isinstance(p2, Bias): + eff_dL_dpsi1 += dL_dpsi2.sum(0) * p2.variance * 2. + else:# np.setdiff1d(p1.active_dims, ar2, assume_unique): # TODO: Careful, not correct for overlapping active_dims + eff_dL_dpsi1 += dL_dpsi2.sum(0) * p2.psi1(Z, variational_posterior) * 2. + p1.update_gradients_expectations(dL_dpsi0, eff_dL_dpsi1, dL_dpsi2, Z, variational_posterior) + + def gradients_Z_expectations(self, dL_psi0, dL_dpsi1, dL_dpsi2, Z, variational_posterior): + from static import White, Bias + target = np.zeros(Z.shape) + for p1 in self.parts: + #compute the effective dL_dpsi1. extra terms appear becaue of the cross terms in psi2! + eff_dL_dpsi1 = dL_dpsi1.copy() + for p2 in self.parts: + if p2 is p1: + continue + if isinstance(p2, White): + continue + elif isinstance(p2, Bias): + eff_dL_dpsi1 += dL_dpsi2.sum(0) * p2.variance * 2. + else: + eff_dL_dpsi1 += dL_dpsi2.sum(0) * p2.psi1(Z, variational_posterior) * 2. + target += p1.gradients_Z_expectations(dL_psi0, eff_dL_dpsi1, dL_dpsi2, Z, variational_posterior) + return target + + def gradients_qX_expectations(self, dL_dpsi0, dL_dpsi1, dL_dpsi2, Z, variational_posterior): + from static import White, Bias + target_grads = [np.zeros(v.shape) for v in variational_posterior.parameters] + for p1 in self.parameters: + #compute the effective dL_dpsi1. extra terms appear becaue of the cross terms in psi2! + eff_dL_dpsi1 = dL_dpsi1.copy() + for p2 in self.parameters: + if p2 is p1: + continue + if isinstance(p2, White): + continue + elif isinstance(p2, Bias): + eff_dL_dpsi1 += dL_dpsi2.sum(0) * p2.variance * 2. + else: + eff_dL_dpsi1 += dL_dpsi2.sum(0) * p2.psi1(Z, variational_posterior) * 2. + grads = p1.gradients_qX_expectations(dL_dpsi0, eff_dL_dpsi1, dL_dpsi2, Z, variational_posterior) + [np.add(target_grads[i],grads[i],target_grads[i]) for i in xrange(len(grads))] + return target_grads + + def add(self, other): + if isinstance(other, Add): + other_params = other.parameters[:] + for p in other_params: + other.unlink_parameter(p) + self.link_parameters(*other_params) + else: + self.link_parameter(other) + self.input_dim, self.active_dims = self.get_input_dim_active_dims(self.parts) + return self + + def input_sensitivity(self, summarize=True): + if summarize: + return reduce(np.add, [k.input_sensitivity(summarize) for k in self.parts]) + else: + i_s = np.zeros((len(self.parts), self.input_dim)) + from operator import setitem + [setitem(i_s, (i, Ellipsis), k.input_sensitivity(summarize)) for i, k in enumerate(self.parts)] + return i_s diff --git a/GPy/kern/_src/brownian.py b/GPy/kern/_src/brownian.py new file mode 100644 index 00000000..fd79973c --- /dev/null +++ b/GPy/kern/_src/brownian.py @@ -0,0 +1,50 @@ +# Copyright (c) 2012, GPy authors (see AUTHORS.txt). +# Licensed under the BSD 3-clause license (see LICENSE.txt) + +from kern import Kern +from ...core.parameterization import Param +from ...core.parameterization.transformations import Logexp +import numpy as np + +class Brownian(Kern): + """ + Brownian motion in 1D only. + + Negative times are treated as a separate (backwards!) Brownian motion. + + :param input_dim: the number of input dimensions + :type input_dim: int + :param variance: + :type variance: float + """ + def __init__(self, input_dim=1, variance=1., active_dims=None, name='Brownian'): + assert input_dim==1, "Brownian motion in 1D only" + super(Brownian, self).__init__(input_dim, active_dims, name) + + self.variance = Param('variance', variance, Logexp()) + self.link_parameters(self.variance) + + def K(self,X,X2=None): + if X2 is None: + X2 = X + return self.variance*np.where(np.sign(X)==np.sign(X2.T),np.fmin(np.abs(X),np.abs(X2.T)), 0.) + + def Kdiag(self,X): + return self.variance*np.abs(X.flatten()) + + def update_gradients_full(self, dL_dK, X, X2=None): + if X2 is None: + X2 = X + self.variance.gradient = np.sum(dL_dK * np.where(np.sign(X)==np.sign(X2.T),np.fmin(np.abs(X),np.abs(X2.T)), 0.)) + + #def update_gradients_diag(self, dL_dKdiag, X): + #self.variance.gradient = np.dot(np.abs(X.flatten()), dL_dKdiag) + + #def gradients_X(self, dL_dK, X, X2=None): + #if X2 is None: + #return np.sum(self.variance*dL_dK*np.abs(X),1)[:,None] + #else: + #return np.sum(np.where(np.logical_and(np.abs(X)output_dim: + print("Warning: Unusual choice of rank, it should normally be less than the output_dim.") + if W is None: + W = 0.5*np.random.randn(self.output_dim, self.rank)/np.sqrt(self.rank) + else: + assert W.shape==(self.output_dim, self.rank) + self.W = Param('W', W) + if kappa is None: + kappa = 0.5*np.ones(self.output_dim) + else: + assert kappa.shape==(self.output_dim, ) + self.kappa = Param('kappa', kappa, Logexp()) + self.link_parameters(self.W, self.kappa) + + def parameters_changed(self): + self.B = np.dot(self.W, self.W.T) + np.diag(self.kappa) + + def K(self, X, X2=None): + if config.getboolean('weave', 'working'): + try: + return self._K_weave(X, X2) + except: + print "\n Weave compilation failed. Falling back to (slower) numpy implementation\n" + config.set('weave', 'working', 'False') + return self._K_numpy(X, X2) + else: + return self._K_numpy(X, X2) + + + def _K_numpy(self, X, X2=None): + index = np.asarray(X, dtype=np.int) + if X2 is None: + return self.B[index,index.T] + else: + index2 = np.asarray(X2, dtype=np.int) + return self.B[index,index2.T] + + def _K_weave(self, X, X2=None): + """compute the kernel function using scipy.weave""" + index = np.asarray(X, dtype=np.int) + + if X2 is None: + target = np.empty((X.shape[0], X.shape[0]), dtype=np.float64) + code=""" + for(int i=0;i>> index = np.asarray([0,0,0,1,1,1,2,2,2]) + returns + >>> [[slice(0,3,None)],[slice(3,6,None)],[slice(6,9,None)]] + + or, a more complicated example + >>> index = np.asarray([0,0,1,1,0,2,2,2,1,1]) + returns + >>> [[slice(0,2,None),slice(4,5,None)],[slice(2,4,None),slice(8,10,None)],[slice(5,8,None)]] + """ + if len(index)==0: + return[] + + #contruct the return structure + ind = np.asarray(index,dtype=np.int) + ret = [[] for i in range(ind.max()+1)] + + #find the switchpoints + ind_ = np.hstack((ind,ind[0]+ind[-1]+1)) + switchpoints = np.nonzero(ind_ - np.roll(ind_,+1))[0] + + [ret[ind_i].append(slice(*indexes_i)) for ind_i,indexes_i in zip(ind[switchpoints[:-1]],zip(switchpoints,switchpoints[1:]))] + return ret + +class IndependentOutputs(CombinationKernel): + """ + A kernel which can represent several independent functions. this kernel + 'switches off' parts of the matrix where the output indexes are different. + + The index of the functions is given by the last column in the input X the + rest of the columns of X are passed to the underlying kernel for + computation (in blocks). + + :param kernels: either a kernel, or list of kernels to work with. If it is + a list of kernels the indices in the index_dim, index the kernels you gave! + """ + def __init__(self, kernels, index_dim=-1, name='independ'): + assert isinstance(index_dim, int), "IndependentOutputs kernel is only defined with one input dimension being the index" + if not isinstance(kernels, list): + self.single_kern = True + self.kern = kernels + kernels = [kernels] + else: + self.single_kern = False + self.kern = kernels + super(IndependentOutputs, self).__init__(kernels=kernels, extra_dims=[index_dim], name=name) + self.index_dim = index_dim + + def K(self,X ,X2=None): + slices = index_to_slices(X[:,self.index_dim]) + kerns = itertools.repeat(self.kern) if self.single_kern else self.kern + if X2 is None: + target = np.zeros((X.shape[0], X.shape[0])) + [[target.__setitem__((s,ss), kern.K(X[s,:], X[ss,:])) for s,ss in itertools.product(slices_i, slices_i)] for kern, slices_i in zip(kerns, slices)] + else: + slices2 = index_to_slices(X2[:,self.index_dim]) + target = np.zeros((X.shape[0], X2.shape[0])) + [[target.__setitem__((s,s2), kern.K(X[s,:],X2[s2,:])) for s,s2 in itertools.product(slices_i, slices_j)] for kern, slices_i,slices_j in zip(kerns, slices,slices2)] + return target + + def Kdiag(self,X): + slices = index_to_slices(X[:,self.index_dim]) + kerns = itertools.repeat(self.kern) if self.single_kern else self.kern + target = np.zeros(X.shape[0]) + [[np.copyto(target[s], kern.Kdiag(X[s])) for s in slices_i] for kern, slices_i in zip(kerns, slices)] + return target + + def update_gradients_full(self,dL_dK,X,X2=None): + slices = index_to_slices(X[:,self.index_dim]) + if self.single_kern: + target = np.zeros(self.kern.size) + kerns = itertools.repeat(self.kern) + else: + kerns = self.kern + target = [np.zeros(kern.size) for kern, _ in zip(kerns, slices)] + def collate_grads(kern, i, dL, X, X2): + kern.update_gradients_full(dL,X,X2) + if self.single_kern: target[:] += kern.gradient + else: target[i][:] += kern.gradient + if X2 is None: + [[collate_grads(kern, i, dL_dK[s,ss], X[s], X[ss]) for s,ss in itertools.product(slices_i, slices_i)] for i,(kern,slices_i) in enumerate(zip(kerns,slices))] + else: + slices2 = index_to_slices(X2[:,self.index_dim]) + [[[collate_grads(kern, i, dL_dK[s,s2],X[s],X2[s2]) for s in slices_i] for s2 in slices_j] for i,(kern,slices_i,slices_j) in enumerate(zip(kerns,slices,slices2))] + if self.single_kern: kern.gradient = target + else:[kern.gradient.__setitem__(Ellipsis, target[i]) for i, [kern, _] in enumerate(zip(kerns, slices))] + + def gradients_X(self,dL_dK, X, X2=None): + target = np.zeros(X.shape) + kerns = itertools.repeat(self.kern) if self.single_kern else self.kern + if X2 is None: + # TODO: make use of index_to_slices + values = np.unique(X[:,self.index_dim]) + slices = [X[:,self.index_dim]==i for i in values] + [target.__setitem__(s, kern.gradients_X(dL_dK[s,s],X[s],None)) + for kern, s in zip(kerns, slices)] + #slices = index_to_slices(X[:,self.index_dim]) + #[[np.add(target[s], kern.gradients_X(dL_dK[s,s], X[s]), out=target[s]) + # for s in slices_i] for kern, slices_i in zip(kerns, slices)] + #import ipdb;ipdb.set_trace() + #[[(np.add(target[s ], kern.gradients_X(dL_dK[s ,ss],X[s ], X[ss]), out=target[s ]), + # np.add(target[ss], kern.gradients_X(dL_dK[ss,s ],X[ss], X[s ]), out=target[ss])) + # for s, ss in itertools.combinations(slices_i, 2)] for kern, slices_i in zip(kerns, slices)] + else: + values = np.unique(X[:,self.index_dim]) + slices = [X[:,self.index_dim]==i for i in values] + slices2 = [X2[:,self.index_dim]==i for i in values] + [target.__setitem__(s, kern.gradients_X(dL_dK[s, :][:, s2],X[s],X2[s2])) + for kern, s, s2 in zip(kerns, slices, slices2)] + # TODO: make work with index_to_slices + #slices = index_to_slices(X[:,self.index_dim]) + #slices2 = index_to_slices(X2[:,self.index_dim]) + #[[target.__setitem__(s, target[s] + kern.gradients_X(dL_dK[s,s2], X[s], X2[s2])) for s, s2 in itertools.product(slices_i, slices_j)] for kern, slices_i,slices_j in zip(kerns, slices,slices2)] + return target + + def gradients_X_diag(self, dL_dKdiag, X): + slices = index_to_slices(X[:,self.index_dim]) + kerns = itertools.repeat(self.kern) if self.single_kern else self.kern + target = np.zeros(X.shape) + [[target.__setitem__(s, kern.gradients_X_diag(dL_dKdiag[s],X[s])) for s in slices_i] for kern, slices_i in zip(kerns, slices)] + return target + + def update_gradients_diag(self, dL_dKdiag, X): + slices = index_to_slices(X[:,self.index_dim]) + kerns = itertools.repeat(self.kern) if self.single_kern else self.kern + if self.single_kern: target = np.zeros(self.kern.size) + else: target = [np.zeros(kern.size) for kern, _ in zip(kerns, slices)] + def collate_grads(kern, i, dL, X): + kern.update_gradients_diag(dL,X) + if self.single_kern: target[:] += kern.gradient + else: target[i][:] += kern.gradient + [[collate_grads(kern, i, dL_dKdiag[s], X[s,:]) for s in slices_i] for i, (kern, slices_i) in enumerate(zip(kerns, slices))] + if self.single_kern: kern.gradient = target + else:[kern.gradient.__setitem__(Ellipsis, target[i]) for i, [kern, _] in enumerate(zip(kerns, slices))] + +class Hierarchical(CombinationKernel): + """ + A kernel which can represent a simple hierarchical model. + + See Hensman et al 2013, "Hierarchical Bayesian modelling of gene expression time + series across irregularly sampled replicates and clusters" + http://www.biomedcentral.com/1471-2105/14/252 + + To construct this kernel, you must pass a list of kernels. the first kernel + will be assumed to be the 'base' kernel, and will be computed everywhere. + For every additional kernel, we assume another layer in the hierachy, with + a corresponding column of the input matrix which indexes which function the + data are in at that level. + + For more, see the ipython notebook documentation on Hierarchical + covariances. + """ + def __init__(self, kernels, name='hierarchy'): + assert all([k.input_dim==kernels[0].input_dim for k in kernels]) + assert len(kernels) > 1 + self.levels = len(kernels) -1 + input_max = max([k.input_dim for k in kernels]) + super(Hierarchical, self).__init__(kernels=kernels, extra_dims = range(input_max, input_max + len(kernels)-1), name=name) + + def K(self,X ,X2=None): + K = self.parts[0].K(X, X2) # compute 'base' kern everywhere + slices = [index_to_slices(X[:,i]) for i in self.extra_dims] + if X2 is None: + [[[np.add(K[s,s], k.K(X[s], None), K[s, s]) for s in slices_i] for slices_i in slices_k] for k, slices_k in zip(self.parts[1:], slices)] + else: + slices2 = [index_to_slices(X2[:,i]) for i in self.extra_dims] + [[[np.add(K[s,ss], k.K(X[s], X2[ss]), K[s, ss]) for s,ss in zip(slices_i, slices_j)] for slices_i, slices_j in zip(slices_k1, slices_k2)] for k, slices_k1, slices_k2 in zip(self.parts[1:], slices, slices2)] + return K + + def Kdiag(self,X): + return np.diag(self.K(X)) + + def gradients_X(self, dL_dK, X, X2=None): + raise NotImplementedError + + def update_gradients_full(self,dL_dK,X,X2=None): + slices = [index_to_slices(X[:,i]) for i in self.extra_dims] + if X2 is None: + self.parts[0].update_gradients_full(dL_dK, X, None) + for k, slices_k in zip(self.parts[1:], slices): + target = np.zeros(k.size) + def collate_grads(dL, X, X2, target): + k.update_gradients_full(dL,X,X2) + target += k.gradient + [[collate_grads(dL_dK[s,s], X[s], None, target) for s in slices_i] for slices_i in slices_k] + k.gradient[:] = target + else: + raise NotImplementedError + + diff --git a/GPy/kern/_src/kern.py b/GPy/kern/_src/kern.py new file mode 100644 index 00000000..57b2bff5 --- /dev/null +++ b/GPy/kern/_src/kern.py @@ -0,0 +1,280 @@ +# Copyright (c) 2012, GPy authors (see AUTHORS.txt). +# Licensed under the BSD 3-clause license (see LICENSE.txt) + +import sys +import numpy as np +from ...core.parameterization.parameterized import Parameterized +from kernel_slice_operations import KernCallsViaSlicerMeta +from ...util.caching import Cache_this +from GPy.core.parameterization.observable_array import ObsAr + + + +class Kern(Parameterized): + #=========================================================================== + # This adds input slice support. The rather ugly code for slicing can be + # found in kernel_slice_operations + __metaclass__ = KernCallsViaSlicerMeta + #=========================================================================== + _support_GPU=False + def __init__(self, input_dim, active_dims, name, useGPU=False, *a, **kw): + """ + The base class for a kernel: a positive definite function + which forms of a covariance function (kernel). + + input_dim: + + is the number of dimensions to work on. Make sure to give the + tight dimensionality of inputs. + You most likely want this to be the integer telling the number of + input dimensions of the kernel. + If this is not an integer (!) we will work on the whole input matrix X, + and not check whether dimensions match or not (!). + + active_dims: + + is the active_dimensions of inputs X we will work on. + All kernels will get sliced Xes as inputs, if active_dims is not None + Only positive integers are allowed in active_dims! + if active_dims is None, slicing is switched off and all X will be passed through as given. + + :param int input_dim: the number of input dimensions to the function + :param array-like|None active_dims: list of indices on which dimensions this kernel works on, or none if no slicing + + Do not instantiate. + """ + super(Kern, self).__init__(name=name, *a, **kw) + self.input_dim = int(input_dim) + + if active_dims is None: + active_dims = np.arange(input_dim) + + self.active_dims = np.atleast_1d(active_dims).astype(int) + + assert self.active_dims.size == self.input_dim, "input_dim={} does not match len(active_dim)={}, active_dims={}".format(self.input_dim, self.active_dims.size, self.active_dims) + + self._sliced_X = 0 + self.useGPU = self._support_GPU and useGPU + self._return_psi2_n_flag = ObsAr(np.zeros(1)).astype(bool) + + @property + def return_psi2_n(self): + """ + Flag whether to pass back psi2 as NxMxM or MxM, by summing out N. + """ + return self._return_psi2_n_flag[0] + @return_psi2_n.setter + def return_psi2_n(self, val): + def visit(self): + if isinstance(self, Kern): + self._return_psi2_n_flag[0]=val + self.traverse(visit) + + @Cache_this(limit=20) + def _slice_X(self, X): + return X[:, self.active_dims] + + def K(self, X, X2): + """ + Compute the kernel function. + + :param X: the first set of inputs to the kernel + :param X2: (optional) the second set of arguments to the kernel. If X2 + is None, this is passed throgh to the 'part' object, which + handLes this as X2 == X. + """ + raise NotImplementedError + def Kdiag(self, X): + raise NotImplementedError + def psi0(self, Z, variational_posterior): + raise NotImplementedError + def psi1(self, Z, variational_posterior): + raise NotImplementedError + def psi2(self, Z, variational_posterior): + raise NotImplementedError + def gradients_X(self, dL_dK, X, X2): + raise NotImplementedError + def gradients_X_diag(self, dL_dKdiag, X): + raise NotImplementedError + + def update_gradients_diag(self, dL_dKdiag, X): + """ update the gradients of all parameters when using only the diagonal elements of the covariance matrix""" + raise NotImplementedError + + def update_gradients_full(self, dL_dK, X, X2): + """Set the gradients of all parameters when doing full (N) inference.""" + raise NotImplementedError + + def update_gradients_expectations(self, dL_dpsi0, dL_dpsi1, dL_dpsi2, Z, variational_posterior): + """ + Set the gradients of all parameters when doing inference with + uncertain inputs, using expectations of the kernel. + + The esential maths is + + dL_d{theta_i} = dL_dpsi0 * dpsi0_d{theta_i} + + dL_dpsi1 * dpsi1_d{theta_i} + + dL_dpsi2 * dpsi2_d{theta_i} + """ + raise NotImplementedError + + def gradients_Z_expectations(self, dL_dpsi0, dL_dpsi1, dL_dpsi2, Z, variational_posterior): + """ + Returns the derivative of the objective wrt Z, using the chain rule + through the expectation variables. + """ + raise NotImplementedError + + def gradients_qX_expectations(self, dL_dpsi0, dL_dpsi1, dL_dpsi2, Z, variational_posterior): + """ + Compute the gradients wrt the parameters of the variational + distruibution q(X), chain-ruling via the expectations of the kernel + """ + raise NotImplementedError + + def plot(self, x=None, fignum=None, ax=None, title=None, plot_limits=None, resolution=None, **mpl_kwargs): + """ + plot this kernel. + :param x: the value to use for the other kernel argument (kernels are a function of two variables!) + :param fignum: figure number of the plot + :param ax: matplotlib axis to plot on + :param title: the matplotlib title + :param plot_limits: the range over which to plot the kernel + :resolution: the resolution of the lines used in plotting + :mpl_kwargs avalid keyword arguments to pass through to matplotlib (e.g. lw=7) + """ + assert "matplotlib" in sys.modules, "matplotlib package has not been imported." + from ...plotting.matplot_dep import kernel_plots + kernel_plots.plot(self, x, fignum, ax, title, plot_limits, resolution, **mpl_kwargs) + + def plot_ARD(self, *args, **kw): + """ + See :class:`~GPy.plotting.matplot_dep.kernel_plots` + """ + import sys + assert "matplotlib" in sys.modules, "matplotlib package has not been imported." + from ...plotting.matplot_dep import kernel_plots + return kernel_plots.plot_ARD(self,*args,**kw) + + def input_sensitivity(self, summarize=True): + """ + Returns the sensitivity for each dimension of this kernel. + """ + return np.zeros(self.input_dim) + + def __add__(self, other): + """ Overloading of the '+' operator. for more control, see self.add """ + return self.add(other) + + def __iadd__(self, other): + return self.add(other) + + def add(self, other, name='add'): + """ + Add another kernel to this one. + + :param other: the other kernel to be added + :type other: GPy.kern + + """ + assert isinstance(other, Kern), "only kernels can be added to kernels..." + from add import Add + return Add([self, other], name=name) + + def __mul__(self, other): + """ Here we overload the '*' operator. See self.prod for more information""" + return self.prod(other) + + def __imul__(self, other): + """ Here we overload the '*' operator. See self.prod for more information""" + return self.prod(other) + + def __pow__(self, other): + """ + Shortcut for tensor `prod`. + """ + assert np.all(self.active_dims == range(self.input_dim)), "Can only use kernels, which have their input_dims defined from 0" + assert np.all(other.active_dims == range(other.input_dim)), "Can only use kernels, which have their input_dims defined from 0" + other.active_dims += self.input_dim + return self.prod(other) + + def prod(self, other, name='mul'): + """ + Multiply two kernels (either on the same space, or on the tensor + product of the input space). + + :param other: the other kernel to be added + :type other: GPy.kern + :param tensor: whether or not to use the tensor space (default is false). + :type tensor: bool + + """ + assert isinstance(other, Kern), "only kernels can be multiplied to kernels..." + from prod import Prod + #kernels = [] + #if isinstance(self, Prod): kernels.extend(self.parameters) + #else: kernels.append(self) + #if isinstance(other, Prod): kernels.extend(other.parameters) + #else: kernels.append(other) + return Prod([self, other], name) + + def _check_input_dim(self, X): + assert X.shape[1] == self.input_dim, "{} did not specify active_dims and X has wrong shape: X_dim={}, whereas input_dim={}".format(self.name, X.shape[1], self.input_dim) + + def _check_active_dims(self, X): + assert X.shape[1] >= len(self.active_dims), "At least {} dimensional X needed, X.shape={!s}".format(len(self.active_dims), X.shape) + + +class CombinationKernel(Kern): + """ + Abstract super class for combination kernels. + A combination kernel combines (a list of) kernels and works on those. + Examples are the HierarchicalKernel or Add and Prod kernels. + """ + def __init__(self, kernels, name, extra_dims=[]): + """ + Abstract super class for combination kernels. + A combination kernel combines (a list of) kernels and works on those. + Examples are the HierarchicalKernel or Add and Prod kernels. + + :param list kernels: List of kernels to combine (can be only one element) + :param str name: name of the combination kernel + :param array-like extra_dims: if needed extra dimensions for the combination kernel to work on + """ + assert all([isinstance(k, Kern) for k in kernels]) + extra_dims = np.array(extra_dims, dtype=int) + input_dim, active_dims = self.get_input_dim_active_dims(kernels, extra_dims) + # initialize the kernel with the full input_dim + super(CombinationKernel, self).__init__(input_dim, active_dims, name) + self.extra_dims = extra_dims + self.link_parameters(*kernels) + + @property + def parts(self): + return self.parameters + + def get_input_dim_active_dims(self, kernels, extra_dims = None): + #active_dims = reduce(np.union1d, (np.r_[x.active_dims] for x in kernels), np.array([], dtype=int)) + #active_dims = np.array(np.concatenate((active_dims, extra_dims if extra_dims is not None else [])), dtype=int) + input_dim = reduce(max, (k.active_dims.max() for k in kernels)) + 1 + + if extra_dims is not None: + input_dim += extra_dims.size + + active_dims = np.arange(input_dim) + return input_dim, active_dims + + def input_sensitivity(self, summarize=True): + """ + If summize is true, we want to get the summerized view of the sensitivities, + otherwise put everything into an array with shape (#kernels, input_dim) + in the order of appearance of the kernels in the parameterized object. + """ + raise NotImplementedError("Choose the kernel you want to get the sensitivity for. You need to override the default behaviour for getting the input sensitivity to be able to get the input sensitivity. For sum kernel it is the sum of all sensitivities, TODO: product kernel? Other kernels?, also TODO: shall we return all the sensitivities here in the combination kernel? So we can combine them however we want? This could lead to just plot all the sensitivities here...") + + def _check_active_dims(self, X): + return + + def _check_input_dim(self, X): + # As combination kernels cannot always know, what their inner kernels have as input dims, the check will be done inside them, respectively + return diff --git a/GPy/kern/_src/kernel_slice_operations.py b/GPy/kern/_src/kernel_slice_operations.py new file mode 100644 index 00000000..3473ffce --- /dev/null +++ b/GPy/kern/_src/kernel_slice_operations.py @@ -0,0 +1,143 @@ +''' +Created on 11 Mar 2014 + +@author: maxz +''' +from ...core.parameterization.parameterized import ParametersChangedMeta +import numpy as np +from functools import wraps + +def put_clean(dct, name, func): + if name in dct: + dct['_clean_{}'.format(name)] = dct[name] + dct[name] = func(dct[name]) + +class KernCallsViaSlicerMeta(ParametersChangedMeta): + def __new__(cls, name, bases, dct): + put_clean(dct, 'K', _slice_K) + put_clean(dct, 'Kdiag', _slice_Kdiag) + put_clean(dct, 'update_gradients_full', _slice_update_gradients_full) + put_clean(dct, 'update_gradients_diag', _slice_update_gradients_diag) + put_clean(dct, 'gradients_X', _slice_gradients_X) + put_clean(dct, 'gradients_X_diag', _slice_gradients_X_diag) + + put_clean(dct, 'psi0', _slice_psi) + put_clean(dct, 'psi1', _slice_psi) + put_clean(dct, 'psi2', _slice_psi) + put_clean(dct, 'update_gradients_expectations', _slice_update_gradients_expectations) + put_clean(dct, 'gradients_Z_expectations', _slice_gradients_Z_expectations) + put_clean(dct, 'gradients_qX_expectations', _slice_gradients_qX_expectations) + return super(KernCallsViaSlicerMeta, cls).__new__(cls, name, bases, dct) + +class _Slice_wrap(object): + def __init__(self, k, X, X2=None): + self.k = k + self.shape = X.shape + assert X.ndim == 2, "only matrices are allowed as inputs to kernels for now, given X.shape={!s}".format(X.shape) + if X2 is not None: + assert X2.ndim == 2, "only matrices are allowed as inputs to kernels for now, given X2.shape={!s}".format(X2.shape) + if (self.k.active_dims is not None) and (self.k._sliced_X == 0): + self.k._check_active_dims(X) + self.X = self.k._slice_X(X) + self.X2 = self.k._slice_X(X2) if X2 is not None else X2 + self.ret = True + else: + self.k._check_input_dim(X) + self.X = X + self.X2 = X2 + self.ret = False + def __enter__(self): + self.k._sliced_X += 1 + return self + def __exit__(self, *a): + self.k._sliced_X -= 1 + def handle_return_array(self, return_val): + if self.ret: + ret = np.zeros(self.shape) + ret[:, self.k.active_dims] = return_val + return ret + return return_val + +def _slice_K(f): + @wraps(f) + def wrap(self, X, X2 = None, *a, **kw): + with _Slice_wrap(self, X, X2) as s: + ret = f(self, s.X, s.X2, *a, **kw) + return ret + return wrap + +def _slice_Kdiag(f): + @wraps(f) + def wrap(self, X, *a, **kw): + with _Slice_wrap(self, X, None) as s: + ret = f(self, s.X, *a, **kw) + return ret + return wrap + +def _slice_update_gradients_full(f): + @wraps(f) + def wrap(self, dL_dK, X, X2=None): + with _Slice_wrap(self, X, X2) as s: + ret = f(self, dL_dK, s.X, s.X2) + return ret + return wrap + +def _slice_update_gradients_diag(f): + @wraps(f) + def wrap(self, dL_dKdiag, X): + with _Slice_wrap(self, X, None) as s: + ret = f(self, dL_dKdiag, s.X) + return ret + return wrap + +def _slice_gradients_X(f): + @wraps(f) + def wrap(self, dL_dK, X, X2=None): + with _Slice_wrap(self, X, X2) as s: + ret = s.handle_return_array(f(self, dL_dK, s.X, s.X2)) + return ret + return wrap + +def _slice_gradients_X_diag(f): + @wraps(f) + def wrap(self, dL_dKdiag, X): + with _Slice_wrap(self, X, None) as s: + ret = s.handle_return_array(f(self, dL_dKdiag, s.X)) + return ret + return wrap + +def _slice_psi(f): + @wraps(f) + def wrap(self, Z, variational_posterior): + with _Slice_wrap(self, Z, variational_posterior) as s: + ret = f(self, s.X, s.X2) + return ret + return wrap + +def _slice_update_gradients_expectations(f): + @wraps(f) + def wrap(self, dL_dpsi0, dL_dpsi1, dL_dpsi2, Z, variational_posterior): + with _Slice_wrap(self, Z, variational_posterior) as s: + ret = f(self, dL_dpsi0, dL_dpsi1, dL_dpsi2, s.X, s.X2) + return ret + return wrap + +def _slice_gradients_Z_expectations(f): + @wraps(f) + def wrap(self, dL_dpsi0, dL_dpsi1, dL_dpsi2, Z, variational_posterior): + with _Slice_wrap(self, Z, variational_posterior) as s: + ret = s.handle_return_array(f(self, dL_dpsi0, dL_dpsi1, dL_dpsi2, s.X, s.X2)) + return ret + return wrap + +def _slice_gradients_qX_expectations(f): + @wraps(f) + def wrap(self, dL_dpsi0, dL_dpsi1, dL_dpsi2, Z, variational_posterior): + with _Slice_wrap(self, variational_posterior, Z) as s: + ret = list(f(self, dL_dpsi0, dL_dpsi1, dL_dpsi2, s.X2, s.X)) + r2 = ret[:2] + ret[0] = s.handle_return_array(r2[0]) + ret[1] = s.handle_return_array(r2[1]) + del r2 + return ret + return wrap diff --git a/GPy/kern/_src/linear.py b/GPy/kern/_src/linear.py new file mode 100644 index 00000000..9d1a956b --- /dev/null +++ b/GPy/kern/_src/linear.py @@ -0,0 +1,177 @@ +# Copyright (c) 2012, GPy authors (see AUTHORS.txt). +# Licensed under the BSD 3-clause license (see LICENSE.txt) + + +import numpy as np +from kern import Kern +from ...util.linalg import tdot +from ...core.parameterization import Param +from ...core.parameterization.transformations import Logexp +from ...util.caching import Cache_this +from ...util.config import * +from .psi_comp import PSICOMP_Linear + +class Linear(Kern): + """ + Linear kernel + + .. math:: + + k(x,y) = \sum_{i=1}^input_dim \sigma^2_i x_iy_i + + :param input_dim: the number of input dimensions + :type input_dim: int + :param variances: the vector of variances :math:`\sigma^2_i` + :type variances: array or list of the appropriate size (or float if there + is only one variance parameter) + :param ARD: Auto Relevance Determination. If False, the kernel has only one + variance parameter \sigma^2, otherwise there is one variance + parameter per dimension. + :type ARD: Boolean + :rtype: kernel object + + """ + + def __init__(self, input_dim, variances=None, ARD=False, active_dims=None, name='linear'): + super(Linear, self).__init__(input_dim, active_dims, name) + self.ARD = ARD + if not ARD: + if variances is not None: + variances = np.asarray(variances) + assert variances.size == 1, "Only one variance needed for non-ARD kernel" + else: + variances = np.ones(1) + else: + if variances is not None: + variances = np.asarray(variances) + assert variances.size == self.input_dim, "bad number of variances, need one ARD variance per input_dim" + else: + variances = np.ones(self.input_dim) + + self.variances = Param('variances', variances, Logexp()) + self.link_parameter(self.variances) + self.psicomp = PSICOMP_Linear() + + @Cache_this(limit=2) + def K(self, X, X2=None): + if self.ARD: + if X2 is None: + return tdot(X*np.sqrt(self.variances)) + else: + rv = np.sqrt(self.variances) + return np.dot(X*rv, (X2*rv).T) + else: + return self._dot_product(X, X2) * self.variances + + @Cache_this(limit=1, ignore_args=(0,)) + def _dot_product(self, X, X2=None): + if X2 is None: + return tdot(X) + else: + return np.dot(X, X2.T) + + def Kdiag(self, X): + return np.sum(self.variances * np.square(X), -1) + + def update_gradients_full(self, dL_dK, X, X2=None): + if self.ARD: + if X2 is None: + #self.variances.gradient = np.array([np.sum(dL_dK * tdot(X[:, i:i + 1])) for i in range(self.input_dim)]) + self.variances.gradient = np.einsum('ij,iq,jq->q', dL_dK, X, X) + else: + #product = X[:, None, :] * X2[None, :, :] + #self.variances.gradient = (dL_dK[:, :, None] * product).sum(0).sum(0) + self.variances.gradient = np.einsum('ij,iq,jq->q', dL_dK, X, X2) + else: + self.variances.gradient = np.sum(self._dot_product(X, X2) * dL_dK) + + def update_gradients_diag(self, dL_dKdiag, X): + tmp = dL_dKdiag[:, None] * X ** 2 + if self.ARD: + self.variances.gradient = tmp.sum(0) + else: + self.variances.gradient = np.atleast_1d(tmp.sum()) + + + def gradients_X(self, dL_dK, X, X2=None): + if X2 is None: + return np.einsum('jq,q,ij->iq', X, 2*self.variances, dL_dK) + else: + #return (((X2[None,:, :] * self.variances)) * dL_dK[:, :, None]).sum(1) + return np.einsum('jq,q,ij->iq', X2, self.variances, dL_dK) + + def gradients_X_diag(self, dL_dKdiag, X): + return 2.*self.variances*dL_dKdiag[:,None]*X + + def input_sensitivity(self, summarize=True): + return np.ones(self.input_dim) * self.variances + + #---------------------------------------# + # PSI statistics # + #---------------------------------------# + + def psi0(self, Z, variational_posterior): + return self.psicomp.psicomputations(self.variances, Z, variational_posterior)[0] + + def psi1(self, Z, variational_posterior): + return self.psicomp.psicomputations(self.variances, Z, variational_posterior)[1] + + def psi2(self, Z, variational_posterior): + return self.psicomp.psicomputations(self.variances, Z, variational_posterior)[2] + + def update_gradients_expectations(self, dL_dpsi0, dL_dpsi1, dL_dpsi2, Z, variational_posterior): + dL_dvar = self.psicomp.psiDerivativecomputations(dL_dpsi0, dL_dpsi1, dL_dpsi2, self.variances, Z, variational_posterior)[0] + if self.ARD: + self.variances.gradient = dL_dvar + else: + self.variances.gradient = dL_dvar.sum() + + def gradients_Z_expectations(self, dL_dpsi0, dL_dpsi1, dL_dpsi2, Z, variational_posterior): + return self.psicomp.psiDerivativecomputations(dL_dpsi0, dL_dpsi1, dL_dpsi2, self.variances, Z, variational_posterior)[1] + + def gradients_qX_expectations(self, dL_dpsi0, dL_dpsi1, dL_dpsi2, Z, variational_posterior): + return self.psicomp.psiDerivativecomputations(dL_dpsi0, dL_dpsi1, dL_dpsi2, self.variances, Z, variational_posterior)[2:] + +class LinearFull(Kern): + def __init__(self, input_dim, rank, W=None, kappa=None, active_dims=None, name='linear_full'): + super(LinearFull, self).__init__(input_dim, active_dims, name) + if W is None: + W = np.ones((input_dim, rank)) + if kappa is None: + kappa = np.ones(input_dim) + assert W.shape == (input_dim, rank) + assert kappa.shape == (input_dim,) + + self.W = Param('W', W) + self.kappa = Param('kappa', kappa, Logexp()) + self.link_parameters(self.W, self.kappa) + + def K(self, X, X2=None): + P = np.dot(self.W, self.W.T) + np.diag(self.kappa) + return np.einsum('ij,jk,lk->il', X, P, X if X2 is None else X2) + + def update_gradients_full(self, dL_dK, X, X2=None): + self.kappa.gradient = np.einsum('ij,ik,kj->j', X, dL_dK, X if X2 is None else X2) + self.W.gradient = np.einsum('ij,kl,ik,lm->jm', X, X if X2 is None else X2, dL_dK, self.W) + self.W.gradient += np.einsum('ij,kl,ik,jm->lm', X, X if X2 is None else X2, dL_dK, self.W) + + def Kdiag(self, X): + P = np.dot(self.W, self.W.T) + np.diag(self.kappa) + return np.einsum('ij,jk,ik->i', X, P, X) + + def update_gradients_diag(self, dL_dKdiag, X): + self.kappa.gradient = np.einsum('ij,i->j', np.square(X), dL_dKdiag) + self.W.gradient = 2.*np.einsum('ij,ik,jl,i->kl', X, X, self.W, dL_dKdiag) + + def gradients_X(self, dL_dK, X, X2=None): + P = np.dot(self.W, self.W.T) + np.diag(self.kappa) + if X2 is None: + return 2.*np.einsum('ij,jk,kl->il', dL_dK, X, P) + else: + return np.einsum('ij,jk,kl->il', dL_dK, X2, P) + + def gradients_X_diag(self, dL_dKdiag, X): + P = np.dot(self.W, self.W.T) + np.diag(self.kappa) + return 2.*np.einsum('jk,i,ij->ik', P, dL_dKdiag, X) + + diff --git a/GPy/kern/_src/mlp.py b/GPy/kern/_src/mlp.py new file mode 100644 index 00000000..badbd60d --- /dev/null +++ b/GPy/kern/_src/mlp.py @@ -0,0 +1,129 @@ +# Copyright (c) 2013, GPy authors (see AUTHORS.txt). +# Licensed under the BSD 3-clause license (see LICENSE.txt) + +from kern import Kern +from ...core.parameterization import Param +from ...core.parameterization.transformations import Logexp +import numpy as np +four_over_tau = 2./np.pi + +class MLP(Kern): + """ + + Multi layer perceptron kernel (also known as arc sine kernel or neural network kernel) + + .. math:: + + k(x,y) = \\sigma^{2}\\frac{2}{\\pi } \\text{asin} \\left ( \\frac{ \\sigma_w^2 x^\\top y+\\sigma_b^2}{\\sqrt{\\sigma_w^2x^\\top x + \\sigma_b^2 + 1}\\sqrt{\\sigma_w^2 y^\\top y \\sigma_b^2 +1}} \\right ) + + + :param input_dim: the number of input dimensions + :type input_dim: int + :param variance: the variance :math:`\sigma^2` + :type variance: float + :param weight_variance: the vector of the variances of the prior over input weights in the neural network :math:`\sigma^2_w` + :type weight_variance: array or list of the appropriate size (or float if there is only one weight variance parameter) + :param bias_variance: the variance of the prior over bias parameters :math:`\sigma^2_b` + :param ARD: Auto Relevance Determination. If equal to "False", the kernel is isotropic (ie. one weight variance parameter \sigma^2_w), otherwise there is one weight variance parameter per dimension. + :type ARD: Boolean + :rtype: Kernpart object + + + """ + + def __init__(self, input_dim, variance=1., weight_variance=1., bias_variance=100., active_dims=None, name='mlp'): + super(MLP, self).__init__(input_dim, active_dims, name) + self.variance = Param('variance', variance, Logexp()) + self.weight_variance = Param('weight_variance', weight_variance, Logexp()) + self.bias_variance = Param('bias_variance', bias_variance, Logexp()) + self.link_parameters(self.variance, self.weight_variance, self.bias_variance) + + + def K(self, X, X2=None): + self._K_computations(X, X2) + return self.variance*self._K_dvar + + def Kdiag(self, X): + """Compute the diagonal of the covariance matrix for X.""" + self._K_diag_computations(X) + return self.variance*self._K_diag_dvar + + def update_gradients_full(self, dL_dK, X, X2=None): + """Derivative of the covariance with respect to the parameters.""" + self._K_computations(X, X2) + self.variance.gradient = np.sum(self._K_dvar*dL_dK) + + denom3 = self._K_denom**3 + base = four_over_tau*self.variance/np.sqrt(1-self._K_asin_arg*self._K_asin_arg) + base_cov_grad = base*dL_dK + + if X2 is None: + vec = np.diag(self._K_inner_prod) + self.weight_variance.gradient = ((self._K_inner_prod/self._K_denom + -.5*self._K_numer/denom3 + *(np.outer((self.weight_variance*vec+self.bias_variance+1.), vec) + +np.outer(vec,(self.weight_variance*vec+self.bias_variance+1.))))*base_cov_grad).sum() + self.bias_variance.gradient = ((1./self._K_denom + -.5*self._K_numer/denom3 + *((vec[None, :]+vec[:, None])*self.weight_variance + +2.*self.bias_variance + 2.))*base_cov_grad).sum() + else: + vec1 = (X*X).sum(1) + vec2 = (X2*X2).sum(1) + self.weight_variance.gradient = ((self._K_inner_prod/self._K_denom + -.5*self._K_numer/denom3 + *(np.outer((self.weight_variance*vec1+self.bias_variance+1.), vec2) + np.outer(vec1, self.weight_variance*vec2 + self.bias_variance+1.)))*base_cov_grad).sum() + self.bias_variance.gradient = ((1./self._K_denom + -.5*self._K_numer/denom3 + *((vec1[:, None]+vec2[None, :])*self.weight_variance + + 2*self.bias_variance + 2.))*base_cov_grad).sum() + + def update_gradients_diag(self, X): + raise NotImplementedError, "TODO" + + + def gradients_X(self, dL_dK, X, X2): + """Derivative of the covariance matrix with respect to X""" + self._K_computations(X, X2) + arg = self._K_asin_arg + numer = self._K_numer + denom = self._K_denom + denom3 = denom*denom*denom + if X2 is not None: + vec2 = (X2*X2).sum(1)*self.weight_variance+self.bias_variance + 1. + return four_over_tau*self.weight_variance*self.variance*((X2[None, :, :]/denom[:, :, None] - vec2[None, :, None]*X[:, None, :]*(numer/denom3)[:, :, None])*(dL_dK/np.sqrt(1-arg*arg))[:, :, None]).sum(1) + else: + vec = (X*X).sum(1)*self.weight_variance+self.bias_variance + 1. + return 2*four_over_tau*self.weight_variance*self.variance*((X[None, :, :]/denom[:, :, None] - vec[None, :, None]*X[:, None, :]*(numer/denom3)[:, :, None])*(dL_dK/np.sqrt(1-arg*arg))[:, :, None]).sum(1) + + def gradients_X_diag(self, dL_dKdiag, X): + """Gradient of diagonal of covariance with respect to X""" + self._K_diag_computations(X) + arg = self._K_diag_asin_arg + denom = self._K_diag_denom + #numer = self._K_diag_numer + return four_over_tau*2.*self.weight_variance*self.variance*X*(1./denom*(1. - arg)*dL_dKdiag/(np.sqrt(1-arg*arg)))[:, None] + + + def _K_computations(self, X, X2): + """Pre-computations for the covariance matrix (used for computing the covariance and its gradients.""" + if X2 is None: + self._K_inner_prod = np.dot(X,X.T) + self._K_numer = self._K_inner_prod*self.weight_variance + self.bias_variance + vec = np.diag(self._K_numer) + 1. + self._K_denom = np.sqrt(np.outer(vec,vec)) + else: + self._K_inner_prod = np.dot(X,X2.T) + self._K_numer = self._K_inner_prod*self.weight_variance + self.bias_variance + vec1 = (X*X).sum(1)*self.weight_variance + self.bias_variance + 1. + vec2 = (X2*X2).sum(1)*self.weight_variance + self.bias_variance + 1. + self._K_denom = np.sqrt(np.outer(vec1,vec2)) + self._K_asin_arg = self._K_numer/self._K_denom + self._K_dvar = four_over_tau*np.arcsin(self._K_asin_arg) + + def _K_diag_computations(self, X): + """Pre-computations concerning the diagonal terms (used for computation of diagonal and its gradients).""" + self._K_diag_numer = (X*X).sum(1)*self.weight_variance + self.bias_variance + self._K_diag_denom = self._K_diag_numer+1. + self._K_diag_asin_arg = self._K_diag_numer/self._K_diag_denom + self._K_diag_dvar = four_over_tau*np.arcsin(self._K_diag_asin_arg) diff --git a/GPy/kern/parts/periodic_Matern52.py b/GPy/kern/_src/periodic.py similarity index 53% rename from GPy/kern/parts/periodic_Matern52.py rename to GPy/kern/_src/periodic.py index 882084fd..e8e16506 100644 --- a/GPy/kern/parts/periodic_Matern52.py +++ b/GPy/kern/_src/periodic.py @@ -2,12 +2,288 @@ # Licensed under the BSD 3-clause license (see LICENSE.txt) -from kernpart import Kernpart import numpy as np -from GPy.util.linalg import mdot -from GPy.util.decorators import silence_errors +from kern import Kern +from ...util.linalg import mdot +from ...util.decorators import silence_errors +from ...core.parameterization.param import Param +from ...core.parameterization.transformations import Logexp -class PeriodicMatern52(Kernpart): +class Periodic(Kern): + def __init__(self, input_dim, variance, lengthscale, period, n_freq, lower, upper, active_dims, name): + """ + :type input_dim: int + :param variance: the variance of the Matern kernel + :type variance: float + :param lengthscale: the lengthscale of the Matern kernel + :type lengthscale: np.ndarray of size (input_dim,) + :param period: the period + :type period: float + :param n_freq: the number of frequencies considered for the periodic subspace + :type n_freq: int + :rtype: kernel object + """ + + assert input_dim==1, "Periodic kernels are only defined for input_dim=1" + super(Periodic, self).__init__(input_dim, active_dims, name) + self.input_dim = input_dim + self.lower,self.upper = lower, upper + self.n_freq = n_freq + self.n_basis = 2*n_freq + self.variance = Param('variance', np.float64(variance), Logexp()) + self.lengthscale = Param('lengthscale', np.float64(lengthscale), Logexp()) + self.period = Param('period', np.float64(period), Logexp()) + self.link_parameters(self.variance, self.lengthscale, self.period) + + def _cos(self, alpha, omega, phase): + def f(x): + return alpha*np.cos(omega*x + phase) + return f + + @silence_errors + def _cos_factorization(self, alpha, omega, phase): + r1 = np.sum(alpha*np.cos(phase),axis=1)[:,None] + r2 = np.sum(alpha*np.sin(phase),axis=1)[:,None] + r = np.sqrt(r1**2 + r2**2) + psi = np.where(r1 != 0, (np.arctan(r2/r1) + (r1<0.)*np.pi),np.arcsin(r2)) + return r,omega[:,0:1], psi + + @silence_errors + def _int_computation(self,r1,omega1,phi1,r2,omega2,phi2): + Gint1 = 1./(omega1+omega2.T)*( np.sin((omega1+omega2.T)*self.upper+phi1+phi2.T) - np.sin((omega1+omega2.T)*self.lower+phi1+phi2.T)) + 1./(omega1-omega2.T)*( np.sin((omega1-omega2.T)*self.upper+phi1-phi2.T) - np.sin((omega1-omega2.T)*self.lower+phi1-phi2.T) ) + Gint2 = 1./(omega1+omega2.T)*( np.sin((omega1+omega2.T)*self.upper+phi1+phi2.T) - np.sin((omega1+omega2.T)*self.lower+phi1+phi2.T)) + np.cos(phi1-phi2.T)*(self.upper-self.lower) + Gint = np.dot(r1,r2.T)/2 * np.where(np.isnan(Gint1),Gint2,Gint1) + return Gint + + def K(self, X, X2=None): + FX = self._cos(self.basis_alpha[None,:],self.basis_omega[None,:],self.basis_phi[None,:])(X) + if X2 is None: + FX2 = FX + else: + FX2 = self._cos(self.basis_alpha[None,:],self.basis_omega[None,:],self.basis_phi[None,:])(X2) + return mdot(FX,self.Gi,FX2.T) + + def Kdiag(self,X): + return np.diag(self.K(X)) + + + + +class PeriodicExponential(Periodic): + """ + Kernel of the periodic subspace (up to a given frequency) of a exponential + (Matern 1/2) RKHS. + + Only defined for input_dim=1. + """ + + def __init__(self, input_dim=1, variance=1., lengthscale=1., period=2.*np.pi, n_freq=10, lower=0., upper=4*np.pi, active_dims=None, name='periodic_exponential'): + super(PeriodicExponential, self).__init__(input_dim, variance, lengthscale, period, n_freq, lower, upper, active_dims, name) + + def parameters_changed(self): + self.a = [1./self.lengthscale, 1.] + self.b = [1] + + self.basis_alpha = np.ones((self.n_basis,)) + self.basis_omega = (2*np.pi*np.arange(1,self.n_freq+1)/self.period).repeat(2) + self.basis_phi = np.zeros(self.n_freq * 2) + self.basis_phi[::2] = -np.pi/2 + + self.G = self.Gram_matrix() + self.Gi = np.linalg.inv(self.G) + + def Gram_matrix(self): + La = np.column_stack((self.a[0]*np.ones((self.n_basis,1)),self.a[1]*self.basis_omega)) + Lo = np.column_stack((self.basis_omega,self.basis_omega)) + Lp = np.column_stack((self.basis_phi,self.basis_phi+np.pi/2)) + r,omega,phi = self._cos_factorization(La,Lo,Lp) + Gint = self._int_computation( r,omega,phi, r,omega,phi) + Flower = np.array(self._cos(self.basis_alpha,self.basis_omega,self.basis_phi)(self.lower))[:,None] + return(self.lengthscale/(2*self.variance) * Gint + 1./self.variance*np.dot(Flower,Flower.T)) + + @silence_errors + def update_gradients_full(self, dL_dK, X, X2=None): + """derivative of the covariance matrix with respect to the parameters (shape is N x num_inducing x num_params)""" + if X2 is None: X2 = X + FX = self._cos(self.basis_alpha[None,:],self.basis_omega[None,:],self.basis_phi[None,:])(X) + FX2 = self._cos(self.basis_alpha[None,:],self.basis_omega[None,:],self.basis_phi[None,:])(X2) + + La = np.column_stack((self.a[0]*np.ones((self.n_basis,1)),self.a[1]*self.basis_omega)) + Lo = np.column_stack((self.basis_omega,self.basis_omega)) + Lp = np.column_stack((self.basis_phi,self.basis_phi+np.pi/2)) + r,omega,phi = self._cos_factorization(La,Lo,Lp) + Gint = self._int_computation( r,omega,phi, r,omega,phi) + + Flower = np.array(self._cos(self.basis_alpha,self.basis_omega,self.basis_phi)(self.lower))[:,None] + + #dK_dvar + dK_dvar = 1./self.variance*mdot(FX,self.Gi,FX2.T) + + #dK_dlen + da_dlen = [-1./self.lengthscale**2,0.] + dLa_dlen = np.column_stack((da_dlen[0]*np.ones((self.n_basis,1)),da_dlen[1]*self.basis_omega)) + r1,omega1,phi1 = self._cos_factorization(dLa_dlen,Lo,Lp) + dGint_dlen = self._int_computation(r1,omega1,phi1, r,omega,phi) + dGint_dlen = dGint_dlen + dGint_dlen.T + dG_dlen = 1./2*Gint + self.lengthscale/2*dGint_dlen + dK_dlen = -mdot(FX,self.Gi,dG_dlen/self.variance,self.Gi,FX2.T) + + #dK_dper + dFX_dper = self._cos(-self.basis_alpha[None,:]*self.basis_omega[None,:]/self.period*X ,self.basis_omega[None,:],self.basis_phi[None,:]+np.pi/2)(X) + dFX2_dper = self._cos(-self.basis_alpha[None,:]*self.basis_omega[None,:]/self.period*X2,self.basis_omega[None,:],self.basis_phi[None,:]+np.pi/2)(X2) + + dLa_dper = np.column_stack((-self.a[0]*self.basis_omega/self.period, -self.a[1]*self.basis_omega**2/self.period)) + dLp_dper = np.column_stack((self.basis_phi+np.pi/2,self.basis_phi+np.pi)) + r1,omega1,phi1 = self._cos_factorization(dLa_dper,Lo,dLp_dper) + + IPPprim1 = self.upper*(1./(omega+omega1.T)*np.cos((omega+omega1.T)*self.upper+phi+phi1.T-np.pi/2) + 1./(omega-omega1.T)*np.cos((omega-omega1.T)*self.upper+phi-phi1.T-np.pi/2)) + IPPprim1 -= self.lower*(1./(omega+omega1.T)*np.cos((omega+omega1.T)*self.lower+phi+phi1.T-np.pi/2) + 1./(omega-omega1.T)*np.cos((omega-omega1.T)*self.lower+phi-phi1.T-np.pi/2)) + # SIMPLIFY!!! IPPprim1 = (self.upper - self.lower)*np.cos((omega+omega1.T)*self.upper+phi+phi1.T-np.pi/2) + 1./(omega-omega1.T)*np.cos((omega-omega1.T)*self.upper+phi-phi1.T-np.pi/2)) + IPPprim2 = self.upper*(1./(omega+omega1.T)*np.cos((omega+omega1.T)*self.upper+phi+phi1.T-np.pi/2) + self.upper*np.cos(phi-phi1.T)) + IPPprim2 -= self.lower*(1./(omega+omega1.T)*np.cos((omega+omega1.T)*self.lower+phi+phi1.T-np.pi/2) + self.lower*np.cos(phi-phi1.T)) + IPPprim = np.where(np.logical_or(np.isnan(IPPprim1), np.isinf(IPPprim1)), IPPprim2, IPPprim1) + + + IPPint1 = 1./(omega+omega1.T)**2*np.cos((omega+omega1.T)*self.upper+phi+phi1.T-np.pi) + 1./(omega-omega1.T)**2*np.cos((omega-omega1.T)*self.upper+phi-phi1.T-np.pi) + IPPint1 -= 1./(omega+omega1.T)**2*np.cos((omega+omega1.T)*self.lower+phi+phi1.T-np.pi) + 1./(omega-omega1.T)**2*np.cos((omega-omega1.T)*self.lower+phi-phi1.T-np.pi) + IPPint2 = 1./(omega+omega1.T)**2*np.cos((omega+omega1.T)*self.upper+phi+phi1.T-np.pi) + 1./2*self.upper**2*np.cos(phi-phi1.T) + IPPint2 -= 1./(omega+omega1.T)**2*np.cos((omega+omega1.T)*self.lower+phi+phi1.T-np.pi) + 1./2*self.lower**2*np.cos(phi-phi1.T) + #IPPint2[0,0] = (self.upper**2 - self.lower**2)*np.cos(phi[0,0])*np.cos(phi1[0,0]) + IPPint = np.where(np.isnan(IPPint1),IPPint2,IPPint1) + + dLa_dper2 = np.column_stack((-self.a[1]*self.basis_omega/self.period)) + dLp_dper2 = np.column_stack((self.basis_phi+np.pi/2)) + r2,omega2,phi2 = dLa_dper2.T,Lo[:,0:1],dLp_dper2.T + + dGint_dper = np.dot(r,r1.T)/2 * (IPPprim - IPPint) + self._int_computation(r2,omega2,phi2, r,omega,phi) + dGint_dper = dGint_dper + dGint_dper.T + + dFlower_dper = np.array(self._cos(-self.lower*self.basis_alpha*self.basis_omega/self.period,self.basis_omega,self.basis_phi+np.pi/2)(self.lower))[:,None] + + dG_dper = 1./self.variance*(self.lengthscale/2*dGint_dper + self.b[0]*(np.dot(dFlower_dper,Flower.T)+np.dot(Flower,dFlower_dper.T))) + + dK_dper = mdot(dFX_dper,self.Gi,FX2.T) - mdot(FX,self.Gi,dG_dper,self.Gi,FX2.T) + mdot(FX,self.Gi,dFX2_dper.T) + + self.variance.gradient = np.sum(dK_dvar*dL_dK) + self.lengthscale.gradient = np.sum(dK_dlen*dL_dK) + self.period.gradient = np.sum(dK_dper*dL_dK) + + + +class PeriodicMatern32(Periodic): + """ + Kernel of the periodic subspace (up to a given frequency) of a Matern 3/2 RKHS. Only defined for input_dim=1. + + :param input_dim: the number of input dimensions + :type input_dim: int + :param variance: the variance of the Matern kernel + :type variance: float + :param lengthscale: the lengthscale of the Matern kernel + :type lengthscale: np.ndarray of size (input_dim,) + :param period: the period + :type period: float + :param n_freq: the number of frequencies considered for the periodic subspace + :type n_freq: int + :rtype: kernel object + + """ + + def __init__(self, input_dim=1, variance=1., lengthscale=1., period=2.*np.pi, n_freq=10, lower=0., upper=4*np.pi, active_dims=None, name='periodic_Matern32'): + super(PeriodicMatern32, self).__init__(input_dim, variance, lengthscale, period, n_freq, lower, upper, active_dims, name) + def parameters_changed(self): + self.a = [3./self.lengthscale**2, 2*np.sqrt(3)/self.lengthscale, 1.] + self.b = [1,self.lengthscale**2/3] + + self.basis_alpha = np.ones((self.n_basis,)) + self.basis_omega = (2*np.pi*np.arange(1,self.n_freq+1)/self.period).repeat(2) + self.basis_phi = np.zeros(self.n_freq * 2) + self.basis_phi[::2] = -np.pi/2 + + self.G = self.Gram_matrix() + self.Gi = np.linalg.inv(self.G) + + def Gram_matrix(self): + La = np.column_stack((self.a[0]*np.ones((self.n_basis,1)),self.a[1]*self.basis_omega,self.a[2]*self.basis_omega**2)) + Lo = np.column_stack((self.basis_omega,self.basis_omega,self.basis_omega)) + Lp = np.column_stack((self.basis_phi,self.basis_phi+np.pi/2,self.basis_phi+np.pi)) + r,omega,phi = self._cos_factorization(La,Lo,Lp) + Gint = self._int_computation( r,omega,phi, r,omega,phi) + + Flower = np.array(self._cos(self.basis_alpha,self.basis_omega,self.basis_phi)(self.lower))[:,None] + F1lower = np.array(self._cos(self.basis_alpha*self.basis_omega,self.basis_omega,self.basis_phi+np.pi/2)(self.lower))[:,None] + return(self.lengthscale**3/(12*np.sqrt(3)*self.variance) * Gint + 1./self.variance*np.dot(Flower,Flower.T) + self.lengthscale**2/(3.*self.variance)*np.dot(F1lower,F1lower.T)) + + + @silence_errors + def update_gradients_full(self,dL_dK,X,X2): + """derivative of the covariance matrix with respect to the parameters (shape is num_data x num_inducing x num_params)""" + if X2 is None: X2 = X + FX = self._cos(self.basis_alpha[None,:],self.basis_omega[None,:],self.basis_phi[None,:])(X) + FX2 = self._cos(self.basis_alpha[None,:],self.basis_omega[None,:],self.basis_phi[None,:])(X2) + + La = np.column_stack((self.a[0]*np.ones((self.n_basis,1)),self.a[1]*self.basis_omega,self.a[2]*self.basis_omega**2)) + Lo = np.column_stack((self.basis_omega,self.basis_omega,self.basis_omega)) + Lp = np.column_stack((self.basis_phi,self.basis_phi+np.pi/2,self.basis_phi+np.pi)) + r,omega,phi = self._cos_factorization(La,Lo,Lp) + Gint = self._int_computation( r,omega,phi, r,omega,phi) + + Flower = np.array(self._cos(self.basis_alpha,self.basis_omega,self.basis_phi)(self.lower))[:,None] + F1lower = np.array(self._cos(self.basis_alpha*self.basis_omega,self.basis_omega,self.basis_phi+np.pi/2)(self.lower))[:,None] + + #dK_dvar + dK_dvar = 1./self.variance*mdot(FX,self.Gi,FX2.T) + + #dK_dlen + da_dlen = [-6/self.lengthscale**3,-2*np.sqrt(3)/self.lengthscale**2,0.] + db_dlen = [0.,2*self.lengthscale/3.] + dLa_dlen = np.column_stack((da_dlen[0]*np.ones((self.n_basis,1)),da_dlen[1]*self.basis_omega,da_dlen[2]*self.basis_omega**2)) + r1,omega1,phi1 = self._cos_factorization(dLa_dlen,Lo,Lp) + dGint_dlen = self._int_computation(r1,omega1,phi1, r,omega,phi) + dGint_dlen = dGint_dlen + dGint_dlen.T + dG_dlen = self.lengthscale**2/(4*np.sqrt(3))*Gint + self.lengthscale**3/(12*np.sqrt(3))*dGint_dlen + db_dlen[0]*np.dot(Flower,Flower.T) + db_dlen[1]*np.dot(F1lower,F1lower.T) + dK_dlen = -mdot(FX,self.Gi,dG_dlen/self.variance,self.Gi,FX2.T) + + #dK_dper + dFX_dper = self._cos(-self.basis_alpha[None,:]*self.basis_omega[None,:]/self.period*X ,self.basis_omega[None,:],self.basis_phi[None,:]+np.pi/2)(X) + dFX2_dper = self._cos(-self.basis_alpha[None,:]*self.basis_omega[None,:]/self.period*X2,self.basis_omega[None,:],self.basis_phi[None,:]+np.pi/2)(X2) + + dLa_dper = np.column_stack((-self.a[0]*self.basis_omega/self.period, -self.a[1]*self.basis_omega**2/self.period, -self.a[2]*self.basis_omega**3/self.period)) + dLp_dper = np.column_stack((self.basis_phi+np.pi/2,self.basis_phi+np.pi,self.basis_phi+np.pi*3/2)) + r1,omega1,phi1 = self._cos_factorization(dLa_dper,Lo,dLp_dper) + + IPPprim1 = self.upper*(1./(omega+omega1.T)*np.cos((omega+omega1.T)*self.upper+phi+phi1.T-np.pi/2) + 1./(omega-omega1.T)*np.cos((omega-omega1.T)*self.upper+phi-phi1.T-np.pi/2)) + IPPprim1 -= self.lower*(1./(omega+omega1.T)*np.cos((omega+omega1.T)*self.lower+phi+phi1.T-np.pi/2) + 1./(omega-omega1.T)*np.cos((omega-omega1.T)*self.lower+phi-phi1.T-np.pi/2)) + IPPprim2 = self.upper*(1./(omega+omega1.T)*np.cos((omega+omega1.T)*self.upper+phi+phi1.T-np.pi/2) + self.upper*np.cos(phi-phi1.T)) + IPPprim2 -= self.lower*(1./(omega+omega1.T)*np.cos((omega+omega1.T)*self.lower+phi+phi1.T-np.pi/2) + self.lower*np.cos(phi-phi1.T)) + IPPprim = np.where(np.isnan(IPPprim1),IPPprim2,IPPprim1) + + IPPint1 = 1./(omega+omega1.T)**2*np.cos((omega+omega1.T)*self.upper+phi+phi1.T-np.pi) + 1./(omega-omega1.T)**2*np.cos((omega-omega1.T)*self.upper+phi-phi1.T-np.pi) + IPPint1 -= 1./(omega+omega1.T)**2*np.cos((omega+omega1.T)*self.lower+phi+phi1.T-np.pi) + 1./(omega-omega1.T)**2*np.cos((omega-omega1.T)*self.lower+phi-phi1.T-np.pi) + IPPint2 = 1./(omega+omega1.T)**2*np.cos((omega+omega1.T)*self.upper+phi+phi1.T-np.pi) + 1./2*self.upper**2*np.cos(phi-phi1.T) + IPPint2 -= 1./(omega+omega1.T)**2*np.cos((omega+omega1.T)*self.lower+phi+phi1.T-np.pi) + 1./2*self.lower**2*np.cos(phi-phi1.T) + IPPint = np.where(np.isnan(IPPint1),IPPint2,IPPint1) + + dLa_dper2 = np.column_stack((-self.a[1]*self.basis_omega/self.period, -2*self.a[2]*self.basis_omega**2/self.period)) + dLp_dper2 = np.column_stack((self.basis_phi+np.pi/2,self.basis_phi+np.pi)) + r2,omega2,phi2 = self._cos_factorization(dLa_dper2,Lo[:,0:2],dLp_dper2) + + dGint_dper = np.dot(r,r1.T)/2 * (IPPprim - IPPint) + self._int_computation(r2,omega2,phi2, r,omega,phi) + dGint_dper = dGint_dper + dGint_dper.T + + dFlower_dper = np.array(self._cos(-self.lower*self.basis_alpha*self.basis_omega/self.period,self.basis_omega,self.basis_phi+np.pi/2)(self.lower))[:,None] + dF1lower_dper = np.array(self._cos(-self.lower*self.basis_alpha*self.basis_omega**2/self.period,self.basis_omega,self.basis_phi+np.pi)(self.lower)+self._cos(-self.basis_alpha*self.basis_omega/self.period,self.basis_omega,self.basis_phi+np.pi/2)(self.lower))[:,None] + + dG_dper = 1./self.variance*(self.lengthscale**3/(12*np.sqrt(3))*dGint_dper + self.b[0]*(np.dot(dFlower_dper,Flower.T)+np.dot(Flower,dFlower_dper.T)) + self.b[1]*(np.dot(dF1lower_dper,F1lower.T)+np.dot(F1lower,dF1lower_dper.T))) + + dK_dper = mdot(dFX_dper,self.Gi,FX2.T) - mdot(FX,self.Gi,dG_dper,self.Gi,FX2.T) + mdot(FX,self.Gi,dFX2_dper.T) + + self.variance.gradient = np.sum(dK_dvar*dL_dK) + self.lengthscale.gradient = np.sum(dK_dlen*dL_dK) + self.period.gradient = np.sum(dK_dper*dL_dK) + + + +class PeriodicMatern52(Periodic): """ Kernel of the periodic subspace (up to a given frequency) of a Matern 5/2 RKHS. Only defined for input_dim=1. @@ -25,67 +301,21 @@ class PeriodicMatern52(Kernpart): """ - def __init__(self,input_dim=1,variance=1.,lengthscale=None,period=2*np.pi,n_freq=10,lower=0.,upper=4*np.pi): - assert input_dim==1, "Periodic kernels are only defined for input_dim=1" - self.name = 'periodic_Mat52' - self.input_dim = input_dim - if lengthscale is not None: - lengthscale = np.asarray(lengthscale) - assert lengthscale.size == 1, "Wrong size: only one lengthscale needed" - else: - lengthscale = np.ones(1) - self.lower,self.upper = lower, upper - self.num_params = 3 - self.n_freq = n_freq - self.n_basis = 2*n_freq - self._set_params(np.hstack((variance,lengthscale,period))) - - def _cos(self,alpha,omega,phase): - def f(x): - return alpha*np.cos(omega*x+phase) - return f - - @silence_errors - def _cos_factorization(self,alpha,omega,phase): - r1 = np.sum(alpha*np.cos(phase),axis=1)[:,None] - r2 = np.sum(alpha*np.sin(phase),axis=1)[:,None] - r = np.sqrt(r1**2 + r2**2) - psi = np.where(r1 != 0, (np.arctan(r2/r1) + (r1<0.)*np.pi),np.arcsin(r2)) - return r,omega[:,0:1], psi - - @silence_errors - def _int_computation(self,r1,omega1,phi1,r2,omega2,phi2): - Gint1 = 1./(omega1+omega2.T)*( np.sin((omega1+omega2.T)*self.upper+phi1+phi2.T) - np.sin((omega1+omega2.T)*self.lower+phi1+phi2.T)) + 1./(omega1-omega2.T)*( np.sin((omega1-omega2.T)*self.upper+phi1-phi2.T) - np.sin((omega1-omega2.T)*self.lower+phi1-phi2.T) ) - Gint2 = 1./(omega1+omega2.T)*( np.sin((omega1+omega2.T)*self.upper+phi1+phi2.T) - np.sin((omega1+omega2.T)*self.lower+phi1+phi2.T)) + np.cos(phi1-phi2.T)*(self.upper-self.lower) - #Gint2[0,0] = 2.*(self.upper-self.lower)*np.cos(phi1[0,0])*np.cos(phi2[0,0]) - Gint = np.dot(r1,r2.T)/2 * np.where(np.isnan(Gint1),Gint2,Gint1) - return Gint - - def _get_params(self): - """return the value of the parameters.""" - return np.hstack((self.variance,self.lengthscale,self.period)) - - def _set_params(self,x): - """set the value of the parameters.""" - assert x.size==3 - self.variance = x[0] - self.lengthscale = x[1] - self.period = x[2] + def __init__(self, input_dim=1, variance=1., lengthscale=1., period=2.*np.pi, n_freq=10, lower=0., upper=4*np.pi, active_dims=None, name='periodic_Matern52'): + super(PeriodicMatern52, self).__init__(input_dim, variance, lengthscale, period, n_freq, lower, upper, active_dims, name) + def parameters_changed(self): self.a = [5*np.sqrt(5)/self.lengthscale**3, 15./self.lengthscale**2,3*np.sqrt(5)/self.lengthscale, 1.] self.b = [9./8, 9*self.lengthscale**4/200., 3*self.lengthscale**2/5., 3*self.lengthscale**2/(5*8.), 3*self.lengthscale**2/(5*8.)] self.basis_alpha = np.ones((2*self.n_freq,)) - self.basis_omega = np.array(sum([[i*2*np.pi/self.period]*2 for i in range(1,self.n_freq+1)],[])) - self.basis_phi = np.array(sum([[-np.pi/2, 0.] for i in range(1,self.n_freq+1)],[])) + self.basis_omega = (2*np.pi*np.arange(1,self.n_freq+1)/self.period).repeat(2) + self.basis_phi = np.zeros(self.n_freq * 2) + self.basis_phi[::2] = -np.pi/2 self.G = self.Gram_matrix() self.Gi = np.linalg.inv(self.G) - def _get_param_names(self): - """return parameter names.""" - return ['variance','lengthscale','period'] - def Gram_matrix(self): La = np.column_stack((self.a[0]*np.ones((self.n_basis,1)), self.a[1]*self.basis_omega, self.a[2]*self.basis_omega**2, self.a[3]*self.basis_omega**3)) Lo = np.column_stack((self.basis_omega, self.basis_omega, self.basis_omega, self.basis_omega)) @@ -99,23 +329,8 @@ class PeriodicMatern52(Kernpart): lower_terms = self.b[0]*np.dot(Flower,Flower.T) + self.b[1]*np.dot(F2lower,F2lower.T) + self.b[2]*np.dot(F1lower,F1lower.T) + self.b[3]*np.dot(F2lower,Flower.T) + self.b[4]*np.dot(Flower,F2lower.T) return(3*self.lengthscale**5/(400*np.sqrt(5)*self.variance) * Gint + 1./self.variance*lower_terms) - def K(self,X,X2,target): - """Compute the covariance matrix between X and X2.""" - FX = self._cos(self.basis_alpha[None,:],self.basis_omega[None,:],self.basis_phi[None,:])(X) - if X2 is None: - FX2 = FX - else: - FX2 = self._cos(self.basis_alpha[None,:],self.basis_omega[None,:],self.basis_phi[None,:])(X2) - np.add(mdot(FX,self.Gi,FX2.T), target,target) - - def Kdiag(self,X,target): - """Compute the diagonal of the covariance matrix associated to X.""" - FX = self._cos(self.basis_alpha[None,:],self.basis_omega[None,:],self.basis_phi[None,:])(X) - np.add(target,np.diag(mdot(FX,self.Gi,FX.T)),target) - @silence_errors - def dK_dtheta(self,dL_dK,X,X2,target): - """derivative of the covariance matrix with respect to the parameters (shape is num_data x num_inducing x num_params)""" + def update_gradients_full(self, dL_dK, X, X2=None): if X2 is None: X2 = X FX = self._cos(self.basis_alpha[None,:],self.basis_omega[None,:],self.basis_phi[None,:])(X) FX2 = self._cos(self.basis_alpha[None,:],self.basis_omega[None,:],self.basis_phi[None,:])(X2) @@ -156,14 +371,12 @@ class PeriodicMatern52(Kernpart): IPPprim1 -= self.lower*(1./(omega+omega1.T)*np.cos((omega+omega1.T)*self.lower+phi+phi1.T-np.pi/2) + 1./(omega-omega1.T)*np.cos((omega-omega1.T)*self.lower+phi-phi1.T-np.pi/2)) IPPprim2 = self.upper*(1./(omega+omega1.T)*np.cos((omega+omega1.T)*self.upper+phi+phi1.T-np.pi/2) + self.upper*np.cos(phi-phi1.T)) IPPprim2 -= self.lower*(1./(omega+omega1.T)*np.cos((omega+omega1.T)*self.lower+phi+phi1.T-np.pi/2) + self.lower*np.cos(phi-phi1.T)) - #IPPprim2[0,0] = 2*(self.upper**2 - self.lower**2)*np.cos(phi[0,0])*np.cos(phi1[0,0]) IPPprim = np.where(np.isnan(IPPprim1),IPPprim2,IPPprim1) IPPint1 = 1./(omega+omega1.T)**2*np.cos((omega+omega1.T)*self.upper+phi+phi1.T-np.pi) + 1./(omega-omega1.T)**2*np.cos((omega-omega1.T)*self.upper+phi-phi1.T-np.pi) IPPint1 -= 1./(omega+omega1.T)**2*np.cos((omega+omega1.T)*self.lower+phi+phi1.T-np.pi) + 1./(omega-omega1.T)**2*np.cos((omega-omega1.T)*self.lower+phi-phi1.T-np.pi) IPPint2 = 1./(omega+omega1.T)**2*np.cos((omega+omega1.T)*self.upper+phi+phi1.T-np.pi) + 1./2*self.upper**2*np.cos(phi-phi1.T) IPPint2 -= 1./(omega+omega1.T)**2*np.cos((omega+omega1.T)*self.lower+phi+phi1.T-np.pi) + 1./2*self.lower**2*np.cos(phi-phi1.T) - #IPPint2[0,0] = (self.upper**2 - self.lower**2)*np.cos(phi[0,0])*np.cos(phi1[0,0]) IPPint = np.where(np.isnan(IPPint1),IPPint2,IPPint1) dLa_dper2 = np.column_stack((-self.a[1]*self.basis_omega/self.period, -2*self.a[2]*self.basis_omega**2/self.period, -3*self.a[3]*self.basis_omega**3/self.period)) @@ -186,81 +399,7 @@ class PeriodicMatern52(Kernpart): dG_dper = 1./self.variance*(3*self.lengthscale**5/(400*np.sqrt(5))*dGint_dper + 0.5*dlower_terms_dper) dK_dper = mdot(dFX_dper,self.Gi,FX2.T) - mdot(FX,self.Gi,dG_dper,self.Gi,FX2.T) + mdot(FX,self.Gi,dFX2_dper.T) - # np.add(target[:,:,0],dK_dvar, target[:,:,0]) - target[0] += np.sum(dK_dvar*dL_dK) - #np.add(target[:,:,1],dK_dlen, target[:,:,1]) - target[1] += np.sum(dK_dlen*dL_dK) - #np.add(target[:,:,2],dK_dper, target[:,:,2]) - target[2] += np.sum(dK_dper*dL_dK) + self.variance.gradient = np.sum(dK_dvar*dL_dK) + self.lengthscale.gradient = np.sum(dK_dlen*dL_dK) + self.period.gradient = np.sum(dK_dper*dL_dK) - @silence_errors - def dKdiag_dtheta(self,dL_dKdiag,X,target): - """derivative of the diagonal of the covariance matrix with respect to the parameters""" - FX = self._cos(self.basis_alpha[None,:],self.basis_omega[None,:],self.basis_phi[None,:])(X) - - La = np.column_stack((self.a[0]*np.ones((self.n_basis,1)), self.a[1]*self.basis_omega, self.a[2]*self.basis_omega**2, self.a[3]*self.basis_omega**3)) - Lo = np.column_stack((self.basis_omega, self.basis_omega, self.basis_omega, self.basis_omega)) - Lp = np.column_stack((self.basis_phi, self.basis_phi+np.pi/2, self.basis_phi+np.pi, self.basis_phi+np.pi*3/2)) - r,omega,phi = self._cos_factorization(La,Lo,Lp) - Gint = self._int_computation( r,omega,phi, r,omega,phi) - - Flower = np.array(self._cos(self.basis_alpha,self.basis_omega,self.basis_phi)(self.lower))[:,None] - F1lower = np.array(self._cos(self.basis_alpha*self.basis_omega,self.basis_omega,self.basis_phi+np.pi/2)(self.lower))[:,None] - F2lower = np.array(self._cos(self.basis_alpha*self.basis_omega**2,self.basis_omega,self.basis_phi+np.pi)(self.lower))[:,None] - - #dK_dvar - dK_dvar = 1. / self.variance * mdot(FX, self.Gi, FX.T) - - #dK_dlen - da_dlen = [-3*self.a[0]/self.lengthscale, -2*self.a[1]/self.lengthscale, -self.a[2]/self.lengthscale, 0.] - db_dlen = [0., 4*self.b[1]/self.lengthscale, 2*self.b[2]/self.lengthscale, 2*self.b[3]/self.lengthscale, 2*self.b[4]/self.lengthscale] - dLa_dlen = np.column_stack((da_dlen[0]*np.ones((self.n_basis,1)), da_dlen[1]*self.basis_omega, da_dlen[2]*self.basis_omega**2, da_dlen[3]*self.basis_omega**3)) - r1,omega1,phi1 = self._cos_factorization(dLa_dlen,Lo,Lp) - dGint_dlen = self._int_computation(r1,omega1,phi1, r,omega,phi) - dGint_dlen = dGint_dlen + dGint_dlen.T - dlower_terms_dlen = db_dlen[0]*np.dot(Flower,Flower.T) + db_dlen[1]*np.dot(F2lower,F2lower.T) + db_dlen[2]*np.dot(F1lower,F1lower.T) + db_dlen[3]*np.dot(F2lower,Flower.T) + db_dlen[4]*np.dot(Flower,F2lower.T) - dG_dlen = 15*self.lengthscale**4/(400*np.sqrt(5))*Gint + 3*self.lengthscale**5/(400*np.sqrt(5))*dGint_dlen + dlower_terms_dlen - dK_dlen = -mdot(FX,self.Gi,dG_dlen/self.variance,self.Gi,FX.T) - - #dK_dper - dFX_dper = self._cos(-self.basis_alpha[None,:]*self.basis_omega[None,:]/self.period*X ,self.basis_omega[None,:],self.basis_phi[None,:]+np.pi/2)(X) - - dLa_dper = np.column_stack((-self.a[0]*self.basis_omega/self.period, -self.a[1]*self.basis_omega**2/self.period, -self.a[2]*self.basis_omega**3/self.period, -self.a[3]*self.basis_omega**4/self.period)) - dLp_dper = np.column_stack((self.basis_phi+np.pi/2,self.basis_phi+np.pi,self.basis_phi+np.pi*3/2,self.basis_phi)) - r1,omega1,phi1 = self._cos_factorization(dLa_dper,Lo,dLp_dper) - - IPPprim1 = self.upper*(1./(omega+omega1.T)*np.cos((omega+omega1.T)*self.upper+phi+phi1.T-np.pi/2) + 1./(omega-omega1.T)*np.cos((omega-omega1.T)*self.upper+phi-phi1.T-np.pi/2)) - IPPprim1 -= self.lower*(1./(omega+omega1.T)*np.cos((omega+omega1.T)*self.lower+phi+phi1.T-np.pi/2) + 1./(omega-omega1.T)*np.cos((omega-omega1.T)*self.lower+phi-phi1.T-np.pi/2)) - IPPprim2 = self.upper*(1./(omega+omega1.T)*np.cos((omega+omega1.T)*self.upper+phi+phi1.T-np.pi/2) + self.upper*np.cos(phi-phi1.T)) - IPPprim2 -= self.lower*(1./(omega+omega1.T)*np.cos((omega+omega1.T)*self.lower+phi+phi1.T-np.pi/2) + self.lower*np.cos(phi-phi1.T)) - IPPprim = np.where(np.isnan(IPPprim1),IPPprim2,IPPprim1) - - IPPint1 = 1./(omega+omega1.T)**2*np.cos((omega+omega1.T)*self.upper+phi+phi1.T-np.pi) + 1./(omega-omega1.T)**2*np.cos((omega-omega1.T)*self.upper+phi-phi1.T-np.pi) - IPPint1 -= 1./(omega+omega1.T)**2*np.cos((omega+omega1.T)*self.lower+phi+phi1.T-np.pi) + 1./(omega-omega1.T)**2*np.cos((omega-omega1.T)*self.lower+phi-phi1.T-np.pi) - IPPint2 = 1./(omega+omega1.T)**2*np.cos((omega+omega1.T)*self.upper+phi+phi1.T-np.pi) + .5*self.upper**2*np.cos(phi-phi1.T) - IPPint2 -= 1./(omega+omega1.T)**2*np.cos((omega+omega1.T)*self.lower+phi+phi1.T-np.pi) + .5*self.lower**2*np.cos(phi-phi1.T) - IPPint = np.where(np.isnan(IPPint1),IPPint2,IPPint1) - - dLa_dper2 = np.column_stack((-self.a[1]*self.basis_omega/self.period, -2*self.a[2]*self.basis_omega**2/self.period, -3*self.a[3]*self.basis_omega**3/self.period)) - dLp_dper2 = np.column_stack((self.basis_phi+np.pi/2, self.basis_phi+np.pi, self.basis_phi+np.pi*3/2)) - r2,omega2,phi2 = self._cos_factorization(dLa_dper2,Lo[:,0:2],dLp_dper2) - - dGint_dper = np.dot(r,r1.T)/2 * (IPPprim - IPPint) + self._int_computation(r2,omega2,phi2, r,omega,phi) - dGint_dper = dGint_dper + dGint_dper.T - - dFlower_dper = np.array(self._cos(-self.lower*self.basis_alpha*self.basis_omega/self.period,self.basis_omega,self.basis_phi+np.pi/2)(self.lower))[:,None] - dF1lower_dper = np.array(self._cos(-self.lower*self.basis_alpha*self.basis_omega**2/self.period,self.basis_omega,self.basis_phi+np.pi)(self.lower)+self._cos(-self.basis_alpha*self.basis_omega/self.period,self.basis_omega,self.basis_phi+np.pi/2)(self.lower))[:,None] - dF2lower_dper = np.array(self._cos(-self.lower*self.basis_alpha*self.basis_omega**3/self.period,self.basis_omega,self.basis_phi+np.pi*3/2)(self.lower) + self._cos(-2*self.basis_alpha*self.basis_omega**2/self.period,self.basis_omega,self.basis_phi+np.pi)(self.lower))[:,None] - - dlower_terms_dper = self.b[0] * (np.dot(dFlower_dper,Flower.T) + np.dot(Flower.T,dFlower_dper)) - dlower_terms_dper += self.b[1] * (np.dot(dF2lower_dper,F2lower.T) + np.dot(F2lower,dF2lower_dper.T)) - 4*self.b[1]/self.period*np.dot(F2lower,F2lower.T) - dlower_terms_dper += self.b[2] * (np.dot(dF1lower_dper,F1lower.T) + np.dot(F1lower,dF1lower_dper.T)) - 2*self.b[2]/self.period*np.dot(F1lower,F1lower.T) - dlower_terms_dper += self.b[3] * (np.dot(dF2lower_dper,Flower.T) + np.dot(F2lower,dFlower_dper.T)) - 2*self.b[3]/self.period*np.dot(F2lower,Flower.T) - dlower_terms_dper += self.b[4] * (np.dot(dFlower_dper,F2lower.T) + np.dot(Flower,dF2lower_dper.T)) - 2*self.b[4]/self.period*np.dot(Flower,F2lower.T) - - dG_dper = 1./self.variance*(3*self.lengthscale**5/(400*np.sqrt(5))*dGint_dper + 0.5*dlower_terms_dper) - dK_dper = 2*mdot(dFX_dper,self.Gi,FX.T) - mdot(FX,self.Gi,dG_dper,self.Gi,FX.T) - - target[0] += np.sum(np.diag(dK_dvar)*dL_dKdiag) - target[1] += np.sum(np.diag(dK_dlen)*dL_dKdiag) - target[2] += np.sum(np.diag(dK_dper)*dL_dKdiag) diff --git a/GPy/kern/_src/poly.py b/GPy/kern/_src/poly.py new file mode 100644 index 00000000..b90e8f8f --- /dev/null +++ b/GPy/kern/_src/poly.py @@ -0,0 +1,41 @@ +# Copyright (c) 2014, James Hensman +# Licensed under the BSD 3-clause license (see LICENSE.txt) + +import numpy as np +from kern import Kern +from ...core.parameterization import Param +from ...core.parameterization.transformations import Logexp +class Poly(Kern): + """ + Polynomial kernel + """ + + def __init__(self, input_dim, variance=1., order=3., active_dims=None, name='poly'): + super(Poly, self).__init__(input_dim, active_dims, name) + self.variance = Param('variance', variance, Logexp()) + self.link_parameter(self.variance) + self.order=order + + def K(self, X, X2=None): + return (self._dot_product(X, X2) + 1.)**self.order * self.variance + + def _dot_product(self, X, X2=None): + if X2 is None: + return np.dot(X, X.T) + else: + return np.dot(X, X2.T) + + def Kdiag(self, X): + return self.variance*(np.square(X).sum(1) + 1.)**self.order + + def update_gradients_full(self, dL_dK, X, X2=None): + self.variance.gradient = np.sum(dL_dK * (self._dot_product(X, X2) + 1.)**self.order) + + def update_gradients_diag(self, dL_dKdiag, X): + raise NotImplementedError + + def gradients_X(self, dL_dK, X, X2=None): + raise NotImplementedError + + def gradients_X_diag(self, dL_dKdiag, X): + raise NotImplementedError diff --git a/GPy/kern/_src/prod.py b/GPy/kern/_src/prod.py new file mode 100644 index 00000000..dd9a5fe4 --- /dev/null +++ b/GPy/kern/_src/prod.py @@ -0,0 +1,66 @@ +# Copyright (c) 2012, GPy authors (see AUTHORS.txt). +# Licensed under the BSD 3-clause license (see LICENSE.txt) + +import numpy as np +from kern import CombinationKernel +from ...util.caching import Cache_this +import itertools + +class Prod(CombinationKernel): + """ + Computes the product of 2 kernels + + :param k1, k2: the kernels to multiply + :type k1, k2: Kern + :param tensor: The kernels are either multiply as functions defined on the same input space (default) or on the product of the input spaces + :type tensor: Boolean + :rtype: kernel object + + """ + def __init__(self, kernels, name='mul'): + for i, kern in enumerate(kernels[:]): + if isinstance(kern, Prod): + del kernels[i] + for part in kern.parts[::-1]: + kern.unlink_parameter(part) + kernels.insert(i, part) + super(Prod, self).__init__(kernels, name) + + @Cache_this(limit=2, force_kwargs=['which_parts']) + def K(self, X, X2=None, which_parts=None): + if which_parts is None: + which_parts = self.parts + elif not isinstance(which_parts, (list, tuple)): + # if only one part is given + which_parts = [which_parts] + return reduce(np.multiply, (p.K(X, X2) for p in which_parts)) + + @Cache_this(limit=2, force_kwargs=['which_parts']) + def Kdiag(self, X, which_parts=None): + if which_parts is None: + which_parts = self.parts + return reduce(np.multiply, (p.Kdiag(X) for p in which_parts)) + + def update_gradients_full(self, dL_dK, X, X2=None): + k = self.K(X,X2)*dL_dK + for p in self.parts: + p.update_gradients_full(k/p.K(X,X2),X,X2) + + def update_gradients_diag(self, dL_dKdiag, X): + k = self.Kdiag(X)*dL_dKdiag + for p in self.parts: + p.update_gradients_diag(k/p.Kdiag(X),X) + + def gradients_X(self, dL_dK, X, X2=None): + target = np.zeros(X.shape) + k = self.K(X,X2)*dL_dK + for p in self.parts: + target += p.gradients_X(k/p.K(X,X2),X,X2) + return target + + def gradients_X_diag(self, dL_dKdiag, X): + target = np.zeros(X.shape) + k = self.Kdiag(X)*dL_dKdiag + for p in self.parts: + target += p.gradients_X_diag(k/p.Kdiag(X),X) + return target diff --git a/GPy/kern/_src/psi_comp/__init__.py b/GPy/kern/_src/psi_comp/__init__.py new file mode 100644 index 00000000..a277ff02 --- /dev/null +++ b/GPy/kern/_src/psi_comp/__init__.py @@ -0,0 +1,55 @@ +# Copyright (c) 2012, GPy authors (see AUTHORS.txt). +# Licensed under the BSD 3-clause license (see LICENSE.txt) + +from ....core.parameterization.parameter_core import Pickleable +from GPy.util.caching import Cache_this +from ....core.parameterization import variational +import rbf_psi_comp +import ssrbf_psi_comp +import sslinear_psi_comp +import linear_psi_comp + +class PSICOMP_RBF(Pickleable): + @Cache_this(limit=2, ignore_args=(0,)) + def psicomputations(self, variance, lengthscale, Z, variational_posterior): + if isinstance(variational_posterior, variational.NormalPosterior): + return rbf_psi_comp.psicomputations(variance, lengthscale, Z, variational_posterior) + elif isinstance(variational_posterior, variational.SpikeAndSlabPosterior): + return ssrbf_psi_comp.psicomputations(variance, lengthscale, Z, variational_posterior) + else: + raise ValueError, "unknown distriubtion received for psi-statistics" + + @Cache_this(limit=2, ignore_args=(0,1,2,3)) + def psiDerivativecomputations(self, dL_dpsi0, dL_dpsi1, dL_dpsi2, variance, lengthscale, Z, variational_posterior): + if isinstance(variational_posterior, variational.NormalPosterior): + return rbf_psi_comp.psiDerivativecomputations(dL_dpsi0, dL_dpsi1, dL_dpsi2, variance, lengthscale, Z, variational_posterior) + elif isinstance(variational_posterior, variational.SpikeAndSlabPosterior): + return ssrbf_psi_comp.psiDerivativecomputations(dL_dpsi0, dL_dpsi1, dL_dpsi2, variance, lengthscale, Z, variational_posterior) + else: + raise ValueError, "unknown distriubtion received for psi-statistics" + + def _setup_observers(self): + pass + +class PSICOMP_Linear(Pickleable): + + @Cache_this(limit=2, ignore_args=(0,)) + def psicomputations(self, variance, Z, variational_posterior): + if isinstance(variational_posterior, variational.NormalPosterior): + return linear_psi_comp.psicomputations(variance, Z, variational_posterior) + elif isinstance(variational_posterior, variational.SpikeAndSlabPosterior): + return sslinear_psi_comp.psicomputations(variance, Z, variational_posterior) + else: + raise ValueError, "unknown distriubtion received for psi-statistics" + + @Cache_this(limit=2, ignore_args=(0,1,2,3)) + def psiDerivativecomputations(self, dL_dpsi0, dL_dpsi1, dL_dpsi2, variance, Z, variational_posterior): + if isinstance(variational_posterior, variational.NormalPosterior): + return linear_psi_comp.psiDerivativecomputations(dL_dpsi0, dL_dpsi1, dL_dpsi2, variance, Z, variational_posterior) + elif isinstance(variational_posterior, variational.SpikeAndSlabPosterior): + return sslinear_psi_comp.psiDerivativecomputations(dL_dpsi0, dL_dpsi1, dL_dpsi2, variance, Z, variational_posterior) + else: + raise ValueError, "unknown distriubtion received for psi-statistics" + + def _setup_observers(self): + pass \ No newline at end of file diff --git a/GPy/kern/_src/psi_comp/linear_psi_comp.py b/GPy/kern/_src/psi_comp/linear_psi_comp.py new file mode 100644 index 00000000..50090428 --- /dev/null +++ b/GPy/kern/_src/psi_comp/linear_psi_comp.py @@ -0,0 +1,77 @@ +# Copyright (c) 2012, GPy authors (see AUTHORS.txt). +# Licensed under the BSD 3-clause license (see LICENSE.txt) + +""" +The package for the Psi statistics computation of the linear kernel for Bayesian GPLVM +""" + +import numpy as np +from ....util.linalg import tdot + +def psicomputations(variance, Z, variational_posterior): + """ + Compute psi-statistics for ss-linear kernel + """ + # here are the "statistics" for psi0, psi1 and psi2 + # Produced intermediate results: + # psi0 N + # psi1 NxM + # psi2 MxM + mu = variational_posterior.mean + S = variational_posterior.variance + + psi0 = (variance*(np.square(mu)+S)).sum(axis=1) + psi1 = np.dot(mu,(variance*Z).T) + psi2 = np.dot(S.sum(axis=0)*np.square(variance)*Z,Z.T)+ tdot(psi1.T) + + return psi0, psi1, psi2 + +def psiDerivativecomputations(dL_dpsi0, dL_dpsi1, dL_dpsi2, variance, Z, variational_posterior): + mu = variational_posterior.mean + S = variational_posterior.variance + + dL_dvar, dL_dmu, dL_dS, dL_dZ = _psi2computations(dL_dpsi2, variance, Z, mu, S) + + # Compute for psi0 and psi1 + mu2S = np.square(mu)+S + dL_dpsi0_var = dL_dpsi0[:,None]*variance[None,:] + dL_dpsi1_mu = np.dot(dL_dpsi1.T,mu) + dL_dvar += (dL_dpsi0[:,None]*mu2S).sum(axis=0)+ (dL_dpsi1_mu*Z).sum(axis=0) + dL_dmu += 2.*dL_dpsi0_var*mu+np.dot(dL_dpsi1,Z)*variance + dL_dS += dL_dpsi0_var + dL_dZ += dL_dpsi1_mu*variance + + return dL_dvar, dL_dZ, dL_dmu, dL_dS + +def _psi2computations(dL_dpsi2, variance, Z, mu, S): + """ + Z - MxQ + mu - NxQ + S - NxQ + gamma - NxQ + """ + # here are the "statistics" for psi1 and psi2 + # Produced intermediate results: + # _psi2_dvariance Q + # _psi2_dZ MxQ + # _psi2_dmu NxQ + # _psi2_dS NxQ + + variance2 = np.square(variance) + common_sum = np.dot(mu,(variance*Z).T) + Z_expect = (np.dot(dL_dpsi2,Z)*Z).sum(axis=0) + dL_dpsi2T = dL_dpsi2+dL_dpsi2.T + common_expect = np.dot(common_sum,np.dot(dL_dpsi2T,Z)) + Z2_expect = np.inner(common_sum,dL_dpsi2T) + Z1_expect = np.dot(dL_dpsi2T,Z) + + dL_dvar = 2.*S.sum(axis=0)*variance*Z_expect+(common_expect*mu).sum(axis=0) + + dL_dmu = common_expect*variance + + dL_dS = np.empty(S.shape) + dL_dS[:] = Z_expect*variance2 + + dL_dZ = variance2*S.sum(axis=0)*Z1_expect+np.dot(Z2_expect.T,variance*mu) + + return dL_dvar, dL_dmu, dL_dS, dL_dZ diff --git a/GPy/kern/_src/psi_comp/rbf_psi_comp.py b/GPy/kern/_src/psi_comp/rbf_psi_comp.py new file mode 100644 index 00000000..e7a67d16 --- /dev/null +++ b/GPy/kern/_src/psi_comp/rbf_psi_comp.py @@ -0,0 +1,161 @@ +""" +The module for psi-statistics for RBF kernel +""" + +import numpy as np +from GPy.util.caching import Cacher + +def psicomputations(variance, lengthscale, Z, variational_posterior): + """ + Z - MxQ + mu - NxQ + S - NxQ + gamma - NxQ + """ + # here are the "statistics" for psi0, psi1 and psi2 + # Produced intermediate results: + # _psi1 NxM + mu = variational_posterior.mean + S = variational_posterior.variance + + psi0 = np.empty(mu.shape[0]) + psi0[:] = variance + psi1 = _psi1computations(variance, lengthscale, Z, mu, S) + psi2 = _psi2computations(variance, lengthscale, Z, mu, S).sum(axis=0) + return psi0, psi1, psi2 + +def __psi1computations(variance, lengthscale, Z, mu, S): + """ + Z - MxQ + mu - NxQ + S - NxQ + gamma - NxQ + """ + # here are the "statistics" for psi1 + # Produced intermediate results: + # _psi1 NxM + + lengthscale2 = np.square(lengthscale) + + # psi1 + _psi1_logdenom = np.log(S/lengthscale2+1.).sum(axis=-1) # N + _psi1_log = (_psi1_logdenom[:,None]+np.einsum('nmq,nq->nm',np.square(mu[:,None,:]-Z[None,:,:]),1./(S+lengthscale2)))/(-2.) + _psi1 = variance*np.exp(_psi1_log) + + return _psi1 + +def __psi2computations(variance, lengthscale, Z, mu, S): + """ + Z - MxQ + mu - NxQ + S - NxQ + gamma - NxQ + """ + # here are the "statistics" for psi2 + # Produced intermediate results: + # _psi2 MxM + + lengthscale2 = np.square(lengthscale) + + _psi2_logdenom = np.log(2.*S/lengthscale2+1.).sum(axis=-1)/(-2.) # N + _psi2_exp1 = (np.square(Z[:,None,:]-Z[None,:,:])/lengthscale2).sum(axis=-1)/(-4.) #MxM + Z_hat = (Z[:,None,:]+Z[None,:,:])/2. #MxMxQ + denom = 1./(2.*S+lengthscale2) + _psi2_exp2 = -(np.square(mu)*denom).sum(axis=-1)[:,None,None]+2.*np.einsum('nq,moq,nq->nmo',mu,Z_hat,denom)-np.einsum('moq,nq->nmo',np.square(Z_hat),denom) + _psi2 = variance*variance*np.exp(_psi2_logdenom[:,None,None]+_psi2_exp1[None,:,:]+_psi2_exp2) + + + return _psi2 + +def psiDerivativecomputations(dL_dpsi0, dL_dpsi1, dL_dpsi2, variance, lengthscale, Z, variational_posterior): + ARD = (len(lengthscale)!=1) + + dvar_psi1, dl_psi1, dZ_psi1, dmu_psi1, dS_psi1 = _psi1compDer(dL_dpsi1, variance, lengthscale, Z, variational_posterior.mean, variational_posterior.variance) + dvar_psi2, dl_psi2, dZ_psi2, dmu_psi2, dS_psi2 = _psi2compDer(dL_dpsi2, variance, lengthscale, Z, variational_posterior.mean, variational_posterior.variance) + + dL_dvar = np.sum(dL_dpsi0) + dvar_psi1 + dvar_psi2 + + dL_dlengscale = dl_psi1 + dl_psi2 + if not ARD: + dL_dlengscale = dL_dlengscale.sum() + + dL_dmu = dmu_psi1 + dmu_psi2 + dL_dS = dS_psi1 + dS_psi2 + dL_dZ = dZ_psi1 + dZ_psi2 + + return dL_dvar, dL_dlengscale, dL_dZ, dL_dmu, dL_dS + +def _psi1compDer(dL_dpsi1, variance, lengthscale, Z, mu, S): + """ + dL_dpsi1 - NxM + Z - MxQ + mu - NxQ + S - NxQ + gamma - NxQ + """ + # here are the "statistics" for psi1 + # Produced intermediate results: dL_dparams w.r.t. psi1 + # _dL_dvariance 1 + # _dL_dlengthscale Q + # _dL_dZ MxQ + # _dL_dgamma NxQ + # _dL_dmu NxQ + # _dL_dS NxQ + + lengthscale2 = np.square(lengthscale) + + _psi1 = _psi1computations(variance, lengthscale, Z, mu, S) + Lpsi1 = dL_dpsi1*_psi1 + Zmu = Z[None,:,:]-mu[:,None,:] # NxMxQ + denom = 1./(S+lengthscale2) + Zmu2_denom = np.square(Zmu)*denom[:,None,:] #NxMxQ + _dL_dvar = Lpsi1.sum()/variance + _dL_dmu = np.einsum('nm,nmq,nq->nq',Lpsi1,Zmu,denom) + _dL_dS = np.einsum('nm,nmq,nq->nq',Lpsi1,(Zmu2_denom-1.),denom)/2. + _dL_dZ = -np.einsum('nm,nmq,nq->mq',Lpsi1,Zmu,denom) + _dL_dl = np.einsum('nm,nmq,nq->q',Lpsi1,(Zmu2_denom+(S/lengthscale2)[:,None,:]),denom*lengthscale) + + return _dL_dvar, _dL_dl, _dL_dZ, _dL_dmu, _dL_dS + +def _psi2compDer(dL_dpsi2, variance, lengthscale, Z, mu, S): + """ + Z - MxQ + mu - NxQ + S - NxQ + gamma - NxQ + dL_dpsi2 - MxM + """ + # here are the "statistics" for psi2 + # Produced the derivatives w.r.t. psi2: + # _dL_dvariance 1 + # _dL_dlengthscale Q + # _dL_dZ MxQ + # _dL_dgamma NxQ + # _dL_dmu NxQ + # _dL_dS NxQ + + lengthscale2 = np.square(lengthscale) + denom = 1./(2*S+lengthscale2) + denom2 = np.square(denom) + + _psi2 = _psi2computations(variance, lengthscale, Z, mu, S) # NxMxM + Lpsi2 = dL_dpsi2*_psi2 # dL_dpsi2 is MxM, using broadcast to multiply N out + Lpsi2sum = np.einsum('nmo->n',Lpsi2) #N + Lpsi2Z = np.einsum('nmo,oq->nq',Lpsi2,Z) #NxQ + Lpsi2Z2 = np.einsum('nmo,oq,oq->nq',Lpsi2,Z,Z) #NxQ + Lpsi2Z2p = np.einsum('nmo,mq,oq->nq',Lpsi2,Z,Z) #NxQ + Lpsi2Zhat = Lpsi2Z + Lpsi2Zhat2 = (Lpsi2Z2+Lpsi2Z2p)/2 + + _dL_dvar = Lpsi2sum.sum()*2/variance + _dL_dmu = (-2*denom) * (mu*Lpsi2sum[:,None]-Lpsi2Zhat) + _dL_dS = (2*np.square(denom))*(np.square(mu)*Lpsi2sum[:,None]-2*mu*Lpsi2Zhat+Lpsi2Zhat2) - denom*Lpsi2sum[:,None] + _dL_dZ = -np.einsum('nmo,oq->oq',Lpsi2,Z)/lengthscale2+np.einsum('nmo,oq->mq',Lpsi2,Z)/lengthscale2+ \ + 2*np.einsum('nmo,nq,nq->mq',Lpsi2,mu,denom) - np.einsum('nmo,nq,mq->mq',Lpsi2,denom,Z) - np.einsum('nmo,oq,nq->mq',Lpsi2,Z,denom) + _dL_dl = 2*lengthscale* ((S/lengthscale2*denom+np.square(mu*denom))*Lpsi2sum[:,None]+(Lpsi2Z2-Lpsi2Z2p)/(2*np.square(lengthscale2))- + (2*mu*denom2)*Lpsi2Zhat+denom2*Lpsi2Zhat2).sum(axis=0) + + return _dL_dvar, _dL_dl, _dL_dZ, _dL_dmu, _dL_dS + +_psi1computations = Cacher(__psi1computations, limit=1) +_psi2computations = Cacher(__psi2computations, limit=1) diff --git a/GPy/kern/_src/psi_comp/rbf_psi_gpucomp.py b/GPy/kern/_src/psi_comp/rbf_psi_gpucomp.py new file mode 100644 index 00000000..dda68bdf --- /dev/null +++ b/GPy/kern/_src/psi_comp/rbf_psi_gpucomp.py @@ -0,0 +1,411 @@ +""" +The module for psi-statistics for RBF kernel +""" + +import numpy as np +from ....util.caching import Cache_this +from . import PSICOMP_RBF +from ....util import gpu_init + +try: + import pycuda.gpuarray as gpuarray + from pycuda.compiler import SourceModule + from ....util.linalg_gpu import sum_axis +except: + pass + +gpu_code = """ + // define THREADNUM + + #define IDX_NMQ(n,m,q) ((q*M+m)*N+n) + #define IDX_NMM(n,m1,m2) ((m2*M+m1)*N+n) + #define IDX_NQ(n,q) (q*N+n) + #define IDX_NM(n,m) (m*N+n) + #define IDX_MQ(m,q) (q*M+m) + #define IDX_MM(m1,m2) (m2*M+m1) + #define IDX_NQB(n,q,b) ((b*Q+q)*N+n) + #define IDX_QB(q,b) (b*Q+q) + + // Divide data evenly + __device__ void divide_data(int total_data, int psize, int pidx, int *start, int *end) { + int residue = (total_data)%psize; + if(pidx= blockDim.x) { + for(int i=blockDim.x+threadIdx.x; i=1;s=s/2) { + if(threadIdx.x < s) {array[threadIdx.x] += array[s+threadIdx.x];} + __syncthreads(); + } + } + + __global__ void compDenom(double *log_denom1, double *log_denom2, double *l, double *S, int N, int Q) + { + int n_start, n_end; + divide_data(N, gridDim.x, blockIdx.x, &n_start, &n_end); + + for(int i=n_start*Q+threadIdx.x; iq',dL_dpsi0,gamma,mu2S) + np.einsum('nm,nq,mq,nq->q',dL_dpsi1,gamma,Z,mu) + dL_dgamma += np.einsum('n,q,nq->nq',dL_dpsi0,variance,mu2S) + np.einsum('nm,q,mq,nq->nq',dL_dpsi1,variance,Z,mu) + dL_dmu += np.einsum('n,nq,q,nq->nq',dL_dpsi0,gamma,2.*variance,mu) + np.einsum('nm,nq,q,mq->nq',dL_dpsi1,gamma,variance,Z) + dL_dS += np.einsum('n,nq,q->nq',dL_dpsi0,gamma,variance) + dL_dZ += np.einsum('nm,nq,q,nq->mq',dL_dpsi1,gamma, variance,mu) + + return dL_dvar, dL_dZ, dL_dmu, dL_dS, dL_dgamma + +def _psi2computations(dL_dpsi2, variance, Z, mu, S, gamma): + """ + Z - MxQ + mu - NxQ + S - NxQ + gamma - NxQ + """ + # here are the "statistics" for psi1 and psi2 + # Produced intermediate results: + # _psi2_dvariance Q + # _psi2_dZ MxQ + # _psi2_dgamma NxQ + # _psi2_dmu NxQ + # _psi2_dS NxQ + + mu2 = np.square(mu) + gamma2 = np.square(gamma) + variance2 = np.square(variance) + mu2S = mu2+S # NxQ + gvm = np.einsum('nq,nq,q->nq',gamma,mu,variance) + common_sum = np.einsum('nq,mq->nm',gvm,Z) +# common_sum = np.einsum('nq,q,mq,nq->nm',gamma,variance,Z,mu) # NxM + Z_expect = np.einsum('mo,mq,oq->q',dL_dpsi2,Z,Z) + dL_dpsi2T = dL_dpsi2+dL_dpsi2.T + tmp = np.einsum('mo,oq->mq',dL_dpsi2T,Z) + common_expect = np.einsum('mq,nm->nq',tmp,common_sum) +# common_expect = np.einsum('mo,mq,no->nq',dL_dpsi2+dL_dpsi2.T,Z,common_sum) + Z2_expect = np.einsum('om,nm->no',dL_dpsi2T,common_sum) + Z1_expect = np.einsum('om,mq->oq',dL_dpsi2T,Z) + + dL_dvar = np.einsum('nq,q,q->q',2.*(gamma*mu2S-gamma2*mu2),variance,Z_expect)+\ + np.einsum('nq,nq,nq->q',common_expect,gamma,mu) + + dL_dgamma = np.einsum('q,q,nq->nq',Z_expect,variance2,(mu2S-2.*gamma*mu2))+\ + np.einsum('nq,q,nq->nq',common_expect,variance,mu) + + dL_dmu = np.einsum('q,q,nq,nq->nq',Z_expect,variance2,mu,2.*(gamma-gamma2))+\ + np.einsum('nq,nq,q->nq',common_expect,gamma,variance) + + dL_dS = np.einsum('q,nq,q->nq',Z_expect,gamma,variance2) + +# dL_dZ = 2.*(np.einsum('om,nq,q,mq,nq->oq',dL_dpsi2,gamma,variance2,Z,(mu2S-gamma*mu2))+np.einsum('om,nq,q,nq,nm->oq',dL_dpsi2,gamma,variance,mu,common_sum)) + dL_dZ = Z1_expect*np.einsum('nq,q,nq->q',gamma,variance2,(mu2S-gamma*mu2))+np.einsum('nq,q,nq,nm->mq',gamma,variance,mu,Z2_expect) + + return dL_dvar, dL_dgamma, dL_dmu, dL_dS, dL_dZ diff --git a/GPy/kern/_src/psi_comp/ssrbf_psi_comp.py b/GPy/kern/_src/psi_comp/ssrbf_psi_comp.py new file mode 100644 index 00000000..18a4d751 --- /dev/null +++ b/GPy/kern/_src/psi_comp/ssrbf_psi_comp.py @@ -0,0 +1,394 @@ +# Copyright (c) 2012, GPy authors (see AUTHORS.txt). +# Licensed under the BSD 3-clause license (see LICENSE.txt) + +""" +The package for the psi statistics computation +""" + +import numpy as np + +try: + from scipy import weave + + def _psicomputations(variance, lengthscale, Z, variational_posterior): + """ + Z - MxQ + mu - NxQ + S - NxQ + gamma - NxQ + """ + # here are the "statistics" for psi0, psi1 and psi2 + # Produced intermediate results: + # _psi1 NxM + mu = variational_posterior.mean + S = variational_posterior.variance + + N,M,Q = mu.shape[0],Z.shape[0],mu.shape[1] + l2 = np.square(lengthscale) + log_denom1 = np.log(S/l2+1) + log_denom2 = np.log(2*S/l2+1) + log_gamma,log_gamma1 = variational_posterior.gamma_log_prob() + variance = float(variance) + psi0 = np.empty(N) + psi0[:] = variance + psi1 = np.empty((N,M)) + psi2n = np.empty((N,M,M)) + + from ....util.misc import param_to_array + S = param_to_array(S) + mu = param_to_array(mu) + Z = param_to_array(Z) + + support_code = """ + #include + """ + code = """ + for(int n=0; npsi1_exp2)?psi1_exp1+log1p(exp(psi1_exp2-psi1_exp1)):psi1_exp2+log1p(exp(psi1_exp1-psi1_exp2)); + } + // Compute Psi_2 + double muZhat = mu(n,q) - (Zm1q+Zm2q)/2.; + double Z2 = Zm1q*Zm1q+ Zm2q*Zm2q; + double dZ = Zm1q - Zm2q; + + double psi2_exp1 = dZ*dZ/(-4.*lq)-muZhat*muZhat/(2.*Snq+lq) - log_denom2(n,q)/2. + log_gamma(n,q); + double psi2_exp2 = log_gamma1(n,q) - Z2/(2.*lq); + log_psi2_n += (psi2_exp1>psi2_exp2)?psi2_exp1+log1p(exp(psi2_exp2-psi2_exp1)):psi2_exp2+log1p(exp(psi2_exp1-psi2_exp2)); + } + double exp_psi2_n = exp(log_psi2_n); + psi2n(n,m1,m2) = variance*variance*exp_psi2_n; + if(m1!=m2) { psi2n(n,m2,m1) = variance*variance*exp_psi2_n;} + } + psi1(n,m1) = variance*exp(log_psi1); + } + } + """ + weave.inline(code, support_code=support_code, arg_names=['psi1','psi2n','N','M','Q','variance','l2','Z','mu','S','log_denom1','log_denom2','log_gamma','log_gamma1'], type_converters=weave.converters.blitz) + + psi2 = psi2n.sum(axis=0) + return psi0,psi1,psi2,psi2n + + from GPy.util.caching import Cacher + psicomputations = Cacher(_psicomputations, limit=1) + + def psiDerivativecomputations(dL_dpsi0, dL_dpsi1, dL_dpsi2, variance, lengthscale, Z, variational_posterior): + ARD = (len(lengthscale)!=1) + + _,psi1,_,psi2n = psicomputations(variance, lengthscale, Z, variational_posterior) + + mu = variational_posterior.mean + S = variational_posterior.variance + N,M,Q = mu.shape[0],Z.shape[0],mu.shape[1] + l2 = np.square(lengthscale) + log_denom1 = np.log(S/l2+1) + log_denom2 = np.log(2*S/l2+1) + log_gamma,log_gamma1 = variational_posterior.gamma_log_prob() + gamma, gamma1 = variational_posterior.gamma_probabilities() + variance = float(variance) + + dvar = np.zeros(1) + dmu = np.zeros((N,Q)) + dS = np.zeros((N,Q)) + dgamma = np.zeros((N,Q)) + dl = np.zeros(Q) + dZ = np.zeros((M,Q)) + dvar += np.sum(dL_dpsi0) + + from ....util.misc import param_to_array + S = param_to_array(S) + mu = param_to_array(mu) + Z = param_to_array(Z) + + support_code = """ + #include + """ + code = """ + for(int n=0; nexp2) { + d_exp1 = 1.; + d_exp2 = exp(exp2-exp1); + } else { + d_exp1 = exp(exp1-exp2); + d_exp2 = 1.; + } + double exp_sum = d_exp1+d_exp2; + + dmu(n,q) += lpsi1*Zmu*d_exp1/(denom*exp_sum); + dS(n,q) += lpsi1*(Zmu2_denom-1.)*d_exp1/(denom*exp_sum)/2.; + dgamma(n,q) += lpsi1*(d_exp1*g1nq-d_exp2*gnq)/exp_sum; + dl(q) += lpsi1*((Zmu2_denom+Snq/lq)/denom*d_exp1+Zm1q*Zm1q/(lq*lq)*d_exp2)/(2.*exp_sum); + dZ(m1,q) += lpsi1*(-Zmu/denom*d_exp1-Zm1q/lq*d_exp2)/exp_sum; + } + // Compute Psi_2 + double lpsi2 = psi2n(n,m1,m2)*dL_dpsi2(m1,m2); + if(q==0) {dvar(0) += lpsi2*2/variance;} + + double dZm1m2 = Zm1q - Zm2q; + double Z2 = Zm1q*Zm1q+Zm2q*Zm2q; + double muZhat = mu_nq - (Zm1q + Zm2q)/2.; + double denom = 2.*Snq+lq; + double muZhat2_denom = muZhat*muZhat/denom; + + double exp1 = dZm1m2*dZm1m2/(-4.*lq)-muZhat*muZhat/(2.*Snq+lq) - log_denom2(n,q)/2. + log_gamma(n,q); + double exp2 = log_gamma1(n,q) - Z2/(2.*lq); + double d_exp1,d_exp2; + if(exp1>exp2) { + d_exp1 = 1.; + d_exp2 = exp(exp2-exp1); + } else { + d_exp1 = exp(exp1-exp2); + d_exp2 = 1.; + } + double exp_sum = d_exp1+d_exp2; + + dmu(n,q) += -2.*lpsi2*muZhat/denom*d_exp1/exp_sum; + dS(n,q) += lpsi2*(2.*muZhat2_denom-1.)/denom*d_exp1/exp_sum; + dgamma(n,q) += lpsi2*(d_exp1*g1nq-d_exp2*gnq)/exp_sum; + dl(q) += lpsi2*(((Snq/lq+muZhat2_denom)/denom+dZm1m2*dZm1m2/(4.*lq*lq))*d_exp1+Z2/(2.*lq*lq)*d_exp2)/exp_sum; + dZ(m1,q) += 2.*lpsi2*((muZhat/denom-dZm1m2/(2*lq))*d_exp1-Zm1q/lq*d_exp2)/exp_sum; + } + } + } + } + """ + weave.inline(code, support_code=support_code, arg_names=['dL_dpsi1','dL_dpsi2','psi1','psi2n','N','M','Q','variance','l2','Z','mu','S','gamma','gamma1','log_denom1','log_denom2','log_gamma','log_gamma1','dvar','dl','dmu','dS','dgamma','dZ'], type_converters=weave.converters.blitz) + + dl *= 2.*lengthscale + if not ARD: + dl = dl.sum() + + return dvar, dl, dZ, dmu, dS, dgamma + +except: + + def psicomputations(variance, lengthscale, Z, variational_posterior): + """ + Z - MxQ + mu - NxQ + S - NxQ + gamma - NxQ + """ + # here are the "statistics" for psi0, psi1 and psi2 + # Produced intermediate results: + # _psi1 NxM + mu = variational_posterior.mean + S = variational_posterior.variance + gamma = variational_posterior.binary_prob + + psi0 = np.empty(mu.shape[0]) + psi0[:] = variance + psi1 = _psi1computations(variance, lengthscale, Z, mu, S, gamma) + psi2 = _psi2computations(variance, lengthscale, Z, mu, S, gamma) + return psi0, psi1, psi2 + + def _psi1computations(variance, lengthscale, Z, mu, S, gamma): + """ + Z - MxQ + mu - NxQ + S - NxQ + gamma - NxQ + """ + # here are the "statistics" for psi1 + # Produced intermediate results: + # _psi1 NxM + + lengthscale2 = np.square(lengthscale) + + # psi1 + _psi1_denom = S[:, None, :] / lengthscale2 + 1. # Nx1xQ + _psi1_denom_sqrt = np.sqrt(_psi1_denom) #Nx1xQ + _psi1_dist = Z[None, :, :] - mu[:, None, :] # NxMxQ + _psi1_dist_sq = np.square(_psi1_dist) / (lengthscale2 * _psi1_denom) # NxMxQ + _psi1_common = gamma[:,None,:] / (lengthscale2*_psi1_denom*_psi1_denom_sqrt) #Nx1xQ + _psi1_exponent1 = np.log(gamma[:,None,:]) - (_psi1_dist_sq + np.log(_psi1_denom))/2. # NxMxQ + _psi1_exponent2 = np.log(1.-gamma[:,None,:]) - (np.square(Z[None,:,:])/lengthscale2)/2. # NxMxQ + _psi1_exponent_max = np.maximum(_psi1_exponent1,_psi1_exponent2) + _psi1_exponent = _psi1_exponent_max+np.log(np.exp(_psi1_exponent1-_psi1_exponent_max) + np.exp(_psi1_exponent2-_psi1_exponent_max)) #NxMxQ + _psi1_exp_sum = _psi1_exponent.sum(axis=-1) #NxM + _psi1 = variance * np.exp(_psi1_exp_sum) # NxM + + return _psi1 + + def _psi2computations(variance, lengthscale, Z, mu, S, gamma): + """ + Z - MxQ + mu - NxQ + S - NxQ + gamma - NxQ + """ + # here are the "statistics" for psi2 + # Produced intermediate results: + # _psi2 MxM + + lengthscale2 = np.square(lengthscale) + + _psi2_Zhat = 0.5 * (Z[:, None, :] + Z[None, :, :]) # M,M,Q + _psi2_Zdist = 0.5 * (Z[:, None, :] - Z[None, :, :]) # M,M,Q + _psi2_Zdist_sq = np.square(_psi2_Zdist / lengthscale) # M,M,Q + _psi2_Z_sq_sum = (np.square(Z[:,None,:])+np.square(Z[None,:,:]))/lengthscale2 # MxMxQ + + # psi2 + _psi2_denom = 2.*S[:, None, None, :] / lengthscale2 + 1. # Nx1x1xQ + _psi2_denom_sqrt = np.sqrt(_psi2_denom) + _psi2_mudist = mu[:,None,None,:]-_psi2_Zhat #N,M,M,Q + _psi2_mudist_sq = np.square(_psi2_mudist)/(lengthscale2*_psi2_denom) + _psi2_common = gamma[:,None,None,:]/(lengthscale2 * _psi2_denom * _psi2_denom_sqrt) # Nx1x1xQ + _psi2_exponent1 = -_psi2_Zdist_sq -_psi2_mudist_sq -0.5*np.log(_psi2_denom)+np.log(gamma[:,None,None,:]) #N,M,M,Q + _psi2_exponent2 = np.log(1.-gamma[:,None,None,:]) - 0.5*(_psi2_Z_sq_sum) # NxMxMxQ + _psi2_exponent_max = np.maximum(_psi2_exponent1, _psi2_exponent2) + _psi2_exponent = _psi2_exponent_max+np.log(np.exp(_psi2_exponent1-_psi2_exponent_max) + np.exp(_psi2_exponent2-_psi2_exponent_max)) + _psi2_exp_sum = _psi2_exponent.sum(axis=-1) #NxM + _psi2 = variance*variance * (np.exp(_psi2_exp_sum).sum(axis=0)) # MxM + + return _psi2 + + def psiDerivativecomputations(dL_dpsi0, dL_dpsi1, dL_dpsi2, variance, lengthscale, Z, variational_posterior): + ARD = (len(lengthscale)!=1) + + dvar_psi1, dl_psi1, dZ_psi1, dmu_psi1, dS_psi1, dgamma_psi1 = _psi1compDer(dL_dpsi1, variance, lengthscale, Z, variational_posterior.mean, variational_posterior.variance, variational_posterior.binary_prob) + dvar_psi2, dl_psi2, dZ_psi2, dmu_psi2, dS_psi2, dgamma_psi2 = _psi2compDer(dL_dpsi2, variance, lengthscale, Z, variational_posterior.mean, variational_posterior.variance, variational_posterior.binary_prob) + + dL_dvar = np.sum(dL_dpsi0) + dvar_psi1 + dvar_psi2 + + dL_dlengscale = dl_psi1 + dl_psi2 + if not ARD: + dL_dlengscale = dL_dlengscale.sum() + + dL_dgamma = dgamma_psi1 + dgamma_psi2 + dL_dmu = dmu_psi1 + dmu_psi2 + dL_dS = dS_psi1 + dS_psi2 + dL_dZ = dZ_psi1 + dZ_psi2 + + return dL_dvar, dL_dlengscale, dL_dZ, dL_dmu, dL_dS, dL_dgamma + + def _psi1compDer(dL_dpsi1, variance, lengthscale, Z, mu, S, gamma): + """ + dL_dpsi1 - NxM + Z - MxQ + mu - NxQ + S - NxQ + gamma - NxQ + """ + # here are the "statistics" for psi1 + # Produced intermediate results: dL_dparams w.r.t. psi1 + # _dL_dvariance 1 + # _dL_dlengthscale Q + # _dL_dZ MxQ + # _dL_dgamma NxQ + # _dL_dmu NxQ + # _dL_dS NxQ + + lengthscale2 = np.square(lengthscale) + + # psi1 + _psi1_denom = S / lengthscale2 + 1. # NxQ + _psi1_denom_sqrt = np.sqrt(_psi1_denom) #NxQ + _psi1_dist = Z[None, :, :] - mu[:, None, :] # NxMxQ + _psi1_dist_sq = np.square(_psi1_dist) / (lengthscale2 * _psi1_denom[:,None,:]) # NxMxQ + _psi1_common = gamma / (lengthscale2*_psi1_denom*_psi1_denom_sqrt) #NxQ + _psi1_exponent1 = np.log(gamma[:,None,:]) -0.5 * (_psi1_dist_sq + np.log(_psi1_denom[:, None,:])) # NxMxQ + _psi1_exponent2 = np.log(1.-gamma[:,None,:]) -0.5 * (np.square(Z[None,:,:])/lengthscale2) # NxMxQ + _psi1_exponent_max = np.maximum(_psi1_exponent1,_psi1_exponent2) + _psi1_exponent = _psi1_exponent_max+np.log(np.exp(_psi1_exponent1-_psi1_exponent_max) + np.exp(_psi1_exponent2-_psi1_exponent_max)) #NxMxQ + _psi1_exp_sum = _psi1_exponent.sum(axis=-1) #NxM + _psi1_exp_dist_sq = np.exp(-0.5*_psi1_dist_sq) # NxMxQ + _psi1_exp_Z = np.exp(-0.5*np.square(Z[None,:,:])/lengthscale2) # 1xMxQ + _psi1_q = variance * np.exp(_psi1_exp_sum[:,:,None] - _psi1_exponent) # NxMxQ + _psi1 = variance * np.exp(_psi1_exp_sum) # NxM + _dL_dvariance = np.einsum('nm,nm->',dL_dpsi1, _psi1)/variance # 1 + _dL_dgamma = np.einsum('nm,nmq,nmq->nq',dL_dpsi1, _psi1_q, (_psi1_exp_dist_sq/_psi1_denom_sqrt[:,None,:]-_psi1_exp_Z)) # NxQ + _dL_dmu = np.einsum('nm, nmq, nmq, nmq, nq->nq',dL_dpsi1,_psi1_q,_psi1_exp_dist_sq,_psi1_dist,_psi1_common) # NxQ + _dL_dS = np.einsum('nm,nmq,nmq,nq,nmq->nq',dL_dpsi1,_psi1_q,_psi1_exp_dist_sq,_psi1_common,(_psi1_dist_sq-1.))/2. # NxQ + _dL_dZ = np.einsum('nm,nmq,nmq->mq',dL_dpsi1,_psi1_q, (- _psi1_common[:,None,:] * _psi1_dist * _psi1_exp_dist_sq - (1-gamma[:,None,:])/lengthscale2*Z[None,:,:]*_psi1_exp_Z)) + _dL_dlengthscale = lengthscale* np.einsum('nm,nmq,nmq->q',dL_dpsi1,_psi1_q,(_psi1_common[:,None,:]*(S[:,None,:]/lengthscale2+_psi1_dist_sq)*_psi1_exp_dist_sq + (1-gamma[:,None,:])*np.square(Z[None,:,:]/lengthscale2)*_psi1_exp_Z)) + + return _dL_dvariance, _dL_dlengthscale, _dL_dZ, _dL_dmu, _dL_dS, _dL_dgamma + + def _psi2compDer(dL_dpsi2, variance, lengthscale, Z, mu, S, gamma): + """ + Z - MxQ + mu - NxQ + S - NxQ + gamma - NxQ + dL_dpsi2 - MxM + """ + # here are the "statistics" for psi2 + # Produced the derivatives w.r.t. psi2: + # _dL_dvariance 1 + # _dL_dlengthscale Q + # _dL_dZ MxQ + # _dL_dgamma NxQ + # _dL_dmu NxQ + # _dL_dS NxQ + + lengthscale2 = np.square(lengthscale) + + _psi2_Zhat = 0.5 * (Z[:, None, :] + Z[None, :, :]) # M,M,Q + _psi2_Zdist = 0.5 * (Z[:, None, :] - Z[None, :, :]) # M,M,Q + _psi2_Zdist_sq = np.square(_psi2_Zdist / lengthscale) # M,M,Q + _psi2_Z_sq_sum = (np.square(Z[:,None,:])+np.square(Z[None,:,:]))/lengthscale2 # MxMxQ + + # psi2 + _psi2_denom = 2.*S / lengthscale2 + 1. # NxQ + _psi2_denom_sqrt = np.sqrt(_psi2_denom) + _psi2_mudist = mu[:,None,None,:]-_psi2_Zhat #N,M,M,Q + _psi2_mudist_sq = np.square(_psi2_mudist)/(lengthscale2*_psi2_denom[:,None,None,:]) + _psi2_common = gamma/(lengthscale2 * _psi2_denom * _psi2_denom_sqrt) # NxQ + _psi2_exponent1 = -_psi2_Zdist_sq -_psi2_mudist_sq -0.5*np.log(_psi2_denom[:,None,None,:])+np.log(gamma[:,None,None,:]) #N,M,M,Q + _psi2_exponent2 = np.log(1.-gamma[:,None,None,:]) - 0.5*(_psi2_Z_sq_sum) # NxMxMxQ + _psi2_exponent_max = np.maximum(_psi2_exponent1, _psi2_exponent2) + _psi2_exponent = _psi2_exponent_max+np.log(np.exp(_psi2_exponent1-_psi2_exponent_max) + np.exp(_psi2_exponent2-_psi2_exponent_max)) + _psi2_exp_sum = _psi2_exponent.sum(axis=-1) #NxM + _psi2_q = variance*variance * np.exp(_psi2_exp_sum[:,:,:,None]-_psi2_exponent) # NxMxMxQ + _psi2_exp_dist_sq = np.exp(-_psi2_Zdist_sq -_psi2_mudist_sq) # NxMxMxQ + _psi2_exp_Z = np.exp(-0.5*_psi2_Z_sq_sum) # MxMxQ + _psi2 = variance*variance * (np.exp(_psi2_exp_sum).sum(axis=0)) # MxM + _dL_dvariance = np.einsum('mo,mo->',dL_dpsi2,_psi2)*2./variance + _dL_dgamma = np.einsum('mo,nmoq,nmoq->nq',dL_dpsi2,_psi2_q,(_psi2_exp_dist_sq/_psi2_denom_sqrt[:,None,None,:] - _psi2_exp_Z)) + _dL_dmu = -2.*np.einsum('mo,nmoq,nq,nmoq,nmoq->nq',dL_dpsi2,_psi2_q,_psi2_common,_psi2_mudist,_psi2_exp_dist_sq) + _dL_dS = np.einsum('mo,nmoq,nq,nmoq,nmoq->nq',dL_dpsi2,_psi2_q, _psi2_common, (2.*_psi2_mudist_sq-1.), _psi2_exp_dist_sq) + _dL_dZ = 2.*np.einsum('mo,nmoq,nmoq->mq',dL_dpsi2,_psi2_q,(_psi2_common[:,None,None,:]*(-_psi2_Zdist*_psi2_denom[:,None,None,:]+_psi2_mudist)*_psi2_exp_dist_sq - (1-gamma[:,None,None,:])*Z[:,None,:]/lengthscale2*_psi2_exp_Z)) + _dL_dlengthscale = 2.*lengthscale* np.einsum('mo,nmoq,nmoq->q',dL_dpsi2,_psi2_q,(_psi2_common[:,None,None,:]*(S[:,None,None,:]/lengthscale2+_psi2_Zdist_sq*_psi2_denom[:,None,None,:]+_psi2_mudist_sq)*_psi2_exp_dist_sq+(1-gamma[:,None,None,:])*_psi2_Z_sq_sum*0.5/lengthscale2*_psi2_exp_Z)) + + return _dL_dvariance, _dL_dlengthscale, _dL_dZ, _dL_dmu, _dL_dS, _dL_dgamma diff --git a/GPy/kern/_src/psi_comp/ssrbf_psi_gpucomp.py b/GPy/kern/_src/psi_comp/ssrbf_psi_gpucomp.py new file mode 100644 index 00000000..1a9d2058 --- /dev/null +++ b/GPy/kern/_src/psi_comp/ssrbf_psi_gpucomp.py @@ -0,0 +1,474 @@ + +""" +The module for psi-statistics for RBF kernel for Spike-and-Slab GPLVM +""" + +import numpy as np +from ....util.caching import Cache_this +from . import PSICOMP_RBF +from ....util import gpu_init + +try: + import pycuda.gpuarray as gpuarray + from pycuda.compiler import SourceModule + from ....util.linalg_gpu import sum_axis +except: + pass + +gpu_code = """ + // define THREADNUM + + #define IDX_NMQ(n,m,q) ((q*M+m)*N+n) + #define IDX_NMM(n,m1,m2) ((m2*M+m1)*N+n) + #define IDX_NQ(n,q) (q*N+n) + #define IDX_NM(n,m) (m*N+n) + #define IDX_MQ(m,q) (q*M+m) + #define IDX_MM(m1,m2) (m2*M+m1) + #define IDX_NQB(n,q,b) ((b*Q+q)*N+n) + #define IDX_QB(q,b) (b*Q+q) + + // Divide data evenly + __device__ void divide_data(int total_data, int psize, int pidx, int *start, int *end) { + int residue = (total_data)%psize; + if(pidx= blockDim.x) { + for(int i=blockDim.x+threadIdx.x; i=1;s=s/2) { + if(threadIdx.x < s) {array[threadIdx.x] += array[s+threadIdx.x];} + __syncthreads(); + } + } + + __global__ void compDenom(double *log_denom1, double *log_denom2, double *log_gamma, double*log_gamma1, double *gamma, double *l, double *S, int N, int Q) + { + int n_start, n_end; + divide_data(N, gridDim.x, blockIdx.x, &n_start, &n_end); + + for(int i=n_start*Q+threadIdx.x; iexp2)?exp1+log1p(exp(exp2-exp1)):exp2+log1p(exp(exp1-exp2)); + } + psi1[IDX_NM(n,m)] = var*exp(log_psi1); + } + } + } + + __global__ void psi2computations(double *psi2, double *psi2n, double *log_denom2, double *log_gamma, double*log_gamma1, double var, double *l, double *Z, double *mu, double *S, int N, int M, int Q) + { + int psi2_idx_start, psi2_idx_end; + __shared__ double psi2_local[THREADNUM]; + divide_data((M+1)*M/2, gridDim.x, blockIdx.x, &psi2_idx_start, &psi2_idx_end); + + for(int psi2_idx=psi2_idx_start; psi2_idxexp2)?exp1+log1p(exp(exp2-exp1)):exp2+log1p(exp(exp1-exp2)); + } + double exp_psi2_n = exp(log_psi2_n); + psi2n[IDX_NMM(n,m1,m2)] = var*var*exp_psi2_n; + if(m1!=m2) { psi2n[IDX_NMM(n,m2,m1)] = var*var*exp_psi2_n;} + psi2_local[threadIdx.x] += exp_psi2_n; + } + __syncthreads(); + reduce_sum(psi2_local, THREADNUM); + if(threadIdx.x==0) { + psi2[IDX_MM(m1,m2)] = var*var*psi2_local[0]; + if(m1!=m2) { psi2[IDX_MM(m2,m1)] = var*var*psi2_local[0]; } + } + __syncthreads(); + } + } + + __global__ void psi1compDer(double *dvar, double *dl, double *dZ, double *dmu, double *dS, double *dgamma, double *dL_dpsi1, double *psi1, double *log_denom1, double *log_gamma, double*log_gamma1, double var, double *l, double *Z, double *mu, double *S, double *gamma, int N, int M, int Q) + { + int m_start, m_end; + __shared__ double g_local[THREADNUM]; + divide_data(M, gridDim.x, blockIdx.x, &m_start, &m_end); + int P = int(ceil(double(N)/THREADNUM)); + + double dvar_local = 0; + for(int q=0;qexp2) { + d_exp1 = 1.; + d_exp2 = exp(exp2-exp1); + } else { + d_exp1 = exp(exp1-exp2); + d_exp2 = 1.; + } + double exp_sum = d_exp1+d_exp2; + + dmu_local += lpsi1*Zmu*d_exp1/(denom*exp_sum); + dS_local += lpsi1*(Zmu2_denom-1.)*d_exp1/(denom*exp_sum); + dgamma_local += lpsi1*(d_exp1/gnq-d_exp2/(1.-gnq))/exp_sum; + dl_local += lpsi1*((Zmu2_denom+Snq/lq)/denom*d_exp1+Zmq*Zmq/(lq*lq)*d_exp2)/(2.*exp_sum); + g_local[threadIdx.x] = lpsi1*(-Zmu/denom*d_exp1-Zmq/lq*d_exp2)/exp_sum; + } + __syncthreads(); + reduce_sum(g_local, pexp2) { + d_exp1 = 1.; + d_exp2 = exp(exp2-exp1); + } else { + d_exp1 = exp(exp1-exp2); + d_exp2 = 1.; + } + double exp_sum = d_exp1+d_exp2; + + dmu_local += lpsi2*muZhat/denom*d_exp1/exp_sum; + dS_local += lpsi2*(2.*muZhat2_denom-1.)/denom*d_exp1/exp_sum; + dgamma_local += lpsi2*(d_exp1/gnq-d_exp2/(1.-gnq))/exp_sum; + dl_local += lpsi2*(((Snq/lq+muZhat2_denom)/denom+dZ*dZ/(4.*lq*lq))*d_exp1+Z2/(2.*lq*lq)*d_exp2)/exp_sum; + g_local[threadIdx.x] += 2.*lpsi2*((muZhat/denom-dZ/(2*lq))*d_exp1-Zm1q/lq*d_exp2)/exp_sum; + } + } + __syncthreads(); + reduce_sum(g_local, pX.shape[0]/2: + return K + + slices = index_to_slices(X[:,self.index_dim]) + idx_start = slices[1][0].start + idx_end = idx_start+self.idx_p + K_c = K[idx_start:idx_end,idx_start:idx_end].copy() + K[idx_start:idx_end,:] = K[:self.idx_p,:] + K[:,idx_start:idx_end] = K[:,:self.idx_p] + K[idx_start:idx_end,idx_start:idx_end] = K_c + + return K + + def Kdiag(self,X): + Kdiag = self.kern.Kdiag(X) + + if self.idx_p<=0 or self.idx_p>X.shape[0]/2: + return Kdiag + + slices = index_to_slices(X[:,self.index_dim]) + idx_start = slices[1][0].start + idx_end = idx_start+self.idx_p + Kdiag[idx_start:idx_end] = Kdiag[:self.idx_p] + + return Kdiag + + def update_gradients_full(self,dL_dK,X,X2=None): + assert X2==None + if self.idx_p<=0 or self.idx_p>X.shape[0]/2: + self.kern.update_gradients_full(dL_dK, X) + return + + slices = index_to_slices(X[:,self.index_dim]) + idx_start = slices[1][0].start + idx_end = idx_start+self.idx_p + + self.kern.update_gradients_full(dL_dK[idx_start:idx_end,:], X[:self.idx_p],X) + grad_p1 = self.kern.gradient.copy() + self.kern.update_gradients_full(dL_dK[:,idx_start:idx_end], X, X[:self.idx_p]) + grad_p2 = self.kern.gradient.copy() + self.kern.update_gradients_full(dL_dK[idx_start:idx_end,idx_start:idx_end], X[:self.idx_p],X[idx_start:idx_end]) + grad_p3 = self.kern.gradient.copy() + self.kern.update_gradients_full(dL_dK[idx_start:idx_end,idx_start:idx_end], X[idx_start:idx_end], X[:self.idx_p]) + grad_p4 = self.kern.gradient.copy() + + self.kern.update_gradients_full(dL_dK[idx_start:idx_end,:], X[idx_start:idx_end],X) + grad_n1 = self.kern.gradient.copy() + self.kern.update_gradients_full(dL_dK[:,idx_start:idx_end], X, X[idx_start:idx_end]) + grad_n2 = self.kern.gradient.copy() + self.kern.update_gradients_full(dL_dK[idx_start:idx_end,idx_start:idx_end], X[idx_start:idx_end], X[idx_start:idx_end]) + grad_n3 = self.kern.gradient.copy() + + self.kern.update_gradients_full(dL_dK, X) + self.kern.gradient += grad_p1+grad_p2-grad_p3-grad_p4-grad_n1-grad_n2+2*grad_n3 + + def update_gradients_diag(self, dL_dKdiag, X): + pass + +class SplitKern(CombinationKernel): + + def __init__(self, kernel, Xp, index_dim=-1, name='SplitKern'): + assert isinstance(index_dim, int), "The index dimension must be an integer!" + self.kern = kernel + self.kern_cross = SplitKern_cross(kernel,Xp) + super(SplitKern, self).__init__(kernels=[self.kern, self.kern_cross], extra_dims=[index_dim], name=name) + self.index_dim = index_dim + + def K(self,X ,X2=None): + slices = index_to_slices(X[:,self.index_dim]) + assert len(slices)<=2, 'The Split kernel only support two different indices' + if X2 is None: + target = np.zeros((X.shape[0], X.shape[0])) + # diagonal blocks + [[target.__setitem__((s,ss), self.kern.K(X[s,:], X[ss,:])) for s,ss in itertools.product(slices_i, slices_i)] for slices_i in slices] + if len(slices)>1: + # cross blocks + [target.__setitem__((s,ss), self.kern_cross.K(X[s,:], X[ss,:])) for s,ss in itertools.product(slices[0], slices[1])] + # cross blocks + [target.__setitem__((s,ss), self.kern_cross.K(X[s,:], X[ss,:])) for s,ss in itertools.product(slices[1], slices[0])] + else: + slices2 = index_to_slices(X2[:,self.index_dim]) + assert len(slices2)<=2, 'The Split kernel only support two different indices' + target = np.zeros((X.shape[0], X2.shape[0])) + # diagonal blocks + [[target.__setitem__((s,s2), self.kern.K(X[s,:],X2[s2,:])) for s,s2 in itertools.product(slices[i], slices2[i])] for i in xrange(min(len(slices),len(slices2)))] + if len(slices)>1: + [target.__setitem__((s,s2), self.kern_cross.K(X[s,:],X2[s2,:])) for s,s2 in itertools.product(slices[1], slices2[0])] + if len(slices2)>1: + [target.__setitem__((s,s2), self.kern_cross.K(X[s,:],X2[s2,:])) for s,s2 in itertools.product(slices[0], slices2[1])] + return target + + def Kdiag(self,X): + return self.kern.Kdiag(X) + + def update_gradients_full(self,dL_dK,X,X2=None): + slices = index_to_slices(X[:,self.index_dim]) + target = np.zeros(self.kern.size) + + def collate_grads(dL, X, X2, cross=False): + if cross: + self.kern_cross.update_gradients_full(dL,X,X2) + target[:] += self.kern_cross.kern.gradient + else: + self.kern.update_gradients_full(dL,X,X2) + target[:] += self.kern.gradient + + if X2 is None: + assert dL_dK.shape==(X.shape[0],X.shape[0]) + [[collate_grads(dL_dK[s,ss], X[s], X[ss]) for s,ss in itertools.product(slices_i, slices_i)] for slices_i in slices] + if len(slices)>1: + [collate_grads(dL_dK[s,ss], X[s], X[ss], True) for s,ss in itertools.product(slices[0], slices[1])] + [collate_grads(dL_dK[s,ss], X[s], X[ss], True) for s,ss in itertools.product(slices[1], slices[0])] + else: + assert dL_dK.shape==(X.shape[0],X2.shape[0]) + slices2 = index_to_slices(X2[:,self.index_dim]) + [[collate_grads(dL_dK[s,s2],X[s],X2[s2]) for s,s2 in itertools.product(slices[i], slices2[i])] for i in xrange(min(len(slices),len(slices2)))] + if len(slices)>1: + [collate_grads(dL_dK[s,s2], X[s], X2[s2], True) for s,s2 in itertools.product(slices[1], slices2[0])] + if len(slices2)>1: + [collate_grads(dL_dK[s,s2], X[s], X2[s2], True) for s,s2 in itertools.product(slices[0], slices2[1])] + self.kern.gradient = target + + def update_gradients_diag(self, dL_dKdiag, X): + self.kern.update_gradients_diag(self, dL_dKdiag, X) + +class SplitKern_cross(Kern): + + def __init__(self, kernel, Xp, name='SplitKern_cross'): + assert isinstance(kernel, Kern) + self.kern = kernel + if not isinstance(Xp,np.ndarray): + Xp = np.array([[Xp]]) + self.Xp = Xp + super(SplitKern_cross, self).__init__(input_dim=kernel.input_dim, active_dims=None, name=name) + + def K(self, X, X2=None): + if X2 is None: + return np.dot(self.kern.K(X,self.Xp),self.kern.K(self.Xp,X))/self.kern.K(self.Xp,self.Xp) + else: + return np.dot(self.kern.K(X,self.Xp),self.kern.K(self.Xp,X2))/self.kern.K(self.Xp,self.Xp) + + def Kdiag(self, X): + return np.inner(self.kern.K(X,self.Xp),self.kern.K(self.Xp,X).T)/self.kern.K(self.Xp,self.Xp) + + def update_gradients_full(self, dL_dK, X, X2=None): + if X2 is None: + X2 = X + + k1 = self.kern.K(X,self.Xp) + k2 = self.kern.K(self.Xp,X2) + k3 = self.kern.K(self.Xp,self.Xp) + dL_dk1 = np.einsum('ij,j->i',dL_dK,k2[0])/k3[0,0] + dL_dk2 = np.einsum('ij,i->j',dL_dK,k1[:,0])/k3[0,0] + dL_dk3 = np.einsum('ij,ij->',dL_dK,-np.dot(k1,k2)/(k3[0,0]*k3[0,0])) + + self.kern.update_gradients_full(dL_dk1[:,None],X,self.Xp) + grad = self.kern.gradient.copy() + self.kern.update_gradients_full(dL_dk2[None,:],self.Xp,X2) + grad += self.kern.gradient.copy() + self.kern.update_gradients_full(np.array([[dL_dk3]]),self.Xp,self.Xp) + grad += self.kern.gradient.copy() + + self.kern.gradient = grad + + def update_gradients_diag(self, dL_dKdiag, X): + k1 = self.kern.K(X,self.Xp) + k2 = self.kern.K(self.Xp,X) + k3 = self.kern.K(self.Xp,self.Xp) + dL_dk1 = dL_dKdiag*k2[0]/k3 + dL_dk2 = dL_dKdiag*k1[:,0]/k3 + dL_dk3 = -dL_dKdiag*(k1[:,0]*k2[0]).sum()/(k3*k3) + + self.kern.update_gradients_full(dL_dk1[:,None],X,self.Xp) + grad1 = self.kern.gradient.copy() + self.kern.update_gradients_full(dL_dk2[None,:],self.Xp,X) + grad2 = self.kern.gradient.copy() + self.kern.update_gradients_full(np.array([[dL_dk3]]),self.Xp,self.Xp) + grad3 = self.kern.gradient.copy() + + self.kern.gradient = grad1+grad2+grad3 + + diff --git a/GPy/kern/_src/static.py b/GPy/kern/_src/static.py new file mode 100644 index 00000000..f4223bf4 --- /dev/null +++ b/GPy/kern/_src/static.py @@ -0,0 +1,122 @@ +# Copyright (c) 2012, GPy authors (see AUTHORS.txt). +# Licensed under the BSD 3-clause license (see LICENSE.txt) + + +from kern import Kern +import numpy as np +from ...core.parameterization import Param +from ...core.parameterization.transformations import Logexp + +class Static(Kern): + def __init__(self, input_dim, variance, active_dims, name): + super(Static, self).__init__(input_dim, active_dims, name) + self.variance = Param('variance', variance, Logexp()) + self.link_parameters(self.variance) + + def Kdiag(self, X): + ret = np.empty((X.shape[0],), dtype=np.float64) + ret[:] = self.variance + return ret + + def gradients_X(self, dL_dK, X, X2=None): + return np.zeros(X.shape) + + def gradients_X_diag(self, dL_dKdiag, X): + return np.zeros(X.shape) + + def gradients_Z_expectations(self, dL_dpsi0, dL_dpsi1, dL_dpsi2, Z, variational_posterior): + return np.zeros(Z.shape) + + def gradients_qX_expectations(self, dL_dpsi0, dL_dpsi1, dL_dpsi2, Z, variational_posterior): + return np.zeros(variational_posterior.shape), np.zeros(variational_posterior.shape) + + def psi0(self, Z, variational_posterior): + return self.Kdiag(variational_posterior.mean) + + def psi1(self, Z, variational_posterior): + return self.K(variational_posterior.mean, Z) + + def psi2(self, Z, variational_posterior): + K = self.K(variational_posterior.mean, Z) + return np.einsum('ij,ik->jk',K,K) #K[:,:,None]*K[:,None,:] # NB. more efficient implementations on inherriting classes + + def input_sensitivity(self, summarize=True): + if summarize: + return super(Static, self).input_sensitivity(summarize=summarize) + else: + return np.ones(self.input_dim) * self.variance + +class White(Static): + def __init__(self, input_dim, variance=1., active_dims=None, name='white'): + super(White, self).__init__(input_dim, variance, active_dims, name) + + def K(self, X, X2=None): + if X2 is None: + return np.eye(X.shape[0])*self.variance + else: + return np.zeros((X.shape[0], X2.shape[0])) + + def psi2(self, Z, variational_posterior): + return np.zeros((Z.shape[0], Z.shape[0]), dtype=np.float64) + + def update_gradients_full(self, dL_dK, X, X2=None): + self.variance.gradient = np.trace(dL_dK) + + def update_gradients_diag(self, dL_dKdiag, X): + self.variance.gradient = dL_dKdiag.sum() + + def update_gradients_expectations(self, dL_dpsi0, dL_dpsi1, dL_dpsi2, Z, variational_posterior): + self.variance.gradient = dL_dpsi0.sum() + +class Bias(Static): + def __init__(self, input_dim, variance=1., active_dims=None, name='bias'): + super(Bias, self).__init__(input_dim, variance, active_dims, name) + + def K(self, X, X2=None): + shape = (X.shape[0], X.shape[0] if X2 is None else X2.shape[0]) + ret = np.empty(shape, dtype=np.float64) + ret[:] = self.variance + return ret + + def update_gradients_full(self, dL_dK, X, X2=None): + self.variance.gradient = dL_dK.sum() + + def update_gradients_diag(self, dL_dKdiag, X): + self.variance.gradient = dL_dKdiag.sum() + + def psi2(self, Z, variational_posterior): + ret = np.empty((Z.shape[0], Z.shape[0]), dtype=np.float64) + ret[:] = self.variance*self.variance*variational_posterior.shape[0] + return ret + + def update_gradients_expectations(self, dL_dpsi0, dL_dpsi1, dL_dpsi2, Z, variational_posterior): + self.variance.gradient = dL_dpsi0.sum() + dL_dpsi1.sum() + 2.*self.variance*dL_dpsi2.sum()*variational_posterior.shape[0] + +class Fixed(Static): + def __init__(self, input_dim, covariance_matrix, variance=1., active_dims=None, name='fixed'): + """ + :param input_dim: the number of input dimensions + :type input_dim: int + :param variance: the variance of the kernel + :type variance: float + """ + super(Fixed, self).__init__(input_dim, variance, active_dims, name) + self.fixed_K = covariance_matrix + def K(self, X, X2): + return self.variance * self.fixed_K + + def Kdiag(self, X): + return self.variance * self.fixed_K.diag() + + def update_gradients_full(self, dL_dK, X, X2=None): + self.variance.gradient = np.einsum('ij,ij', dL_dK, self.fixed_K) + + def update_gradients_diag(self, dL_dKdiag, X): + self.variance.gradient = np.einsum('i,i', dL_dKdiag, self.fixed_K) + + def psi2(self, Z, variational_posterior): + return np.zeros((Z.shape[0], Z.shape[0]), dtype=np.float64) + + def update_gradients_expectations(self, dL_dpsi0, dL_dpsi1, dL_dpsi2, Z, variational_posterior): + self.variance.gradient = dL_dpsi0.sum() + diff --git a/GPy/kern/_src/stationary.py b/GPy/kern/_src/stationary.py new file mode 100644 index 00000000..443871af --- /dev/null +++ b/GPy/kern/_src/stationary.py @@ -0,0 +1,484 @@ +# Copyright (c) 2012, GPy authors (see AUTHORS.txt). +# Licensed under the BSD 3-clause license (see LICENSE.txt) + + +from kern import Kern +from ...core.parameterization import Param +from ...core.parameterization.transformations import Logexp +from ...util.linalg import tdot +from ... import util +import numpy as np +from scipy import integrate, weave +from ...util.config import config # for assesing whether to use weave +from ...util.caching import Cache_this + +class Stationary(Kern): + """ + Stationary kernels (covariance functions). + + Stationary covariance fucntion depend only on r, where r is defined as + + r = \sqrt{ \sum_{q=1}^Q (x_q - x'_q)^2 } + + The covariance function k(x, x' can then be written k(r). + + In this implementation, r is scaled by the lengthscales parameter(s): + + r = \sqrt{ \sum_{q=1}^Q \frac{(x_q - x'_q)^2}{\ell_q^2} }. + + By default, there's only one lengthscale: seaprate lengthscales for each + dimension can be enables by setting ARD=True. + + To implement a stationary covariance function using this class, one need + only define the covariance function k(r), and it derivative. + + ... + def K_of_r(self, r): + return foo + def dK_dr(self, r): + return bar + + The lengthscale(s) and variance parameters are added to the structure automatically. + + """ + + def __init__(self, input_dim, variance, lengthscale, ARD, active_dims, name, useGPU=False): + super(Stationary, self).__init__(input_dim, active_dims, name,useGPU=useGPU) + self.ARD = ARD + if not ARD: + if lengthscale is None: + lengthscale = np.ones(1) + else: + lengthscale = np.asarray(lengthscale) + assert lengthscale.size == 1, "Only 1 lengthscale needed for non-ARD kernel" + else: + if lengthscale is not None: + lengthscale = np.asarray(lengthscale) + assert lengthscale.size in [1, input_dim], "Bad number of lengthscales" + if lengthscale.size != input_dim: + lengthscale = np.ones(input_dim)*lengthscale + else: + lengthscale = np.ones(self.input_dim) + self.lengthscale = Param('lengthscale', lengthscale, Logexp()) + self.variance = Param('variance', variance, Logexp()) + assert self.variance.size==1 + self.link_parameters(self.variance, self.lengthscale) + + def K_of_r(self, r): + raise NotImplementedError, "implement the covariance function as a fn of r to use this class" + + def dK_dr(self, r): + raise NotImplementedError, "implement derivative of the covariance function wrt r to use this class" + + @Cache_this(limit=5, ignore_args=()) + def K(self, X, X2=None): + """ + Kernel function applied on inputs X and X2. + In the stationary case there is an inner function depending on the + distances from X to X2, called r. + + K(X, X2) = K_of_r((X-X2)**2) + """ + r = self._scaled_dist(X, X2) + return self.K_of_r(r) + + @Cache_this(limit=3, ignore_args=()) + def dK_dr_via_X(self, X, X2): + #a convenience function, so we can cache dK_dr + return self.dK_dr(self._scaled_dist(X, X2)) + + def _unscaled_dist(self, X, X2=None): + """ + Compute the Euclidean distance between each row of X and X2, or between + each pair of rows of X if X2 is None. + """ + #X, = self._slice_X(X) + if X2 is None: + Xsq = np.sum(np.square(X),1) + r2 = -2.*tdot(X) + (Xsq[:,None] + Xsq[None,:]) + util.diag.view(r2)[:,]= 0. # force diagnoal to be zero: sometime numerically a little negative + r2 = np.clip(r2, 0, np.inf) + return np.sqrt(r2) + else: + #X2, = self._slice_X(X2) + X1sq = np.sum(np.square(X),1) + X2sq = np.sum(np.square(X2),1) + r2 = -2.*np.dot(X, X2.T) + X1sq[:,None] + X2sq[None,:] + r2 = np.clip(r2, 0, np.inf) + return np.sqrt(r2) + + @Cache_this(limit=5, ignore_args=()) + def _scaled_dist(self, X, X2=None): + """ + Efficiently compute the scaled distance, r. + + r = \sqrt( \sum_{q=1}^Q (x_q - x'q)^2/l_q^2 ) + + Note that if thre is only one lengthscale, l comes outside the sum. In + this case we compute the unscaled distance first (in a separate + function for caching) and divide by lengthscale afterwards + + """ + if self.ARD: + if X2 is not None: + X2 = X2 / self.lengthscale + return self._unscaled_dist(X/self.lengthscale, X2) + else: + return self._unscaled_dist(X, X2)/self.lengthscale + + def Kdiag(self, X): + ret = np.empty(X.shape[0]) + ret[:] = self.variance + return ret + + def update_gradients_diag(self, dL_dKdiag, X): + """ + Given the derivative of the objective with respect to the diagonal of + the covariance matrix, compute the derivative wrt the parameters of + this kernel and stor in the .gradient field. + + See also update_gradients_full + """ + self.variance.gradient = np.sum(dL_dKdiag) + self.lengthscale.gradient = 0. + + def update_gradients_full(self, dL_dK, X, X2=None): + """ + Given the derivative of the objective wrt the covariance matrix + (dL_dK), compute the gradient wrt the parameters of this kernel, + and store in the parameters object as e.g. self.variance.gradient + """ + self.variance.gradient = np.einsum('ij,ij,i', self.K(X, X2), dL_dK, 1./self.variance) + + #now the lengthscale gradient(s) + dL_dr = self.dK_dr_via_X(X, X2) * dL_dK + if self.ARD: + #rinv = self._inv_dis# this is rather high memory? Should we loop instead?t(X, X2) + #d = X[:, None, :] - X2[None, :, :] + #x_xl3 = np.square(d) + #self.lengthscale.gradient = -((dL_dr*rinv)[:,:,None]*x_xl3).sum(0).sum(0)/self.lengthscale**3 + tmp = dL_dr*self._inv_dist(X, X2) + if X2 is None: X2 = X + + + if config.getboolean('weave', 'working'): + try: + self.lengthscale.gradient = self.weave_lengthscale_grads(tmp, X, X2) + except: + print "\n Weave compilation failed. Falling back to (slower) numpy implementation\n" + config.set('weave', 'working', 'False') + self.lengthscale.gradient = np.array([np.einsum('ij,ij,...', tmp, np.square(X[:,q:q+1] - X2[:,q:q+1].T), -1./self.lengthscale[q]**3) for q in xrange(self.input_dim)]) + else: + self.lengthscale.gradient = np.array([np.einsum('ij,ij,...', tmp, np.square(X[:,q:q+1] - X2[:,q:q+1].T), -1./self.lengthscale[q]**3) for q in xrange(self.input_dim)]) + else: + r = self._scaled_dist(X, X2) + self.lengthscale.gradient = -np.sum(dL_dr*r)/self.lengthscale + + + def _inv_dist(self, X, X2=None): + """ + Compute the elementwise inverse of the distance matrix, expecpt on the + diagonal, where we return zero (the distance on the diagonal is zero). + This term appears in derviatives. + """ + dist = self._scaled_dist(X, X2).copy() + return 1./np.where(dist != 0., dist, np.inf) + + def weave_lengthscale_grads(self, tmp, X, X2): + """Use scipy.weave to compute derivatives wrt the lengthscales""" + N,M = tmp.shape + Q = X.shape[1] + if hasattr(X, 'values'):X = X.values + if hasattr(X2, 'values'):X2 = X2.values + grads = np.zeros(self.input_dim) + code = """ + double gradq; + for(int q=0; q + #include + """ + weave_options = {'headers' : [''], + 'extra_compile_args': ['-fopenmp -O3'], # -march=native'], + 'extra_link_args' : ['-lgomp']} + weave.inline(code, ['ret', 'N', 'D', 'M', 'tmp', 'X', 'X2'], type_converters=weave.converters.blitz, support_code=support_code, **weave_options) + return ret/self.lengthscale**2 + + def gradients_X_diag(self, dL_dKdiag, X): + return np.zeros(X.shape) + + def input_sensitivity(self, summarize=True): + return np.ones(self.input_dim)/self.lengthscale**2 + +class Exponential(Stationary): + def __init__(self, input_dim, variance=1., lengthscale=None, ARD=False, active_dims=None, name='Exponential'): + super(Exponential, self).__init__(input_dim, variance, lengthscale, ARD, active_dims, name) + + def K_of_r(self, r): + return self.variance * np.exp(-0.5 * r) + + def dK_dr(self, r): + return -0.5*self.K_of_r(r) + + +class OU(Stationary): + """ + OU kernel: + + .. math:: + + k(r) = \\sigma^2 \exp(- r) \\ \\ \\ \\ \\text{ where } r = \sqrt{\sum_{i=1}^input_dim \\frac{(x_i-y_i)^2}{\ell_i^2} } + + """ + + def __init__(self, input_dim, variance=1., lengthscale=None, ARD=False, active_dims=None, name='OU'): + super(OU, self).__init__(input_dim, variance, lengthscale, ARD, active_dims, name) + + def K_of_r(self, r): + return self.variance * np.exp(-r) + + def dK_dr(self,r): + return -1.*self.variance*np.exp(-r) + + +class Matern32(Stationary): + """ + Matern 3/2 kernel: + + .. math:: + + k(r) = \\sigma^2 (1 + \\sqrt{3} r) \exp(- \sqrt{3} r) \\ \\ \\ \\ \\text{ where } r = \sqrt{\sum_{i=1}^input_dim \\frac{(x_i-y_i)^2}{\ell_i^2} } + + """ + + def __init__(self, input_dim, variance=1., lengthscale=None, ARD=False, active_dims=None, name='Mat32'): + super(Matern32, self).__init__(input_dim, variance, lengthscale, ARD, active_dims, name) + + def K_of_r(self, r): + return self.variance * (1. + np.sqrt(3.) * r) * np.exp(-np.sqrt(3.) * r) + + def dK_dr(self,r): + return -3.*self.variance*r*np.exp(-np.sqrt(3.)*r) + + def Gram_matrix(self, F, F1, F2, lower, upper): + """ + Return the Gram matrix of the vector of functions F with respect to the + RKHS norm. The use of this function is limited to input_dim=1. + + :param F: vector of functions + :type F: np.array + :param F1: vector of derivatives of F + :type F1: np.array + :param F2: vector of second derivatives of F + :type F2: np.array + :param lower,upper: boundaries of the input domain + :type lower,upper: floats + """ + assert self.input_dim == 1 + def L(x, i): + return(3. / self.lengthscale ** 2 * F[i](x) + 2 * np.sqrt(3) / self.lengthscale * F1[i](x) + F2[i](x)) + n = F.shape[0] + G = np.zeros((n, n)) + for i in range(n): + for j in range(i, n): + G[i, j] = G[j, i] = integrate.quad(lambda x : L(x, i) * L(x, j), lower, upper)[0] + Flower = np.array([f(lower) for f in F])[:, None] + F1lower = np.array([f(lower) for f in F1])[:, None] + return(self.lengthscale ** 3 / (12.*np.sqrt(3) * self.variance) * G + 1. / self.variance * np.dot(Flower, Flower.T) + self.lengthscale ** 2 / (3.*self.variance) * np.dot(F1lower, F1lower.T)) + + +class Matern52(Stationary): + """ + Matern 5/2 kernel: + + .. math:: + + k(r) = \sigma^2 (1 + \sqrt{5} r + \\frac53 r^2) \exp(- \sqrt{5} r) + """ + def __init__(self, input_dim, variance=1., lengthscale=None, ARD=False, active_dims=None, name='Mat52'): + super(Matern52, self).__init__(input_dim, variance, lengthscale, ARD, active_dims, name) + + def K_of_r(self, r): + return self.variance*(1+np.sqrt(5.)*r+5./3*r**2)*np.exp(-np.sqrt(5.)*r) + + def dK_dr(self, r): + return self.variance*(10./3*r -5.*r -5.*np.sqrt(5.)/3*r**2)*np.exp(-np.sqrt(5.)*r) + + def Gram_matrix(self, F, F1, F2, F3, lower, upper): + """ + Return the Gram matrix of the vector of functions F with respect to the RKHS norm. The use of this function is limited to input_dim=1. + + :param F: vector of functions + :type F: np.array + :param F1: vector of derivatives of F + :type F1: np.array + :param F2: vector of second derivatives of F + :type F2: np.array + :param F3: vector of third derivatives of F + :type F3: np.array + :param lower,upper: boundaries of the input domain + :type lower,upper: floats + """ + assert self.input_dim == 1 + def L(x,i): + return(5*np.sqrt(5)/self.lengthscale**3*F[i](x) + 15./self.lengthscale**2*F1[i](x)+ 3*np.sqrt(5)/self.lengthscale*F2[i](x) + F3[i](x)) + n = F.shape[0] + G = np.zeros((n,n)) + for i in range(n): + for j in range(i,n): + G[i,j] = G[j,i] = integrate.quad(lambda x : L(x,i)*L(x,j),lower,upper)[0] + G_coef = 3.*self.lengthscale**5/(400*np.sqrt(5)) + Flower = np.array([f(lower) for f in F])[:,None] + F1lower = np.array([f(lower) for f in F1])[:,None] + F2lower = np.array([f(lower) for f in F2])[:,None] + orig = 9./8*np.dot(Flower,Flower.T) + 9.*self.lengthscale**4/200*np.dot(F2lower,F2lower.T) + orig2 = 3./5*self.lengthscale**2 * ( np.dot(F1lower,F1lower.T) + 1./8*np.dot(Flower,F2lower.T) + 1./8*np.dot(F2lower,Flower.T)) + return(1./self.variance* (G_coef*G + orig + orig2)) + + +class ExpQuad(Stationary): + """ + The Exponentiated quadratic covariance function. + + .. math:: + + k(r) = \sigma^2 (1 + \sqrt{5} r + \\frac53 r^2) \exp(- \sqrt{5} r) + + notes:: + - Yes, this is exactly the same as the RBF covariance function, but the + RBF implementation also has some features for doing variational kernels + (the psi-statistics). + + """ + def __init__(self, input_dim, variance=1., lengthscale=None, ARD=False, active_dims=None, name='ExpQuad'): + super(ExpQuad, self).__init__(input_dim, variance, lengthscale, ARD, active_dims, name) + + def K_of_r(self, r): + return self.variance * np.exp(-0.5 * r**2) + + def dK_dr(self, r): + return -r*self.K_of_r(r) + +class Cosine(Stationary): + def __init__(self, input_dim, variance=1., lengthscale=None, ARD=False, active_dims=None, name='Cosine'): + super(Cosine, self).__init__(input_dim, variance, lengthscale, ARD, active_dims, name) + + def K_of_r(self, r): + return self.variance * np.cos(r) + + def dK_dr(self, r): + return -self.variance * np.sin(r) + + +class RatQuad(Stationary): + """ + Rational Quadratic Kernel + + .. math:: + + k(r) = \sigma^2 \\bigg( 1 + \\frac{r^2}{2} \\bigg)^{- \\alpha} + + """ + + + def __init__(self, input_dim, variance=1., lengthscale=None, power=2., ARD=False, active_dims=None, name='RatQuad'): + super(RatQuad, self).__init__(input_dim, variance, lengthscale, ARD, active_dims, name) + self.power = Param('power', power, Logexp()) + self.link_parameters(self.power) + + def K_of_r(self, r): + r2 = np.power(r, 2.) + return self.variance*np.power(1. + r2/2., -self.power) + + def dK_dr(self, r): + r2 = np.power(r, 2.) + return -self.variance*self.power*r*np.power(1. + r2/2., - self.power - 1.) + + def update_gradients_full(self, dL_dK, X, X2=None): + super(RatQuad, self).update_gradients_full(dL_dK, X, X2) + r = self._scaled_dist(X, X2) + r2 = np.power(r, 2.) + dK_dpow = -self.variance * np.power(2., self.power) * np.power(r2 + 2., -self.power) * np.log(0.5*(r2+2.)) + grad = np.sum(dL_dK*dK_dpow) + self.power.gradient = grad + + def update_gradients_diag(self, dL_dKdiag, X): + super(RatQuad, self).update_gradients_diag(dL_dKdiag, X) + self.power.gradient = 0. + + diff --git a/GPy/kern/_src/symbolic.py b/GPy/kern/_src/symbolic.py new file mode 100644 index 00000000..006af9dc --- /dev/null +++ b/GPy/kern/_src/symbolic.py @@ -0,0 +1,75 @@ +# Check Matthew Rocklin's blog post. +import sympy as sym +import numpy as np +from kern import Kern +from ...core.symbolic import Symbolic_core + + +class Symbolic(Kern, Symbolic_core): + """ + """ + def __init__(self, input_dim, k=None, output_dim=1, name='symbolic', parameters=None, active_dims=None, operators=None, func_modules=[]): + + if k is None: + raise ValueError, "You must provide an argument for the covariance function." + + Kern.__init__(self, input_dim, active_dims, name=name) + kdiag = k + self.cacheable = ['X', 'Z'] + Symbolic_core.__init__(self, {'k':k,'kdiag':kdiag}, cacheable=self.cacheable, derivatives = ['X', 'theta'], parameters=parameters, func_modules=func_modules) + self.output_dim = output_dim + + def __add__(self,other): + return spkern(self._sym_k+other._sym_k) + + def _set_expressions(self, expressions): + """This method is overwritten because we need to modify kdiag by substituting z for x. We do this by calling the parent expression method to extract variables from expressions, then subsitute the z variables that are present with x.""" + Symbolic_core._set_expressions(self, expressions) + Symbolic_core._set_variables(self, self.cacheable) + # Substitute z with x to obtain kdiag. + for x, z in zip(self.variables['X'], self.variables['Z']): + expressions['kdiag'] = expressions['kdiag'].subs(z, x) + Symbolic_core._set_expressions(self, expressions) + + + def K(self,X,X2=None): + if X2 is None: + return self.eval_function('k', X=X, Z=X) + else: + return self.eval_function('k', X=X, Z=X2) + + + def Kdiag(self,X): + d = self.eval_function('kdiag', X=X) + if not d.shape[0] == X.shape[0]: + d = np.tile(d, (X.shape[0], 1)) + return d + + + def gradients_X(self, dL_dK, X, X2=None): + #if self._X is None or X.base is not self._X.base or X2 is not None: + g = self.eval_gradients_X('k', dL_dK, X=X, Z=X2) + if X2 is None: + g *= 2 + return g + + def gradients_X_diag(self, dL_dK, X): + return self.eval_gradients_X('kdiag', dL_dK, X=X) + + def update_gradients_full(self, dL_dK, X, X2=None): + # Need to extract parameters to local variables first + if X2 is None: + # need to double this inside ... + gradients = self.eval_update_gradients('k', dL_dK, X=X) + else: + gradients = self.eval_update_gradients('k', dL_dK, X=X, Z=X2) + + for name, val in gradients: + setattr(getattr(self, name), 'gradient', val) + + + def update_gradients_diag(self, dL_dKdiag, X): + gradients = self.eval_update_gradients('kdiag', dL_dKdiag, X) + for name, val in gradients: + setattr(getattr(self, name), 'gradient', val) + diff --git a/GPy/kern/parts/sympy_helpers.cpp b/GPy/kern/_src/sympy_helpers.cpp similarity index 100% rename from GPy/kern/parts/sympy_helpers.cpp rename to GPy/kern/_src/sympy_helpers.cpp diff --git a/GPy/kern/parts/sympy_helpers.h b/GPy/kern/_src/sympy_helpers.h similarity index 100% rename from GPy/kern/parts/sympy_helpers.h rename to GPy/kern/_src/sympy_helpers.h diff --git a/GPy/kern/parts/ODE_1.py b/GPy/kern/_src/todo/ODE_1.py similarity index 99% rename from GPy/kern/parts/ODE_1.py rename to GPy/kern/_src/todo/ODE_1.py index 8c5f123f..fe8f6610 100644 --- a/GPy/kern/parts/ODE_1.py +++ b/GPy/kern/_src/todo/ODE_1.py @@ -90,7 +90,7 @@ class ODE_1(Kernpart): np.add(self.varianceU*self.varianceY*(k1+k2+k3), target, target) - def dK_dtheta(self, dL_dK, X, X2, target): + def _param_grad_helper(self, dL_dK, X, X2, target): """derivative of the covariance matrix with respect to the parameters.""" if X2 is None: X2 = X dist = np.abs(X - X2.T) diff --git a/GPy/kern/parts/eq_ode1.py b/GPy/kern/_src/todo/eq_ode1.py similarity index 99% rename from GPy/kern/parts/eq_ode1.py rename to GPy/kern/_src/todo/eq_ode1.py index 70e3c49d..bf0ca7e4 100644 --- a/GPy/kern/parts/eq_ode1.py +++ b/GPy/kern/_src/todo/eq_ode1.py @@ -124,7 +124,7 @@ class Eq_ode1(Kernpart): #target += np.diag(self.B)[np.asarray(index,dtype=np.int).flatten()] pass - def dK_dtheta(self,dL_dK,X,X2,target): + def _param_grad_helper(self,dL_dK,X,X2,target): # First extract times and indices. self._extract_t_indices(X, X2, dL_dK=dL_dK) @@ -193,7 +193,7 @@ class Eq_ode1(Kernpart): def dKdiag_dtheta(self,dL_dKdiag,index,target): pass - def dK_dX(self,dL_dK,X,X2,target): + def gradients_X(self,dL_dK,X,X2,target): pass def _extract_t_indices(self, X, X2=None, dL_dK=None): diff --git a/GPy/kern/parts/finite_dimensional.py b/GPy/kern/_src/todo/finite_dimensional.py similarity index 98% rename from GPy/kern/parts/finite_dimensional.py rename to GPy/kern/_src/todo/finite_dimensional.py index 6cc2325f..9e54fb34 100644 --- a/GPy/kern/parts/finite_dimensional.py +++ b/GPy/kern/_src/todo/finite_dimensional.py @@ -50,7 +50,7 @@ class FiniteDimensional(Kernpart): def Kdiag(self,X,target): product = np.diag(self.K(X, X)) np.add(target,product,target) - def dK_dtheta(self,X,X2,target): + def _param_grad_helper(self,X,X2,target): """Return shape is NxMx(Ntheta)""" if X2 is None: X2 = X FX = np.column_stack([f(X) for f in self.F]) diff --git a/GPy/kern/parts/fixed.py b/GPy/kern/_src/todo/fixed.py similarity index 90% rename from GPy/kern/parts/fixed.py rename to GPy/kern/_src/todo/fixed.py index 67baea91..680f0b14 100644 --- a/GPy/kern/parts/fixed.py +++ b/GPy/kern/_src/todo/fixed.py @@ -31,10 +31,10 @@ class Fixed(Kernpart): def K(self, X, X2, target): target += self.variance * self.fixed_K - def dK_dtheta(self, partial, X, X2, target): + def _param_grad_helper(self, partial, X, X2, target): target += (partial * self.fixed_K).sum() - def dK_dX(self, partial, X, X2, target): + def gradients_X(self, partial, X, X2, target): pass def dKdiag_dX(self, partial, X, target): diff --git a/GPy/kern/parts/gibbs.py b/GPy/kern/_src/todo/gibbs.py similarity index 96% rename from GPy/kern/parts/gibbs.py rename to GPy/kern/_src/todo/gibbs.py index f47144e1..68241245 100644 --- a/GPy/kern/parts/gibbs.py +++ b/GPy/kern/_src/todo/gibbs.py @@ -85,7 +85,7 @@ class Gibbs(Kernpart): """Compute the diagonal of the covariance matrix for X.""" np.add(target, self.variance, target) - def dK_dtheta(self, dL_dK, X, X2, target): + def _param_grad_helper(self, dL_dK, X, X2, target): """Derivative of the covariance with respect to the parameters.""" self._K_computations(X, X2) self._dK_computations(dL_dK) @@ -97,7 +97,7 @@ class Gibbs(Kernpart): target+= np.hstack([(dL_dK*self._K_dvar).sum(), gmapping]) - def dK_dX(self, dL_dK, X, X2, target): + def gradients_X(self, dL_dK, X, X2, target): """Derivative of the covariance matrix with respect to X.""" # First account for gradients arising from presence of X in exponent. self._K_computations(X, X2) @@ -105,8 +105,8 @@ class Gibbs(Kernpart): _K_dist = 2*(X[:, None, :] - X[None, :, :]) else: _K_dist = X[:, None, :] - X2[None, :, :] # don't cache this in _K_co - dK_dX = (-2.*self.variance)*np.transpose((self._K_dvar/self._w2)[:, :, None]*_K_dist, (1, 0, 2)) - target += np.sum(dK_dX*dL_dK.T[:, :, None], 0) + gradients_X = (-2.*self.variance)*np.transpose((self._K_dvar/self._w2)[:, :, None]*_K_dist, (1, 0, 2)) + target += np.sum(gradients_X*dL_dK.T[:, :, None], 0) # Now account for gradients arising from presence of X in lengthscale. self._dK_computations(dL_dK) if X2 is None: diff --git a/GPy/kern/parts/hetero.py b/GPy/kern/_src/todo/hetero.py similarity index 97% rename from GPy/kern/parts/hetero.py rename to GPy/kern/_src/todo/hetero.py index c716eaad..8aa9feaa 100644 --- a/GPy/kern/parts/hetero.py +++ b/GPy/kern/_src/todo/hetero.py @@ -79,7 +79,7 @@ class Hetero(Kernpart): """Helper function for computing the diagonal elements of the covariance.""" return self.mapping.f(X).flatten()**2 - def dK_dtheta(self, dL_dK, X, X2, target): + def _param_grad_helper(self, dL_dK, X, X2, target): """Derivative of the covariance with respect to the parameters.""" if (X2 is None) or (X2 is X): dL_dKdiag = dL_dK.flat[::dL_dK.shape[0]+1] @@ -89,7 +89,7 @@ class Hetero(Kernpart): """Gradient of diagonal of covariance with respect to parameters.""" target += 2.*self.mapping.df_dtheta(dL_dKdiag[:, None]*self.mapping.f(X), X) - def dK_dX(self, dL_dK, X, X2, target): + def gradients_X(self, dL_dK, X, X2, target): """Derivative of the covariance matrix with respect to X.""" if X2==None or X2 is X: dL_dKdiag = dL_dK.flat[::dL_dK.shape[0]+1] diff --git a/GPy/kern/parts/odekern1.c b/GPy/kern/_src/todo/odekern1.c similarity index 100% rename from GPy/kern/parts/odekern1.c rename to GPy/kern/_src/todo/odekern1.c diff --git a/GPy/kern/parts/poly.py b/GPy/kern/_src/todo/poly.py similarity index 98% rename from GPy/kern/parts/poly.py rename to GPy/kern/_src/todo/poly.py index 98c520f0..0deb11f4 100644 --- a/GPy/kern/parts/poly.py +++ b/GPy/kern/_src/todo/poly.py @@ -86,7 +86,7 @@ class POLY(Kernpart): self._K_diag_computations(X) target+= self.variance*self._K_diag_dvar - def dK_dtheta(self, dL_dK, X, X2, target): + def _param_grad_helper(self, dL_dK, X, X2, target): """Derivative of the covariance with respect to the parameters.""" self._K_computations(X, X2) base = self.variance*self.degree*self._K_poly_arg**(self.degree-1) @@ -99,7 +99,7 @@ class POLY(Kernpart): target[2] += base_cov_grad.sum() - def dK_dX(self, dL_dK, X, X2, target): + def gradients_X(self, dL_dK, X, X2, target): """Derivative of the covariance matrix with respect to X""" self._K_computations(X, X2) arg = self._K_poly_arg diff --git a/GPy/kern/parts/rbf_inv.py b/GPy/kern/_src/todo/rbf_inv.py similarity index 86% rename from GPy/kern/parts/rbf_inv.py rename to GPy/kern/_src/todo/rbf_inv.py index 1cc05aaa..8405ae84 100644 --- a/GPy/kern/parts/rbf_inv.py +++ b/GPy/kern/_src/todo/rbf_inv.py @@ -4,11 +4,9 @@ from rbf import RBF import numpy as np -import hashlib from scipy import weave from ...util.linalg import tdot -from ...util.config import * - +from ...core.parameterization import Param class RBFInv(RBF): """ @@ -34,9 +32,12 @@ class RBFInv(RBF): .. Note: this object implements both the ARD and 'spherical' version of the function """ - def __init__(self, input_dim, variance=1., inv_lengthscale=None, ARD=False): - self.input_dim = input_dim - self.name = 'rbf_inv' + def __init__(self, input_dim, variance=1., inv_lengthscale=None, ARD=False, name='inverse rbf'): + #self.input_dim = input_dim + #self.name = 'rbf_inv' + if inv_lengthscale is not None: lengthscale = 1./np.array(inv_lengthscale) + else: lengthscale = None + super(RBFInv, self).__init__(input_dim, variance=variance, lengthscale=lengthscale, ARD=ARD, name=name) self.ARD = ARD if not ARD: self.num_params = 2 @@ -52,55 +53,51 @@ class RBFInv(RBF): assert inv_lengthscale.size == self.input_dim, "bad number of lengthscales" else: inv_lengthscale = np.ones(self.input_dim) - - self._set_params(np.hstack((variance, inv_lengthscale.flatten()))) + + self.variance = Param('variance', variance) + self.inv_lengthscale = Param('sensitivity', inv_lengthscale) + self.inv_lengthscale.add_observer(self, self.update_inv_lengthscale) + self.remove_parameter(self.lengthscale) + self.add_parameters(self.variance, self.inv_lengthscale) + #self._set_params(np.hstack((variance, inv_lengthscale.flatten()))) # initialize cache self._Z, self._mu, self._S = np.empty(shape=(3, 1)) self._X, self._X2, self._params = np.empty(shape=(3, 1)) # a set of optional args to pass to weave - weave_options_openmp = {'headers' : [''], - 'extra_compile_args': ['-fopenmp -O3'], - 'extra_link_args' : ['-lgomp'], - 'libraries': ['gomp']} - weave_options_noopenmp = {'extra_compile_args': ['-O3']} + self.weave_options = {'headers' : [''], + 'extra_compile_args': ['-fopenmp -O3'], # -march=native'], + 'extra_link_args' : ['-lgomp']} - if config.getboolean('parallel', 'openmp'): - self.weave_options = weave_options_openmp - self.weave_support_code = """ - #include - #include - """ - else: - self.weave_options = weave_options_noopenmp - self.weave_support_code = """ - #include - """ - def _get_params(self): - return np.hstack((self.variance, self.inv_lengthscale)) - def _set_params(self, x): - assert x.size == (self.num_params) - self.variance = x[0] - self.inv_lengthscale = x[1:] +# def _get_params(self): +# return np.hstack((self.variance, self.inv_lengthscale)) + + def update_inv_lengthscale(self, il): self.inv_lengthscale2 = np.square(self.inv_lengthscale) # TODO: We can rewrite everything with inv_lengthscale and never need to do the below self.lengthscale = 1. / self.inv_lengthscale self.lengthscale2 = np.square(self.lengthscale) + + #def _set_params(self, x): + def parameters_changed(self): + #assert x.size == (self.num_params) + #self.variance = x[0] + #self.inv_lengthscale = x[1:] # reset cached results self._X, self._X2, self._params = np.empty(shape=(3, 1)) self._Z, self._mu, self._S = np.empty(shape=(3, 1)) # cached versions of Z,mu,S - def _get_param_names(self): - if self.num_params == 2: - return ['variance', 'inv_lengthscale'] - else: - return ['variance'] + ['inv_lengthscale%i' % i for i in range(self.inv_lengthscale.size)] +# def _get_param_names(self): +# if self.num_params == 2: +# return ['variance', 'inv_lengthscale'] +# else: +# return ['variance'] + ['inv_lengthscale%i' % i for i in range(self.inv_lengthscale.size)] # TODO: Rewrite computations so that lengthscale is not needed (but only inv. lengthscale) - def dK_dtheta(self, dL_dK, X, X2, target): + def _param_grad_helper(self, dL_dK, X, X2, target): self._K_computations(X, X2) target[0] += np.sum(self._K_dvar * dL_dK) if self.ARD: @@ -123,7 +120,7 @@ class RBFInv(RBF): target(q+1) += var_len3(q)*tmp*(-len2(q)); } """ - num_data, num_inducing, input_dim = int(X.shape[0]), int(X.shape[0]), int(self.input_dim) + num_data, num_inducing, input_dim = X.shape[0], X.shape[0], self.input_dim weave.inline(code, arg_names=['num_data', 'num_inducing', 'input_dim', 'X', 'X2', 'target', 'dvardLdK', 'var_len3', 'len2'], type_converters=weave.converters.blitz, **self.weave_options) else: code = """ @@ -139,20 +136,20 @@ class RBFInv(RBF): target(q+1) += var_len3(q)*tmp*(-len2(q)); } """ - num_data, num_inducing, input_dim = int(X.shape[0]), int(X2.shape[0]), int(self.input_dim) + num_data, num_inducing, input_dim = X.shape[0], X2.shape[0], self.input_dim # [np.add(target[1+q:2+q],var_len3[q]*np.sum(dvardLdK*np.square(X[:,q][:,None]-X2[:,q][None,:])),target[1+q:2+q]) for q in range(self.input_dim)] weave.inline(code, arg_names=['num_data', 'num_inducing', 'input_dim', 'X', 'X2', 'target', 'dvardLdK', 'var_len3', 'len2'], type_converters=weave.converters.blitz, **self.weave_options) else: target[1] += (self.variance / self.lengthscale) * np.sum(self._K_dvar * self._K_dist2 * dL_dK) * (-self.lengthscale2) - def dK_dX(self, dL_dK, X, X2, target): + def gradients_X(self, dL_dK, X, X2, target): self._K_computations(X, X2) - if X2 is None: + if X2 is None: _K_dist = 2*(X[:, None, :] - X[None, :, :]) else: _K_dist = X[:, None, :] - X2[None, :, :] # don't cache this in _K_computations because it is high memory. If this function is being called, chances are we're not in the high memory arena. - dK_dX = (-self.variance * self.inv_lengthscale2) * np.transpose(self._K_dvar[:, :, np.newaxis] * _K_dist, (1, 0, 2)) - target += np.sum(dK_dX * dL_dK.T[:, :, None], 0) + gradients_X = (-self.variance * self.inv_lengthscale2) * np.transpose(self._K_dvar[:, :, np.newaxis] * _K_dist, (1, 0, 2)) + target += np.sum(gradients_X * dL_dK.T[:, :, None], 0) def dKdiag_dX(self, dL_dKdiag, X, target): pass @@ -277,8 +274,8 @@ class RBFInv(RBF): self._Z, self._mu, self._S = Z, mu, S def weave_psi2(self, mu, Zhat): - N, input_dim = int(mu.shape[0]), int(mu.shape[1]) - num_inducing = int(Zhat.shape[0]) + N, input_dim = mu.shape + num_inducing = Zhat.shape[0] mudist = np.empty((N, num_inducing, num_inducing, input_dim)) mudist_sq = np.empty((N, num_inducing, num_inducing, input_dim)) @@ -293,16 +290,10 @@ class RBFInv(RBF): inv_lengthscale2 = self.inv_lengthscale2 else: inv_lengthscale2 = np.ones(input_dim) * self.inv_lengthscale2 - - if config.getboolean('parallel', 'openmp'): - pragma_string = '#pragma omp parallel for private(tmp)' - else: - pragma_string = '' - code = """ double tmp; - %s + #pragma omp parallel for private(tmp) for (int n=0; n + #include + """ + weave.inline(code, support_code=support_code, libraries=['gomp'], arg_names=['N', 'num_inducing', 'input_dim', 'mu', 'Zhat', 'mudist_sq', 'mudist', 'inv_lengthscale2', '_psi2_denom', 'psi2_Zdist_sq', 'psi2_exponent', 'half_log_psi2_denom', 'psi2', 'variance_sq'], type_converters=weave.converters.blitz, **self.weave_options) diff --git a/GPy/kern/parts/spline.py b/GPy/kern/_src/todo/spline.py similarity index 74% rename from GPy/kern/parts/spline.py rename to GPy/kern/_src/todo/spline.py index e675420c..3e57b8a9 100644 --- a/GPy/kern/parts/spline.py +++ b/GPy/kern/_src/todo/spline.py @@ -4,7 +4,8 @@ from kernpart import Kernpart import numpy as np -import hashlib +from ...core.parameterization import Param + def theta(x): """Heaviside step function""" return np.where(x>=0.,1.,0.) @@ -25,16 +26,18 @@ class Spline(Kernpart): assert self.input_dim==1 self.num_params = 1 self.name = 'spline' - self._set_params(np.squeeze(variance)) - - def _get_params(self): - return self.variance - - def _set_params(self,x): - self.variance = x - - def _get_param_names(self): - return ['variance'] + self.variance = Param('variance', variance) + self.lengthscale = Param('lengthscale', lengthscale) + self.add_parameters(self.variance, self.lengthscale) + +# def _get_params(self): +# return self.variance +# +# def _set_params(self,x): +# self.variance = x +# +# def _get_param_names(self): +# return ['variance'] def K(self,X,X2,target): assert np.all(X>0), "Spline covariance is for +ve domain only. TODO: symmetrise" @@ -47,7 +50,7 @@ class Spline(Kernpart): def Kdiag(self,X,target): target += self.variance*X.flatten()**3/3. - def dK_dtheta(self,X,X2,target): + def _param_grad_helper(self,X,X2,target): target += 0.5*(t*s**2) - s**3/6. + (s_t)**3*theta(s_t)/6. def dKdiag_dtheta(self,X,target): diff --git a/GPy/kern/parts/symmetric.py b/GPy/kern/_src/todo/symmetric.py similarity index 72% rename from GPy/kern/parts/symmetric.py rename to GPy/kern/_src/todo/symmetric.py index d836763d..1a3e54b1 100644 --- a/GPy/kern/parts/symmetric.py +++ b/GPy/kern/_src/todo/symmetric.py @@ -24,19 +24,8 @@ class Symmetric(Kernpart): self.num_params = k.num_params self.name = k.name + '_symm' self.k = k - self._set_params(k._get_params()) - - def _get_params(self): - """return the value of the parameters.""" - return self.k._get_params() - - def _set_params(self,x): - """set the value of the parameters.""" - self.k._set_params(x) - - def _get_param_names(self): - """return parameter names.""" - return self.k._get_param_names() + self.add_parameter(k) + #self._set_params(k._get_params()) def K(self,X,X2,target): """Compute the covariance matrix between X and X2.""" @@ -51,7 +40,7 @@ class Symmetric(Kernpart): self.k.K(X,AX2,target) self.k.K(AX,AX2,target) - def dK_dtheta(self,dL_dK,X,X2,target): + def _param_grad_helper(self,dL_dK,X,X2,target): """derivative of the covariance matrix with respect to the parameters.""" AX = np.dot(X,self.transform) if X2 is None: @@ -59,13 +48,13 @@ class Symmetric(Kernpart): AX2 = AX else: AX2 = np.dot(X2, self.transform) - self.k.dK_dtheta(dL_dK,X,X2,target) - self.k.dK_dtheta(dL_dK,AX,X2,target) - self.k.dK_dtheta(dL_dK,X,AX2,target) - self.k.dK_dtheta(dL_dK,AX,AX2,target) + self.k._param_grad_helper(dL_dK,X,X2,target) + self.k._param_grad_helper(dL_dK,AX,X2,target) + self.k._param_grad_helper(dL_dK,X,AX2,target) + self.k._param_grad_helper(dL_dK,AX,AX2,target) - def dK_dX(self,dL_dK,X,X2,target): + def gradients_X(self,dL_dK,X,X2,target): """derivative of the covariance matrix with respect to X.""" AX = np.dot(X,self.transform) if X2 is None: @@ -73,10 +62,10 @@ class Symmetric(Kernpart): ZX2 = AX else: AX2 = np.dot(X2, self.transform) - self.k.dK_dX(dL_dK, X, X2, target) - self.k.dK_dX(dL_dK, AX, X2, target) - self.k.dK_dX(dL_dK, X, AX2, target) - self.k.dK_dX(dL_dK, AX ,AX2, target) + self.k.gradients_X(dL_dK, X, X2, target) + self.k.gradients_X(dL_dK, AX, X2, target) + self.k.gradients_X(dL_dK, X, AX2, target) + self.k.gradients_X(dL_dK, AX ,AX2, target) def Kdiag(self,X,target): """Compute the diagonal of the covariance matrix associated to X.""" diff --git a/GPy/kern/_src/trunclinear.py b/GPy/kern/_src/trunclinear.py new file mode 100644 index 00000000..4ebd51b6 --- /dev/null +++ b/GPy/kern/_src/trunclinear.py @@ -0,0 +1,204 @@ +# Copyright (c) 2012, GPy authors (see AUTHORS.txt). +# Licensed under the BSD 3-clause license (see LICENSE.txt) + + +import numpy as np +from kern import Kern +from ...core.parameterization import Param +from ...core.parameterization.transformations import Logexp +from ...util.caching import Cache_this +from ...util.config import * + +class TruncLinear(Kern): + """ + Truncated Linear kernel + + .. math:: + + k(x,y) = \sum_{i=1}^input_dim \sigma^2_i \max(0, x_iy_i - \simga_q) + + :param input_dim: the number of input dimensions + :type input_dim: int + :param variances: the vector of variances :math:`\sigma^2_i` + :type variances: array or list of the appropriate size (or float if there + is only one variance parameter) + :param ARD: Auto Relevance Determination. If False, the kernel has only one + variance parameter \sigma^2, otherwise there is one variance + parameter per dimension. + :type ARD: Boolean + :rtype: kernel object + + """ + + def __init__(self, input_dim, variances=None, delta=None, ARD=False, active_dims=None, name='linear'): + super(TruncLinear, self).__init__(input_dim, active_dims, name) + self.ARD = ARD + if not ARD: + if variances is not None: + variances = np.asarray(variances) + delta = np.asarray(delta) + assert variances.size == 1, "Only one variance needed for non-ARD kernel" + else: + variances = np.ones(1) + delta = np.zeros(1) + else: + if variances is not None: + variances = np.asarray(variances) + delta = np.asarray(delta) + assert variances.size == self.input_dim, "bad number of variances, need one ARD variance per input_dim" + else: + variances = np.ones(self.input_dim) + delta = np.zeros(self.input_dim) + + self.variances = Param('variances', variances, Logexp()) + self.delta = Param('delta', delta) + self.add_parameter(self.variances) + self.add_parameter(self.delta) + + @Cache_this(limit=2) + def K(self, X, X2=None): + XX = self.variances*self._product(X, X2) + return XX.sum(axis=-1) + + @Cache_this(limit=2) + def _product(self, X, X2=None): + if X2 is None: + X2 = X + XX = np.einsum('nq,mq->nmq',X-self.delta,X2-self.delta) + XX[XX<0] = 0 + return XX + + def Kdiag(self, X): + return (self.variances*np.square(X-self.delta)).sum(axis=-1) + + def update_gradients_full(self, dL_dK, X, X2=None): + dK_dvar = self._product(X, X2) + if X2 is None: + X2=X + dK_ddelta = self.variances*(2*self.delta-X[:,None,:]-X2[None,:,:])*(dK_dvar>0) + if self.ARD: + self.variances.gradient[:] = np.einsum('nmq,nm->q',dK_dvar,dL_dK) + self.delta.gradient[:] = np.einsum('nmq,nm->q',dK_ddelta,dL_dK) + else: + self.variances.gradient[:] = np.einsum('nmq,nm->',dK_dvar,dL_dK) + self.delta.gradient[:] = np.einsum('nmq,nm->',dK_ddelta,dL_dK) + + def update_gradients_diag(self, dL_dKdiag, X): + if self.ARD: + self.variances.gradient[:] = np.einsum('nq,n->q',np.square(X-self.delta),dL_dKdiag) + self.delta.gradient[:] = np.einsum('nq,n->q',2*self.variances*(self.delta-X),dL_dKdiag) + else: + self.variances.gradient[:] = np.einsum('nq,n->',np.square(X-self.delta),dL_dKdiag) + self.delta.gradient[:] = np.einsum('nq,n->',2*self.variances*(self.delta-X),dL_dKdiag) + + def gradients_X(self, dL_dK, X, X2=None): + XX = self._product(X, X2) + if X2 is None: + Xp = (self.variances*(X-self.delta))*(XX>0) + else: + Xp = (self.variances*(X2-self.delta))*(XX>0) + if X2 is None: + return np.einsum('nmq,nm->nq',Xp,dL_dK)+np.einsum('mnq,nm->mq',Xp,dL_dK) + else: + return np.einsum('nmq,nm->nq',Xp,dL_dK) + + def gradients_X_diag(self, dL_dKdiag, X): + return 2.*self.variances*dL_dKdiag[:,None]*(X-self.delta) + + def input_sensitivity(self): + return np.ones(self.input_dim) * self.variances + +class TruncLinear_inf(Kern): + """ + Truncated Linear kernel + + .. math:: + + k(x,y) = \sum_{i=1}^input_dim \sigma^2_i \max(0, x_iy_i - \simga_q) + + :param input_dim: the number of input dimensions + :type input_dim: int + :param variances: the vector of variances :math:`\sigma^2_i` + :type variances: array or list of the appropriate size (or float if there + is only one variance parameter) + :param ARD: Auto Relevance Determination. If False, the kernel has only one + variance parameter \sigma^2, otherwise there is one variance + parameter per dimension. + :type ARD: Boolean + :rtype: kernel object + + """ + + def __init__(self, input_dim, interval, variances=None, ARD=False, active_dims=None, name='linear'): + super(TruncLinear_inf, self).__init__(input_dim, active_dims, name) + self.interval = interval + self.ARD = ARD + if not ARD: + if variances is not None: + variances = np.asarray(variances) + assert variances.size == 1, "Only one variance needed for non-ARD kernel" + else: + variances = np.ones(1) + else: + if variances is not None: + variances = np.asarray(variances) + assert variances.size == self.input_dim, "bad number of variances, need one ARD variance per input_dim" + else: + variances = np.ones(self.input_dim) + + self.variances = Param('variances', variances, Logexp()) + self.add_parameter(self.variances) + + +# @Cache_this(limit=2) + def K(self, X, X2=None): + tmp = self._product(X, X2) + return (self.variances*tmp).sum(axis=-1) + +# @Cache_this(limit=2) + def _product(self, X, X2=None): + if X2 is None: + X2 = X + X_X2 = X[:,None,:]-X2[None,:,:] + tmp = np.abs(X_X2**3)/6+np.einsum('nq,mq->nmq',X,X2)*(self.interval[1]-self.interval[0]) \ + -(X[:,None,:]+X2[None,:,:])*(self.interval[1]*self.interval[1]-self.interval[0]*self.interval[0])/2+(self.interval[1]**3-self.interval[0]**3)/3. + return tmp + + def Kdiag(self, X): + tmp = np.square(X)*(self.interval[1]-self.interval[0]) \ + -X*(self.interval[1]*self.interval[1]-self.interval[0]*self.interval[0])+(self.interval[1]**3-self.interval[0]**3)/3 + return (self.variances*tmp).sum(axis=-1) + + def update_gradients_full(self, dL_dK, X, X2=None): + dK_dvar = self._product(X, X2) + if self.ARD: + self.variances.gradient[:] = np.einsum('nmq,nm->q',dK_dvar,dL_dK) + else: + self.variances.gradient[:] = np.einsum('nmq,nm->',dK_dvar,dL_dK) + + def update_gradients_diag(self, dL_dKdiag, X): + tmp = np.square(X)*(self.interval[1]-self.interval[0]) \ + -X*(self.interval[1]*self.interval[1]-self.interval[0]*self.interval[0])+(self.interval[1]**3-self.interval[0]**3)/3 + if self.ARD: + self.variances.gradient[:] = np.einsum('nq,n->q',tmp,dL_dKdiag) + else: + self.variances.gradient[:] = np.einsum('nq,n->',tmp,dL_dKdiag) + + def gradients_X(self, dL_dK, X, X2=None): + XX = self._product(X, X2) + if X2 is None: + Xp = (self.variances*(X-self.delta))*(XX>0) + else: + Xp = (self.variances*(X2-self.delta))*(XX>0) + if X2 is None: + return np.einsum('nmq,nm->nq',Xp,dL_dK)+np.einsum('mnq,nm->mq',Xp,dL_dK) + else: + return np.einsum('nmq,nm->nq',Xp,dL_dK) + + def gradients_X_diag(self, dL_dKdiag, X): + return 2.*self.variances*dL_dKdiag[:,None]*(X-self.delta) + + def input_sensitivity(self): + return np.ones(self.input_dim) * self.variances + + diff --git a/GPy/kern/constructors.py b/GPy/kern/constructors.py deleted file mode 100644 index 05eaa028..00000000 --- a/GPy/kern/constructors.py +++ /dev/null @@ -1,602 +0,0 @@ -# Copyright (c) 2012, GPy authors (see AUTHORS.txt). -# Licensed under the BSD 3-clause license (see LICENSE.txt) - -import numpy as np -from kern import kern -import parts - - -def rbf_inv(input_dim,variance=1., inv_lengthscale=None,ARD=False): - """ - Construct an RBF kernel - - :param input_dim: dimensionality of the kernel, obligatory - :type input_dim: int - :param variance: the variance of the kernel - :type variance: float - :param lengthscale: the lengthscale of the kernel - :type lengthscale: float - :param ARD: Auto Relevance Determination (one lengthscale per dimension) - :type ARD: Boolean - - """ - part = parts.rbf_inv.RBFInv(input_dim,variance,inv_lengthscale,ARD) - return kern(input_dim, [part]) - -def rbf(input_dim,variance=1., lengthscale=None,ARD=False): - """ - Construct an RBF kernel - - :param input_dim: dimensionality of the kernel, obligatory - :type input_dim: int - :param variance: the variance of the kernel - :type variance: float - :param lengthscale: the lengthscale of the kernel - :type lengthscale: float - :param ARD: Auto Relevance Determination (one lengthscale per dimension) - :type ARD: Boolean - - """ - part = parts.rbf.RBF(input_dim,variance,lengthscale,ARD) - return kern(input_dim, [part]) - -def linear(input_dim,variances=None,ARD=False): - """ - Construct a linear kernel. - - :param input_dim: dimensionality of the kernel, obligatory - :type input_dim: int - :param variances: - :type variances: np.ndarray - :param ARD: Auto Relevance Determination (one lengthscale per dimension) - :type ARD: Boolean - - """ - part = parts.linear.Linear(input_dim,variances,ARD) - return kern(input_dim, [part]) - -def mlp(input_dim,variance=1., weight_variance=None,bias_variance=100.,ARD=False): - """ - Construct an MLP kernel - - :param input_dim: dimensionality of the kernel, obligatory - :type input_dim: int - :param variance: the variance of the kernel - :type variance: float - :param weight_scale: the lengthscale of the kernel - :type weight_scale: vector of weight variances for input weights in neural network (length 1 if kernel is isotropic) - :param bias_variance: the variance of the biases in the neural network. - :type bias_variance: float - :param ARD: Auto Relevance Determination (allows for ARD version of covariance) - :type ARD: Boolean - - """ - part = parts.mlp.MLP(input_dim,variance,weight_variance,bias_variance,ARD) - return kern(input_dim, [part]) - -def gibbs(input_dim,variance=1., mapping=None): - """ - - Gibbs and MacKay non-stationary covariance function. - - .. math:: - - r = \\sqrt{((x_i - x_j)'*(x_i - x_j))} - - k(x_i, x_j) = \\sigma^2*Z*exp(-r^2/(l(x)*l(x) + l(x')*l(x'))) - - Z = \\sqrt{2*l(x)*l(x')/(l(x)*l(x) + l(x')*l(x')} - - Where :math:`l(x)` is a function giving the length scale as a function of space. - - This is the non stationary kernel proposed by Mark Gibbs in his 1997 - thesis. It is similar to an RBF but has a length scale that varies - with input location. This leads to an additional term in front of - the kernel. - - The parameters are :math:`\\sigma^2`, the process variance, and the parameters of l(x) which is a function that can be specified by the user, by default an multi-layer peceptron is used is used. - - :param input_dim: the number of input dimensions - :type input_dim: int - :param variance: the variance :math:`\\sigma^2` - :type variance: float - :param mapping: the mapping that gives the lengthscale across the input space. - :type mapping: GPy.core.Mapping - :param ARD: Auto Relevance Determination. If equal to "False", the kernel is isotropic (ie. one weight variance parameter :math:`\\sigma^2_w`), otherwise there is one weight variance parameter per dimension. - :type ARD: Boolean - :rtype: Kernpart object - - """ - part = parts.gibbs.Gibbs(input_dim,variance,mapping) - return kern(input_dim, [part]) - -def hetero(input_dim, mapping=None, transform=None): - """ - """ - part = parts.hetero.Hetero(input_dim,mapping,transform) - return kern(input_dim, [part]) - -def poly(input_dim,variance=1., weight_variance=None,bias_variance=1.,degree=2, ARD=False): - """ - Construct a polynomial kernel - - :param input_dim: dimensionality of the kernel, obligatory - :type input_dim: int - :param variance: the variance of the kernel - :type variance: float - :param weight_scale: the lengthscale of the kernel - :type weight_scale: vector of weight variances for input weights. - :param bias_variance: the variance of the biases. - :type bias_variance: float - :param degree: the degree of the polynomial - :type degree: int - :param ARD: Auto Relevance Determination (allows for ARD version of covariance) - :type ARD: Boolean - - """ - part = parts.poly.POLY(input_dim,variance,weight_variance,bias_variance,degree,ARD) - return kern(input_dim, [part]) - -def white(input_dim,variance=1.): - """ - Construct a white kernel. - - :param input_dim: dimensionality of the kernel, obligatory - :type input_dim: int - :param variance: the variance of the kernel - :type variance: float - - """ - part = parts.white.White(input_dim,variance) - return kern(input_dim, [part]) - - -def exponential(input_dim,variance=1., lengthscale=None, ARD=False): - """ - Construct an exponential kernel - - :param input_dim: dimensionality of the kernel, obligatory - :type input_dim: int - :param variance: the variance of the kernel - :type variance: float - :param lengthscale: the lengthscale of the kernel - :type lengthscale: float - :param ARD: Auto Relevance Determination (one lengthscale per dimension) - :type ARD: Boolean - - """ - part = parts.exponential.Exponential(input_dim,variance, lengthscale, ARD) - return kern(input_dim, [part]) - -def Matern32(input_dim,variance=1., lengthscale=None, ARD=False): - """ - Construct a Matern 3/2 kernel. - - :param input_dim: dimensionality of the kernel, obligatory - :type input_dim: int - :param variance: the variance of the kernel - :type variance: float - :param lengthscale: the lengthscale of the kernel - :type lengthscale: float - :param ARD: Auto Relevance Determination (one lengthscale per dimension) - :type ARD: Boolean - - """ - part = parts.Matern32.Matern32(input_dim,variance, lengthscale, ARD) - return kern(input_dim, [part]) - -def Matern52(input_dim, variance=1., lengthscale=None, ARD=False): - """ - Construct a Matern 5/2 kernel. - - :param input_dim: dimensionality of the kernel, obligatory - :type input_dim: int - :param variance: the variance of the kernel - :type variance: float - :param lengthscale: the lengthscale of the kernel - :type lengthscale: float - :param ARD: Auto Relevance Determination (one lengthscale per dimension) - :type ARD: Boolean - - """ - part = parts.Matern52.Matern52(input_dim, variance, lengthscale, ARD) - return kern(input_dim, [part]) - -def bias(input_dim, variance=1.): - """ - Construct a bias kernel. - - :param input_dim: dimensionality of the kernel, obligatory - :type input_dim: int - :param variance: the variance of the kernel - :type variance: float - - """ - part = parts.bias.Bias(input_dim, variance) - return kern(input_dim, [part]) - -def finite_dimensional(input_dim, F, G, variances=1., weights=None): - """ - Construct a finite dimensional kernel. - - :param input_dim: the number of input dimensions - :type input_dim: int - :param F: np.array of functions with shape (n,) - the n basis functions - :type F: np.array - :param G: np.array with shape (n,n) - the Gram matrix associated to F - :type G: np.array - :param variances: np.ndarray with shape (n,) - :type: np.ndarray - """ - part = parts.finite_dimensional.FiniteDimensional(input_dim, F, G, variances, weights) - return kern(input_dim, [part]) - -def spline(input_dim, variance=1.): - """ - Construct a spline kernel. - - :param input_dim: Dimensionality of the kernel - :type input_dim: int - :param variance: the variance of the kernel - :type variance: float - - """ - part = parts.spline.Spline(input_dim, variance) - return kern(input_dim, [part]) - -def Brownian(input_dim, variance=1.): - """ - Construct a Brownian motion kernel. - - :param input_dim: Dimensionality of the kernel - :type input_dim: int - :param variance: the variance of the kernel - :type variance: float - - """ - part = parts.Brownian.Brownian(input_dim, variance) - return kern(input_dim, [part]) - -try: - import sympy as sp - sympy_available = True -except ImportError: - sympy_available = False - -if sympy_available: - from parts.sympykern import spkern - from sympy.parsing.sympy_parser import parse_expr - from GPy.util import symbolic - - def rbf_sympy(input_dim, ARD=False, variance=1., lengthscale=1.): - """ - Radial Basis Function covariance. - """ - X = sp.symbols('x_:' + str(input_dim)) - Z = sp.symbols('z_:' + str(input_dim)) - variance = sp.var('variance',positive=True) - if ARD: - lengthscales = sp.symbols('lengthscale_:' + str(input_dim)) - dist_string = ' + '.join(['(x_%i-z_%i)**2/lengthscale%i**2' % (i, i, i) for i in range(input_dim)]) - dist = parse_expr(dist_string) - f = variance*sp.exp(-dist/2.) - else: - lengthscale = sp.var('lengthscale',positive=True) - dist_string = ' + '.join(['(x_%i-z_%i)**2' % (i, i) for i in range(input_dim)]) - dist = parse_expr(dist_string) - f = variance*sp.exp(-dist/(2*lengthscale**2)) - return kern(input_dim, [spkern(input_dim, f, name='rbf_sympy')]) - - def eq_sympy(input_dim, output_dim, ARD=False): - """ - Latent force model covariance, exponentiated quadratic with multiple outputs. Derived from a diffusion equation with the initial spatial condition layed down by a Gaussian process with lengthscale given by shared_lengthscale. - - See IEEE Trans Pattern Anal Mach Intell. 2013 Nov;35(11):2693-705. doi: 10.1109/TPAMI.2013.86. Linear latent force models using Gaussian processes. Alvarez MA, Luengo D, Lawrence ND. - - :param input_dim: Dimensionality of the kernel - :type input_dim: int - :param output_dim: number of outputs in the covariance function. - :type output_dim: int - :param ARD: whether or not to user ARD (default False). - :type ARD: bool - - """ - real_input_dim = input_dim - if output_dim>1: - real_input_dim -= 1 - X = sp.symbols('x_:' + str(real_input_dim)) - Z = sp.symbols('z_:' + str(real_input_dim)) - scale = sp.var('scale_i scale_j',positive=True) - if ARD: - lengthscales = [sp.var('lengthscale%i_i lengthscale%i_j' % i, positive=True) for i in range(real_input_dim)] - shared_lengthscales = [sp.var('shared_lengthscale%i' % i, positive=True) for i in range(real_input_dim)] - dist_string = ' + '.join(['(x_%i-z_%i)**2/(shared_lengthscale%i**2 + lengthscale%i_i**2 + lengthscale%i_j**2)' % (i, i, i) for i in range(real_input_dim)]) - dist = parse_expr(dist_string) - f = variance*sp.exp(-dist/2.) - else: - lengthscales = sp.var('lengthscale_i lengthscale_j',positive=True) - shared_lengthscale = sp.var('shared_lengthscale',positive=True) - dist_string = ' + '.join(['(x_%i-z_%i)**2' % (i, i) for i in range(real_input_dim)]) - dist = parse_expr(dist_string) - f = scale_i*scale_j*sp.exp(-dist/(2*(lengthscale_i**2 + lengthscale_j**2 + shared_lengthscale**2))) - return kern(input_dim, [spkern(input_dim, f, output_dim=output_dim, name='eq_sympy')]) - - def ode1_eq(output_dim=1): - """ - Latent force model covariance, first order differential - equation driven by exponentiated quadratic. - - See N. D. Lawrence, G. Sanguinetti and M. Rattray. (2007) - 'Modelling transcriptional regulation using Gaussian - processes' in B. Schoelkopf, J. C. Platt and T. Hofmann (eds) - Advances in Neural Information Processing Systems, MIT Press, - Cambridge, MA, pp 785--792. - - :param output_dim: number of outputs in the covariance function. - :type output_dim: int - """ - input_dim = 2 - x_0, z_0, decay_i, decay_j, scale_i, scale_j, lengthscale = sp.symbols('x_0, z_0, decay_i, decay_j, scale_i, scale_j, lengthscale') - f = scale_i*scale_j*(symbolic.h(x_0, z_0, decay_i, decay_j, lengthscale) - + symbolic.h(z_0, x_0, decay_j, decay_i, lengthscale)) - return kern(input_dim, [spkern(input_dim, f, output_dim=output_dim, name='ode1_eq')]) - - def sympykern(input_dim, k=None, output_dim=1, name=None, param=None): - """ - A base kernel object, where all the hard work in done by sympy. - - :param k: the covariance function - :type k: a positive definite sympy function of x1, z1, x2, z2... - - To construct a new sympy kernel, you'll need to define: - - a kernel function using a sympy object. Ensure that the kernel is of the form k(x,z). - - that's it! we'll extract the variables from the function k. - - Note: - - to handle multiple inputs, call them x1, z1, etc - - to handle multpile correlated outputs, you'll need to define each covariance function and 'cross' variance function. TODO - """ - return kern(input_dim, [spkern(input_dim, k=k, output_dim=output_dim, name=name, param=param)]) -del sympy_available - -def periodic_exponential(input_dim=1, variance=1., lengthscale=None, period=2 * np.pi, n_freq=10, lower=0., upper=4 * np.pi): - """ - Construct an periodic exponential kernel - - :param input_dim: dimensionality, only defined for input_dim=1 - :type input_dim: int - :param variance: the variance of the kernel - :type variance: float - :param lengthscale: the lengthscale of the kernel - :type lengthscale: float - :param period: the period - :type period: float - :param n_freq: the number of frequencies considered for the periodic subspace - :type n_freq: int - - """ - part = parts.periodic_exponential.PeriodicExponential(input_dim, variance, lengthscale, period, n_freq, lower, upper) - return kern(input_dim, [part]) - -def periodic_Matern32(input_dim, variance=1., lengthscale=None, period=2 * np.pi, n_freq=10, lower=0., upper=4 * np.pi): - """ - Construct a periodic Matern 3/2 kernel. - - :param input_dim: dimensionality, only defined for input_dim=1 - :type input_dim: int - :param variance: the variance of the kernel - :type variance: float - :param lengthscale: the lengthscale of the kernel - :type lengthscale: float - :param period: the period - :type period: float - :param n_freq: the number of frequencies considered for the periodic subspace - :type n_freq: int - - """ - part = parts.periodic_Matern32.PeriodicMatern32(input_dim, variance, lengthscale, period, n_freq, lower, upper) - return kern(input_dim, [part]) - -def periodic_Matern52(input_dim, variance=1., lengthscale=None, period=2 * np.pi, n_freq=10, lower=0., upper=4 * np.pi): - """ - Construct a periodic Matern 5/2 kernel. - - :param input_dim: dimensionality, only defined for input_dim=1 - :type input_dim: int - :param variance: the variance of the kernel - :type variance: float - :param lengthscale: the lengthscale of the kernel - :type lengthscale: float - :param period: the period - :type period: float - :param n_freq: the number of frequencies considered for the periodic subspace - :type n_freq: int - - """ - part = parts.periodic_Matern52.PeriodicMatern52(input_dim, variance, lengthscale, period, n_freq, lower, upper) - return kern(input_dim, [part]) - -def prod(k1,k2,tensor=False): - """ - Construct a product kernel over input_dim from two kernels over input_dim - - :param k1, k2: the kernels to multiply - :type k1, k2: kernpart - :param tensor: The kernels are either multiply as functions defined on the same input space (default) or on the product of the input spaces - :type tensor: Boolean - :rtype: kernel object - - """ - part = parts.prod.Prod(k1, k2, tensor) - return kern(part.input_dim, [part]) - -def symmetric(k): - """ - Construct a symmetric kernel from an existing kernel - - The symmetric kernel works by adding two GP functions together, and computing the overall covariance. - - Let f ~ GP(x | 0, k(x, x')). Now let g = f(x) + f(-x). - - It's easy to see that g is a symmetric function: g(x) = g(-x). - - by construction, g, is a gaussian Process with mean 0 and covariance - - k(x, x') + k(-x, x') + k(x, -x') + k(-x, -x') - - This constructor builds a covariance function of this form from the initial kernel - """ - k_ = k.copy() - k_.parts = [parts.symmetric.Symmetric(p) for p in k.parts] - return k_ - -def coregionalize(output_dim,rank=1, W=None, kappa=None): - """ - Coregionlization matrix B, of the form: - - .. math:: - \mathbf{B} = \mathbf{W}\mathbf{W}^\top + kappa \mathbf{I} - - An intrinsic/linear coregionalization kernel of the form: - - .. math:: - k_2(x, y)=\mathbf{B} k(x, y) - - it is obtainded as the tensor product between a kernel k(x,y) and B. - - :param output_dim: the number of outputs to corregionalize - :type output_dim: int - :param rank: number of columns of the W matrix (this parameter is ignored if parameter W is not None) - :type rank: int - :param W: a low rank matrix that determines the correlations between the different outputs, together with kappa it forms the coregionalization matrix B - :type W: numpy array of dimensionality (num_outpus, rank) - :param kappa: a vector which allows the outputs to behave independently - :type kappa: numpy array of dimensionality (output_dim,) - :rtype: kernel object - - """ - p = parts.coregionalize.Coregionalize(output_dim,rank,W,kappa) - return kern(1,[p]) - - -def rational_quadratic(input_dim, variance=1., lengthscale=1., power=1.): - """ - Construct rational quadratic kernel. - - :param input_dim: the number of input dimensions - :type input_dim: int (input_dim=1 is the only value currently supported) - :param variance: the variance :math:`\sigma^2` - :type variance: float - :param lengthscale: the lengthscale :math:`\ell` - :type lengthscale: float - :rtype: kern object - - """ - part = parts.rational_quadratic.RationalQuadratic(input_dim, variance, lengthscale, power) - return kern(input_dim, [part]) - -def fixed(input_dim, K, variance=1.): - """ - Construct a Fixed effect kernel. - - :param input_dim: the number of input dimensions - :type input_dim: int (input_dim=1 is the only value currently supported) - :param K: the variance :math:`\sigma^2` - :type K: np.array - :param variance: kernel variance - :type variance: float - :rtype: kern object - """ - part = parts.fixed.Fixed(input_dim, K, variance) - return kern(input_dim, [part]) - -def rbfcos(input_dim, variance=1., frequencies=None, bandwidths=None, ARD=False): - """ - construct a rbfcos kernel - """ - part = parts.rbfcos.RBFCos(input_dim, variance, frequencies, bandwidths, ARD) - return kern(input_dim, [part]) - -def independent_outputs(k): - """ - Construct a kernel with independent outputs from an existing kernel - """ - for sl in k.input_slices: - assert (sl.start is None) and (sl.stop is None), "cannot adjust input slices! (TODO)" - _parts = [parts.independent_outputs.IndependentOutputs(p) for p in k.parts] - return kern(k.input_dim+1,_parts) - -def hierarchical(k): - """ - TODO This can't be right! Construct a kernel with independent outputs from an existing kernel - """ - # for sl in k.input_slices: - # assert (sl.start is None) and (sl.stop is None), "cannot adjust input slices! (TODO)" - _parts = [parts.hierarchical.Hierarchical(k.parts)] - return kern(k.input_dim+len(k.parts),_parts) - -def build_lcm(input_dim, output_dim, kernel_list = [], rank=1,W=None,kappa=None): - """ - Builds a kernel of a linear coregionalization model - - :input_dim: Input dimensionality - :output_dim: Number of outputs - :kernel_list: List of coregionalized kernels, each element in the list will be multiplied by a different corregionalization matrix - :type kernel_list: list of GPy kernels - :param rank: number tuples of the corregionalization parameters 'coregion_W' - :type rank: integer - - ..note the kernels dimensionality is overwritten to fit input_dim - - """ - - for k in kernel_list: - if k.input_dim <> input_dim: - k.input_dim = input_dim - warnings.warn("kernel's input dimension overwritten to fit input_dim parameter.") - - k_coreg = coregionalize(output_dim,rank,W,kappa) - kernel = kernel_list[0]**k_coreg.copy() - - for k in kernel_list[1:]: - k_coreg = coregionalize(output_dim,rank,W,kappa) - kernel += k**k_coreg.copy() - - return kernel - -def ODE_1(input_dim=1, varianceU=1., varianceY=1., lengthscaleU=None, lengthscaleY=None): - """ - kernel resultiong from a first order ODE with OU driving GP - - :param input_dim: the number of input dimension, has to be equal to one - :type input_dim: int - :param varianceU: variance of the driving GP - :type varianceU: float - :param lengthscaleU: lengthscale of the driving GP - :type lengthscaleU: float - :param varianceY: 'variance' of the transfer function - :type varianceY: float - :param lengthscaleY: 'lengthscale' of the transfer function - :type lengthscaleY: float - :rtype: kernel object - - """ - part = parts.ODE_1.ODE_1(input_dim, varianceU, varianceY, lengthscaleU, lengthscaleY) - return kern(input_dim, [part]) - -def ODE_UY(input_dim=2, varianceU=1., varianceY=1., lengthscaleU=None, lengthscaleY=None): - """ - kernel resultiong from a first order ODE with OU driving GP - :param input_dim: the number of input dimension, has to be equal to one - :type input_dim: int - :param input_lengthU: the number of input U length - :param varianceU: variance of the driving GP - :type varianceU: float - :param varianceY: 'variance' of the transfer function - :type varianceY: float - :param lengthscaleY: 'lengthscale' of the transfer function - :type lengthscaleY: float - :rtype: kernel object - """ - part = parts.ODE_UY.ODE_UY(input_dim, varianceU, varianceY, lengthscaleU, lengthscaleY) - return kern(input_dim, [part]) diff --git a/GPy/kern/kern.py b/GPy/kern/kern.py deleted file mode 100644 index a6491fef..00000000 --- a/GPy/kern/kern.py +++ /dev/null @@ -1,966 +0,0 @@ -# Copyright (c) 2012, GPy authors (see AUTHORS.txt). -# Licensed under the BSD 3-clause license (see LICENSE.txt) - -import sys -import numpy as np -import pylab as pb -from ..core.parameterized import Parameterized -from parts.kernpart import Kernpart -import itertools -from parts.prod import Prod as prod -from matplotlib.transforms import offset_copy - -class kern(Parameterized): - def __init__(self, input_dim, parts=[], input_slices=None): - """ - This is the main kernel class for GPy. It handles multiple - (additive) kernel functions, and keeps track of various things - like which parameters live where. - - The technical code for kernels is divided into _parts_ (see - e.g. rbf.py). This object contains a list of parts, which are - computed additively. For multiplication, special _prod_ parts - are used. - - :param input_dim: The dimensionality of the kernel's input space - :type input_dim: int - :param parts: the 'parts' (PD functions) of the kernel - :type parts: list of Kernpart objects - :param input_slices: the slices on the inputs which apply to each kernel - :type input_slices: list of slice objects, or list of bools - - """ - self.parts = parts - self.num_parts = len(parts) - self.num_params = sum([p.num_params for p in self.parts]) - - self.input_dim = input_dim - - part_names = [k.name for k in self.parts] - self.name='' - for name in part_names: - self.name += name + '+' - self.name = self.name[:-1] - # deal with input_slices - if input_slices is None: - self.input_slices = [slice(None) for p in self.parts] - else: - assert len(input_slices) == len(self.parts) - self.input_slices = [sl if type(sl) is slice else slice(None) for sl in input_slices] - - for p in self.parts: - assert isinstance(p, Kernpart), "bad kernel part" - - self.compute_param_slices() - - Parameterized.__init__(self) - - def getstate(self): - """ - Get the current state of the class, - here just all the indices, rest can get recomputed - """ - return Parameterized.getstate(self) + [self.parts, - self.num_parts, - self.num_params, - self.input_dim, - self.input_slices, - self.param_slices - ] - - def setstate(self, state): - self.param_slices = state.pop() - self.input_slices = state.pop() - self.input_dim = state.pop() - self.num_params = state.pop() - self.num_parts = state.pop() - self.parts = state.pop() - Parameterized.setstate(self, state) - - - def plot_ARD(self, fignum=None, ax=None, title='', legend=False): - """If an ARD kernel is present, plot a bar representation using matplotlib - - :param fignum: figure number of the plot - :param ax: matplotlib axis to plot on - :param title: - title of the plot, - pass '' to not print a title - pass None for a generic title - """ - if ax is None: - fig = pb.figure(fignum) - ax = fig.add_subplot(111) - else: - fig = ax.figure - from GPy.util import Tango - from matplotlib.textpath import TextPath - Tango.reset() - xticklabels = [] - bars = [] - x0 = 0 - for p in self.parts: - c = Tango.nextMedium() - if hasattr(p, 'ARD') and p.ARD: - if title is None: - ax.set_title('ARD parameters, %s kernel' % p.name) - else: - ax.set_title(title) - if p.name == 'linear': - ard_params = p.variances - else: - ard_params = 1. / p.lengthscale - - x = np.arange(x0, x0 + len(ard_params)) - bars.append(ax.bar(x, ard_params, align='center', color=c, edgecolor='k', linewidth=1.2, label=p.name)) - xticklabels.extend([r"$\mathrm{{{name}}}\ {x}$".format(name=p.name, x=i) for i in np.arange(len(ard_params))]) - x0 += len(ard_params) - x = np.arange(x0) - transOffset = offset_copy(ax.transData, fig=fig, - x=0., y= -2., units='points') - transOffsetUp = offset_copy(ax.transData, fig=fig, - x=0., y=1., units='points') - for bar in bars: - for patch, num in zip(bar.patches, np.arange(len(bar.patches))): - height = patch.get_height() - xi = patch.get_x() + patch.get_width() / 2. - va = 'top' - c = 'w' - t = TextPath((0, 0), "${xi}$".format(xi=xi), rotation=0, ha='center') - transform = transOffset - if patch.get_extents().height <= t.get_extents().height + 3: - va = 'bottom' - c = 'k' - transform = transOffsetUp - ax.text(xi, height, "${xi}$".format(xi=int(num)), color=c, rotation=0, ha='center', va=va, transform=transform) - # for xi, t in zip(x, xticklabels): - # ax.text(xi, maxi / 2, t, rotation=90, ha='center', va='center') - # ax.set_xticklabels(xticklabels, rotation=17) - ax.set_xticks([]) - ax.set_xlim(-.5, x0 - .5) - if legend: - if title is '': - mode = 'expand' - if len(bars) > 1: - mode = 'expand' - ax.legend(bbox_to_anchor=(0., 1.02, 1., 1.02), loc=3, - ncol=len(bars), mode=mode, borderaxespad=0.) - fig.tight_layout(rect=(0, 0, 1, .9)) - else: - ax.legend() - return ax - - def _transform_gradients(self, g): - """ - Apply the transformations of the kernel so that the returned vector - represents the gradient in the transformed space (i.e. that given by - get_params_transformed()) - - :param g: the gradient vector for the current model, usually created by dK_dtheta - """ - x = self._get_params() - [np.put(x, i, x * t.gradfactor(x[i])) for i, t in zip(self.constrained_indices, self.constraints)] - [np.put(g, i, v) for i, v in [(t[0], np.sum(g[t])) for t in self.tied_indices]] - if len(self.tied_indices) or len(self.fixed_indices): - to_remove = np.hstack((self.fixed_indices + [t[1:] for t in self.tied_indices])) - return np.delete(g, to_remove) - else: - return g - - def compute_param_slices(self): - """ - Create a set of slices that can index the parameters of each part. - """ - self.param_slices = [] - count = 0 - for p in self.parts: - self.param_slices.append(slice(count, count + p.num_params)) - count += p.num_params - - def __add__(self, other): - """ Overloading of the '+' operator. for more control, see self.add """ - return self.add(other) - - def add(self, other, tensor=False): - """ - Add another kernel to this one. - - If Tensor is False, both kernels are defined on the same _space_. then - the created kernel will have the same number of inputs as self and - other (which must be the same). - - If Tensor is True, then the dimensions are stacked 'horizontally', so - that the resulting kernel has self.input_dim + other.input_dim - - :param other: the other kernel to be added - :type other: GPy.kern - - """ - if tensor: - D = self.input_dim + other.input_dim - self_input_slices = [slice(*sl.indices(self.input_dim)) for sl in self.input_slices] - other_input_indices = [sl.indices(other.input_dim) for sl in other.input_slices] - other_input_slices = [slice(i[0] + self.input_dim, i[1] + self.input_dim, i[2]) for i in other_input_indices] - - newkern = kern(D, self.parts + other.parts, self_input_slices + other_input_slices) - - # transfer constraints: - newkern.constrained_indices = self.constrained_indices + [x + self.num_params for x in other.constrained_indices] - newkern.constraints = self.constraints + other.constraints - newkern.fixed_indices = self.fixed_indices + [self.num_params + x for x in other.fixed_indices] - newkern.fixed_values = self.fixed_values + other.fixed_values - newkern.constraints = self.constraints + other.constraints - newkern.tied_indices = self.tied_indices + [self.num_params + x for x in other.tied_indices] - else: - assert self.input_dim == other.input_dim - newkern = kern(self.input_dim, self.parts + other.parts, self.input_slices + other.input_slices) - # transfer constraints: - newkern.constrained_indices = self.constrained_indices + [i + self.num_params for i in other.constrained_indices] - newkern.constraints = self.constraints + other.constraints - newkern.fixed_indices = self.fixed_indices + [self.num_params + x for x in other.fixed_indices] - newkern.fixed_values = self.fixed_values + other.fixed_values - newkern.tied_indices = self.tied_indices + [self.num_params + x for x in other.tied_indices] - return newkern - - def __mul__(self, other): - """ Here we overload the '*' operator. See self.prod for more information""" - return self.prod(other) - - def __pow__(self, other, tensor=False): - """ - Shortcut for tensor `prod`. - """ - return self.prod(other, tensor=True) - - def prod(self, other, tensor=False): - """ - Multiply two kernels (either on the same space, or on the tensor product of the input space). - - :param other: the other kernel to be added - :type other: GPy.kern - :param tensor: whether or not to use the tensor space (default is false). - :type tensor: bool - - """ - K1 = self.copy() - K2 = other.copy() - - slices = [] - for sl1, sl2 in itertools.product(K1.input_slices, K2.input_slices): - s1, s2 = [False] * K1.input_dim, [False] * K2.input_dim - s1[sl1], s2[sl2] = [True], [True] - slices += [s1 + s2] - - newkernparts = [prod(k1, k2, tensor) for k1, k2 in itertools.product(K1.parts, K2.parts)] - - if tensor: - newkern = kern(K1.input_dim + K2.input_dim, newkernparts, slices) - else: - newkern = kern(K1.input_dim, newkernparts, slices) - - newkern._follow_constrains(K1, K2) - return newkern - - def _follow_constrains(self, K1, K2): - - # Build the array that allows to go from the initial indices of the param to the new ones - K1_param = [] - n = 0 - for k1 in K1.parts: - K1_param += [range(n, n + k1.num_params)] - n += k1.num_params - n = 0 - K2_param = [] - for k2 in K2.parts: - K2_param += [range(K1.num_params + n, K1.num_params + n + k2.num_params)] - n += k2.num_params - index_param = [] - for p1 in K1_param: - for p2 in K2_param: - index_param += p1 + p2 - index_param = np.array(index_param) - - # Get the ties and constrains of the kernels before the multiplication - prev_ties = K1.tied_indices + [arr + K1.num_params for arr in K2.tied_indices] - - prev_constr_ind = [K1.constrained_indices] + [K1.num_params + i for i in K2.constrained_indices] - prev_constr = K1.constraints + K2.constraints - - # prev_constr_fix = K1.fixed_indices + [arr + K1.num_params for arr in K2.fixed_indices] - # prev_constr_fix_values = K1.fixed_values + K2.fixed_values - - # follow the previous ties - for arr in prev_ties: - for j in arr: - index_param[np.where(index_param == j)[0]] = arr[0] - - # ties and constrains - for i in range(K1.num_params + K2.num_params): - index = np.where(index_param == i)[0] - if index.size > 1: - self.tie_params(index) - for i, t in zip(prev_constr_ind, prev_constr): - self.constrain(np.where(index_param == i)[0], t) - - def _get_params(self): - return np.hstack([p._get_params() for p in self.parts]) - - def _set_params(self, x): - [p._set_params(x[s]) for p, s in zip(self.parts, self.param_slices)] - - def _get_param_names(self): - # this is a bit nasty: we want to distinguish between parts with the same name by appending a count - part_names = np.array([k.name for k in self.parts], dtype=np.str) - counts = [np.sum(part_names == ni) for i, ni in enumerate(part_names)] - cum_counts = [np.sum(part_names[i:] == ni) for i, ni in enumerate(part_names)] - names = [name + '_' + str(cum_count) if count > 1 else name for name, count, cum_count in zip(part_names, counts, cum_counts)] - - return sum([[name + '_' + n for n in k._get_param_names()] for name, k in zip(names, self.parts)], []) - - def K(self, X, X2=None, which_parts='all'): - """ - Compute the kernel function. - - :param X: the first set of inputs to the kernel - :param X2: (optional) the second set of arguments to the kernel. If X2 - is None, this is passed throgh to the 'part' object, which - handles this as X2 == X. - :param which_parts: a list of booleans detailing whether to include - each of the part functions. By default, 'all' - indicates [True]*self.num_parts - """ - if which_parts == 'all': - which_parts = [True] * self.num_parts - assert X.shape[1] == self.input_dim - if X2 is None: - target = np.zeros((X.shape[0], X.shape[0])) - [p.K(X[:, i_s], None, target=target) for p, i_s, part_i_used in zip(self.parts, self.input_slices, which_parts) if part_i_used] - else: - target = np.zeros((X.shape[0], X2.shape[0])) - [p.K(X[:, i_s], X2[:, i_s], target=target) for p, i_s, part_i_used in zip(self.parts, self.input_slices, which_parts) if part_i_used] - return target - - def dK_dtheta(self, dL_dK, X, X2=None): - """ - Compute the gradient of the covariance function with respect to the parameters. - - :param dL_dK: An array of gradients of the objective function with respect to the covariance function. - :type dL_dK: Np.ndarray (num_samples x num_inducing) - :param X: Observed data inputs - :type X: np.ndarray (num_samples x input_dim) - :param X2: Observed data inputs (optional, defaults to X) - :type X2: np.ndarray (num_inducing x input_dim) - - returns: dL_dtheta - """ - assert X.shape[1] == self.input_dim - target = np.zeros(self.num_params) - if X2 is None: - [p.dK_dtheta(dL_dK, X[:, i_s], None, target[ps]) for p, i_s, ps, in zip(self.parts, self.input_slices, self.param_slices)] - else: - [p.dK_dtheta(dL_dK, X[:, i_s], X2[:, i_s], target[ps]) for p, i_s, ps, in zip(self.parts, self.input_slices, self.param_slices)] - - return self._transform_gradients(target) - - def dK_dX(self, dL_dK, X, X2=None): - """Compute the gradient of the objective function with respect to X. - - :param dL_dK: An array of gradients of the objective function with respect to the covariance function. - :type dL_dK: np.ndarray (num_samples x num_inducing) - :param X: Observed data inputs - :type X: np.ndarray (num_samples x input_dim) - :param X2: Observed data inputs (optional, defaults to X) - :type X2: np.ndarray (num_inducing x input_dim)""" - - target = np.zeros_like(X) - if X2 is None: - [p.dK_dX(dL_dK, X[:, i_s], None, target[:, i_s]) for p, i_s in zip(self.parts, self.input_slices)] - else: - [p.dK_dX(dL_dK, X[:, i_s], X2[:, i_s], target[:, i_s]) for p, i_s in zip(self.parts, self.input_slices)] - return target - - def Kdiag(self, X, which_parts='all'): - """Compute the diagonal of the covariance function for inputs X.""" - if which_parts == 'all': - which_parts = [True] * self.num_parts - assert X.shape[1] == self.input_dim - target = np.zeros(X.shape[0]) - [p.Kdiag(X[:, i_s], target=target) for p, i_s, part_on in zip(self.parts, self.input_slices, which_parts) if part_on] - return target - - def dKdiag_dtheta(self, dL_dKdiag, X): - """Compute the gradient of the diagonal of the covariance function with respect to the parameters.""" - assert X.shape[1] == self.input_dim - assert dL_dKdiag.size == X.shape[0] - target = np.zeros(self.num_params) - [p.dKdiag_dtheta(dL_dKdiag, X[:, i_s], target[ps]) for p, i_s, ps in zip(self.parts, self.input_slices, self.param_slices)] - return self._transform_gradients(target) - - def dKdiag_dX(self, dL_dKdiag, X): - assert X.shape[1] == self.input_dim - target = np.zeros_like(X) - [p.dKdiag_dX(dL_dKdiag, X[:, i_s], target[:, i_s]) for p, i_s in zip(self.parts, self.input_slices)] - return target - - def psi0(self, Z, mu, S): - target = np.zeros(mu.shape[0]) - [p.psi0(Z[:, i_s], mu[:, i_s], S[:, i_s], target) for p, i_s in zip(self.parts, self.input_slices)] - return target - - def dpsi0_dtheta(self, dL_dpsi0, Z, mu, S): - target = np.zeros(self.num_params) - [p.dpsi0_dtheta(dL_dpsi0, Z[:, i_s], mu[:, i_s], S[:, i_s], target[ps]) for p, ps, i_s in zip(self.parts, self.param_slices, self.input_slices)] - return self._transform_gradients(target) - - def dpsi0_dZ(self, dL_dpsi0, Z, mu, S): - return np.zeros_like(Z) - - def dpsi0_dmuS(self, dL_dpsi0, Z, mu, S): - target_mu, target_S = np.zeros_like(mu), np.zeros_like(S) - [p.dpsi0_dmuS(dL_dpsi0, Z[:, i_s], mu[:, i_s], S[:, i_s], target_mu[:, i_s], target_S[:, i_s]) for p, i_s in zip(self.parts, self.input_slices)] - return target_mu, target_S - - def psi1(self, Z, mu, S): - target = np.zeros((mu.shape[0], Z.shape[0])) - [p.psi1(Z[:, i_s], mu[:, i_s], S[:, i_s], target) for p, i_s in zip(self.parts, self.input_slices)] - return target - - def dpsi1_dtheta(self, dL_dpsi1, Z, mu, S): - target = np.zeros((self.num_params)) - [p.dpsi1_dtheta(dL_dpsi1, Z[:, i_s], mu[:, i_s], S[:, i_s], target[ps]) for p, ps, i_s in zip(self.parts, self.param_slices, self.input_slices)] - return self._transform_gradients(target) - - def dpsi1_dZ(self, dL_dpsi1, Z, mu, S): - target = np.zeros_like(Z) - [p.dpsi1_dZ(dL_dpsi1, Z[:, i_s], mu[:, i_s], S[:, i_s], target[:, i_s]) for p, i_s in zip(self.parts, self.input_slices)] - return target - - def dpsi1_dmuS(self, dL_dpsi1, Z, mu, S): - """return shapes are num_samples,num_inducing,input_dim""" - target_mu, target_S = np.zeros((2, mu.shape[0], mu.shape[1])) - [p.dpsi1_dmuS(dL_dpsi1, Z[:, i_s], mu[:, i_s], S[:, i_s], target_mu[:, i_s], target_S[:, i_s]) for p, i_s in zip(self.parts, self.input_slices)] - return target_mu, target_S - - def psi2(self, Z, mu, S): - """ - :param Z: np.ndarray of inducing inputs (M x Q) - :param mu, S: np.ndarrays of means and variances (each N x Q) - :returns psi2: np.ndarray (N,M,M) - """ - target = np.zeros((mu.shape[0], Z.shape[0], Z.shape[0])) - [p.psi2(Z[:, i_s], mu[:, i_s], S[:, i_s], target) for p, i_s in zip(self.parts, self.input_slices)] - - # compute the "cross" terms - # TODO: input_slices needed - from parts.white import White - from parts.rbf import RBF - from parts.rbf_inv import RBFInv - from parts.bias import Bias - from parts.linear import Linear - from parts.fixed import Fixed - - for (p1, i1), (p2, i2) in itertools.combinations(itertools.izip(self.parts, self.input_slices), 2): - # white doesn;t combine with anything - if isinstance(p1, White) or isinstance(p2, White): - pass - # rbf X bias - elif isinstance(p1, (Bias, Fixed)) and isinstance(p2, (RBF, RBFInv)): - target += p1.variance * (p2._psi1[:, :, None] + p2._psi1[:, None, :]) - elif isinstance(p2, (Bias, Fixed)) and isinstance(p1, (RBF, RBFInv)): - target += p2.variance * (p1._psi1[:, :, None] + p1._psi1[:, None, :]) - # linear X bias - elif isinstance(p1, (Bias, Fixed)) and isinstance(p2, (Linear, RBF, RBFInv)): - tmp = np.zeros((mu.shape[0], Z.shape[0])) - p2.psi1(Z, mu, S, tmp) - target += p1.variance * (tmp[:, :, None] + tmp[:, None, :]) - elif isinstance(p2, (Bias, Fixed)) and isinstance(p1, (Linear, RBF, RBFInv)): - tmp = np.zeros((mu.shape[0], Z.shape[0])) - p1.psi1(Z, mu, S, tmp) - target += p2.variance * (tmp[:, :, None] + tmp[:, None, :]) - # rbf X any - elif False:#isinstance(p1, (RBF, RBFInv)) or isinstance(p2, (RBF, RBFInv)): - if isinstance(p2, (RBF, RBFInv)) and not isinstance(p1, (RBF, RBFInv)): - p1t = p1; p1 = p2; p2 = p1t; del p1t - N, M = mu.shape[0], Z.shape[0]; NM=N*M - psi11 = np.zeros((N, M)) - psi12 = np.zeros((NM, M)) - p1.psi1(Z, mu, S, psi11) - Mu, Sigma = p1._crossterm_mu_S(Z, mu, S) - Mu, Sigma = Mu.reshape(NM,self.input_dim), Sigma.reshape(NM,self.input_dim) - - p2.psi1(Z, Mu, Sigma, psi12) - eK2 = psi12.reshape(N, M, M) - crossterms = eK2 * (psi11[:, :, None] + psi11[:, None, :]) - target += crossterms - else: - raise NotImplementedError, "psi2 cannot be computed for this kernel" - return target - - def dpsi2_dtheta(self, dL_dpsi2, Z, mu, S): - target = np.zeros(self.num_params) - [p.dpsi2_dtheta(dL_dpsi2, Z[:, i_s], mu[:, i_s], S[:, i_s], target[ps]) for p, i_s, ps in zip(self.parts, self.input_slices, self.param_slices)] - - from parts.white import White - from parts.rbf import RBF - from parts.rbf_inv import RBFInv - from parts.bias import Bias - from parts.linear import Linear - from parts.fixed import Fixed - - # compute the "cross" terms - # TODO: better looping, input_slices - for i1, i2 in itertools.combinations(range(len(self.parts)), 2): - p1, p2 = self.parts[i1], self.parts[i2] - #ipsl1, ipsl2 = self.input_slices[i1], self.input_slices[i2] - ps1, ps2 = self.param_slices[i1], self.param_slices[i2] - if isinstance(p1, White) or isinstance(p2, White): - pass - # rbf X bias - elif isinstance(p1, (Bias, Fixed)) and isinstance(p2, (RBF, RBFInv)): - p2.dpsi1_dtheta(dL_dpsi2.sum(1) * p1.variance * 2., Z, mu, S, target[ps2]) - p1.dpsi1_dtheta(dL_dpsi2.sum(1) * p2._psi1 * 2., Z, mu, S, target[ps1]) - elif isinstance(p2, (Bias, Fixed)) and isinstance(p1, (RBF, RBFInv)): - p1.dpsi1_dtheta(dL_dpsi2.sum(1) * p2.variance * 2., Z, mu, S, target[ps1]) - p2.dpsi1_dtheta(dL_dpsi2.sum(1) * p1._psi1 * 2., Z, mu, S, target[ps2]) - # linear X bias - elif isinstance(p1, (Bias, Fixed)) and isinstance(p2, Linear): - p2.dpsi1_dtheta(dL_dpsi2.sum(1) * p1.variance * 2., Z, mu, S, target[ps2]) # [ps1]) - psi1 = np.zeros((mu.shape[0], Z.shape[0])) - p2.psi1(Z, mu, S, psi1) - p1.dpsi1_dtheta(dL_dpsi2.sum(1) * psi1 * 2., Z, mu, S, target[ps1]) - elif isinstance(p2, (Bias, Fixed)) and isinstance(p1, Linear): - p1.dpsi1_dtheta(dL_dpsi2.sum(1) * p2.variance * 2., Z, mu, S, target[ps1]) - psi1 = np.zeros((mu.shape[0], Z.shape[0])) - p1.psi1(Z, mu, S, psi1) - p2.dpsi1_dtheta(dL_dpsi2.sum(1) * psi1 * 2., Z, mu, S, target[ps2]) - # rbf X any - elif False:#isinstance(p1, (RBF, RBFInv)) or isinstance(p2, (RBF, RBFInv)): - if isinstance(p2, (RBF, RBFInv)) and not isinstance(p1, (RBF, RBFInv)): - # turn around to have rbf in front - p1, p2 = self.parts[i2], self.parts[i1] - ps1, ps2 = self.param_slices[i2], self.param_slices[i1] - - N, M = mu.shape[0], Z.shape[0]; NM=N*M - - psi11 = np.zeros((N, M)) - p1.psi1(Z, mu, S, psi11) - - Mu, Sigma = p1._crossterm_mu_S(Z, mu, S) - Mu, Sigma = Mu.reshape(NM,self.input_dim), Sigma.reshape(NM,self.input_dim) - - tmp1 = np.zeros_like(target[ps1]) - tmp2 = np.zeros_like(target[ps2]) -# for n in range(N): -# for m in range(M): -# for m_prime in range(M): -# p1.dpsi1_dtheta((dL_dpsi2[n:n+1,m:m+1,m_prime:m_prime+1]*psi12_t.reshape(N,M,M)[n:n+1,m:m+1,m_prime:m_prime+1])[0], Z[m:m+1], mu[n:n+1], S[n:n+1], tmp2)#Z[m_prime:m_prime+1], mu[n:n+1], S[n:n+1], tmp2) -# p1.dpsi1_dtheta((dL_dpsi2[n:n+1,m:m+1,m_prime:m_prime+1]*psi12_t.reshape(N,M,M)[n:n+1,m_prime:m_prime+1,m:m+1])[0], Z[m_prime:m_prime+1], mu[n:n+1], S[n:n+1], tmp2) -# Mu, Sigma= Mu.reshape(N,M,self.input_dim), Sigma.reshape(N,M,self.input_dim) -# p2.dpsi1_dtheta((dL_dpsi2[n:n+1,m:m+1,m_prime:m_prime+1]*(psi11[n:n+1,m_prime:m_prime+1]))[0], Z[m:m+1], Mu[n:n+1,m], Sigma[n:n+1,m], target[ps2]) -# p2.dpsi1_dtheta((dL_dpsi2[n:n+1,m:m+1,m_prime:m_prime+1]*(psi11[n:n+1,m:m+1]))[0], Z[m_prime:m_prime+1], Mu[n:n+1, m_prime], Sigma[n:n+1, m_prime], target[ps2])#Z[m_prime:m_prime+1], Mu[n+m:(n+m)+1], Sigma[n+m:(n+m)+1], target[ps2]) - - if isinstance(p1, RBF) and isinstance(p2, RBF): - psi12 = np.zeros((N, M)) - p2.psi1(Z, mu, S, psi12) - Mu2, Sigma2 = p2._crossterm_mu_S(Z, mu, S) - Mu2, Sigma2 = Mu2.reshape(NM,self.input_dim), Sigma2.reshape(NM,self.input_dim) - p1.dpsi1_dtheta((dL_dpsi2*(psi12[:,:,None] + psi12[:,None,:])).reshape(NM,M), Z, Mu2, Sigma2, tmp1) - pass - - if isinstance(p1, RBF) and isinstance(p2, Linear): - #import ipdb;ipdb.set_trace() - pass - - p2.dpsi1_dtheta((dL_dpsi2*(psi11[:,:,None] + psi11[:,None,:])).reshape(NM,M), Z, Mu, Sigma, tmp2) - - target[ps1] += tmp1 - target[ps2] += tmp2 - else: - raise NotImplementedError, "psi2 cannot be computed for this kernel" - - return self._transform_gradients(target) - - def dpsi2_dZ(self, dL_dpsi2, Z, mu, S): - target = np.zeros_like(Z) - [p.dpsi2_dZ(dL_dpsi2, Z[:, i_s], mu[:, i_s], S[:, i_s], target[:, i_s]) for p, i_s in zip(self.parts, self.input_slices)] - - from parts.white import White - from parts.rbf import RBF - from parts.rbf_inv import RBFInv - from parts.bias import Bias - from parts.linear import Linear - from parts.fixed import Fixed - - # compute the "cross" terms - # TODO: better looping, input_slices - for p1, p2 in itertools.combinations(self.parts, 2): - if isinstance(p1, White) or isinstance(p2, White): - pass - # rbf X bias - elif isinstance(p1, (Bias, Fixed)) and isinstance(p2, (RBF, RBFInv)): - p2.dpsi1_dZ(dL_dpsi2.sum(1) * p1.variance, Z, mu, S, target) - elif isinstance(p2, (Bias, Fixed)) and isinstance(p1, (RBF, RBFInv)): - p1.dpsi1_dZ(dL_dpsi2.sum(1) * p2.variance, Z, mu, S, target) - # linear X bias - elif isinstance(p1, (Bias, Fixed)) and isinstance(p2, Linear): - p2.dpsi1_dZ(dL_dpsi2.sum(1) * p1.variance, Z, mu, S, target) - elif isinstance(p2, (Bias, Fixed)) and isinstance(p1, Linear): - p1.dpsi1_dZ(dL_dpsi2.sum(1) * p2.variance, Z, mu, S, target) - # rbf X any - elif False:#isinstance(p1, (RBF, RBFInv)) or isinstance(p2, (RBF, RBFInv)): - if isinstance(p2, (RBF, RBFInv)) and not isinstance(p1, (RBF, RBFInv)): - p1t = p1; p1 = p2; p2 = p1t; del p1t - N, M = mu.shape[0], Z.shape[0]; NM=N*M - psi11 = np.zeros((N, M)) - psi12 = np.zeros((NM, M)) - #psi12_t = np.zeros((N,M)) - - p1.psi1(Z, mu, S, psi11) - Mu, Sigma = p1._crossterm_mu_S(Z, mu, S) - Mu, Sigma = Mu.reshape(NM,self.input_dim), Sigma.reshape(NM,self.input_dim) - - p2.psi1(Z, Mu, Sigma, psi12) - tmp1 = np.zeros_like(target) - p1.dpsi1_dZ((dL_dpsi2*psi12.reshape(N,M,M)).sum(1), Z, mu, S, tmp1) - p1.dpsi1_dZ((dL_dpsi2*psi12.reshape(N,M,M)).sum(2), Z, mu, S, tmp1) - target += tmp1 - - #p2.dpsi1_dtheta((dL_dpsi2*(psi11[:,:,None] + psi11[:,None,:])).reshape(NM,M), Z, Mu, Sigma, target) - p2.dpsi1_dZ((dL_dpsi2*(psi11[:,:,None] + psi11[:,None,:])).reshape(NM,M), Z, Mu, Sigma, target) - else: - raise NotImplementedError, "psi2 cannot be computed for this kernel" - return target * 2 - - def dpsi2_dmuS(self, dL_dpsi2, Z, mu, S): - target_mu, target_S = np.zeros((2, mu.shape[0], mu.shape[1])) - [p.dpsi2_dmuS(dL_dpsi2, Z[:, i_s], mu[:, i_s], S[:, i_s], target_mu[:, i_s], target_S[:, i_s]) for p, i_s in zip(self.parts, self.input_slices)] - - from parts.white import White - from parts.rbf import RBF - from parts.rbf_inv import RBFInv - from parts.bias import Bias - from parts.linear import Linear - from parts.fixed import Fixed - - # compute the "cross" terms - # TODO: better looping, input_slices - for p1, p2 in itertools.combinations(self.parts, 2): - if isinstance(p1, White) or isinstance(p2, White): - pass - # rbf X bias - elif isinstance(p1, (Bias, Fixed)) and isinstance(p2, (RBF, RBFInv)): - p2.dpsi1_dmuS(dL_dpsi2.sum(1) * p1.variance * 2., Z, mu, S, target_mu, target_S) - elif isinstance(p2, (Bias, Fixed)) and isinstance(p1, (RBF, RBFInv)): - p1.dpsi1_dmuS(dL_dpsi2.sum(1) * p2.variance * 2., Z, mu, S, target_mu, target_S) - # linear X bias - elif isinstance(p1, (Bias, Fixed)) and isinstance(p2, Linear): - p2.dpsi1_dmuS(dL_dpsi2.sum(1) * p1.variance * 2., Z, mu, S, target_mu, target_S) - elif isinstance(p2, (Bias, Fixed)) and isinstance(p1, Linear): - p1.dpsi1_dmuS(dL_dpsi2.sum(1) * p2.variance * 2., Z, mu, S, target_mu, target_S) - # rbf X any - elif False:#isinstance(p1, (RBF, RBFInv)) or isinstance(p2, (RBF, RBFInv)): - if isinstance(p2, (RBF, RBFInv)) and not isinstance(p1, (RBF, RBFInv)): - p1t = p1; p1 = p2; p2 = p1t; del p1t - N, M = mu.shape[0], Z.shape[0]; NM=N*M - psi11 = np.zeros((N, M)) - psi12 = np.zeros((NM, M)) - #psi12_t = np.zeros((N,M)) - - p1.psi1(Z, mu, S, psi11) - Mu, Sigma = p1._crossterm_mu_S(Z, mu, S) - Mu, Sigma = Mu.reshape(NM,self.input_dim), Sigma.reshape(NM,self.input_dim) - - p2.psi1(Z, Mu, Sigma, psi12) - p1.dpsi1_dmuS((dL_dpsi2*psi12.reshape(N,M,M)).sum(1), Z, mu, S, target_mu, target_S) - p1.dpsi1_dmuS((dL_dpsi2*psi12.reshape(N,M,M)).sum(2), Z, mu, S, target_mu, target_S) - - #p2.dpsi1_dtheta((dL_dpsi2*(psi11[:,:,None] + psi11[:,None,:])).reshape(NM,M), Z, Mu, Sigma, target) - p2.dpsi1_dmuS((dL_dpsi2*(psi11[:,:,None])).sum(1)*2, Z, Mu.reshape(N,M,self.input_dim).sum(1), Sigma.reshape(N,M,self.input_dim).sum(1), target_mu, target_S) - else: - raise NotImplementedError, "psi2 cannot be computed for this kernel" - return target_mu, target_S - - def plot(self, x=None, plot_limits=None, which_parts='all', resolution=None, *args, **kwargs): - if which_parts == 'all': - which_parts = [True] * self.num_parts - if self.input_dim == 1: - if x is None: - x = np.zeros((1, 1)) - else: - x = np.asarray(x) - assert x.size == 1, "The size of the fixed variable x is not 1" - x = x.reshape((1, 1)) - - if plot_limits == None: - xmin, xmax = (x - 5).flatten(), (x + 5).flatten() - elif len(plot_limits) == 2: - xmin, xmax = plot_limits - else: - raise ValueError, "Bad limits for plotting" - - Xnew = np.linspace(xmin, xmax, resolution or 201)[:, None] - Kx = self.K(Xnew, x, which_parts) - pb.plot(Xnew, Kx, *args, **kwargs) - pb.xlim(xmin, xmax) - pb.xlabel("x") - pb.ylabel("k(x,%0.1f)" % x) - - elif self.input_dim == 2: - if x is None: - x = np.zeros((1, 2)) - else: - x = np.asarray(x) - assert x.size == 2, "The size of the fixed variable x is not 2" - x = x.reshape((1, 2)) - - if plot_limits == None: - xmin, xmax = (x - 5).flatten(), (x + 5).flatten() - elif len(plot_limits) == 2: - xmin, xmax = plot_limits - else: - raise ValueError, "Bad limits for plotting" - - resolution = resolution or 51 - xx, yy = np.mgrid[xmin[0]:xmax[0]:1j * resolution, xmin[1]:xmax[1]:1j * resolution] - xg = np.linspace(xmin[0], xmax[0], resolution) - yg = np.linspace(xmin[1], xmax[1], resolution) - Xnew = np.vstack((xx.flatten(), yy.flatten())).T - Kx = self.K(Xnew, x, which_parts) - Kx = Kx.reshape(resolution, resolution).T - pb.contour(xg, yg, Kx, vmin=Kx.min(), vmax=Kx.max(), cmap=pb.cm.jet, *args, **kwargs) # @UndefinedVariable - pb.xlim(xmin[0], xmax[0]) - pb.ylim(xmin[1], xmax[1]) - pb.xlabel("x1") - pb.ylabel("x2") - pb.title("k(x1,x2 ; %0.1f,%0.1f)" % (x[0, 0], x[0, 1])) - else: - raise NotImplementedError, "Cannot plot a kernel with more than two input dimensions" - -from ..core.model import Model -class Kern_check_model(Model): - """This is a dummy model class used as a base class for checking that the gradients of a given kernel are implemented correctly. It enables checkgradient() to be called independently on a kernel.""" - def __init__(self, kernel=None, dL_dK=None, X=None, X2=None): - num_samples = 20 - num_samples2 = 10 - if kernel==None: - import GPy - kernel = GPy.kern.rbf(1) - del GPy - if X==None: - X = np.random.normal(size=(num_samples, kernel.input_dim)) - if dL_dK==None: - if X2==None: - dL_dK = np.ones((X.shape[0], X.shape[0])) - else: - dL_dK = np.ones((X.shape[0], X2.shape[0])) - - self.kernel=kernel - self.X = X - self.X2 = X2 - self.dL_dK = dL_dK - #self.constrained_indices=[] - #self.constraints=[] - super(Kern_check_model, self).__init__() - - def is_positive_definite(self): - v = np.linalg.eig(self.kernel.K(self.X))[0] - if any(v<-10*sys.float_info.epsilon): - return False - else: - return True - - def _get_params(self): - return self.kernel._get_params() - - def _get_param_names(self): - return self.kernel._get_param_names() - - def _set_params(self, x): - self.kernel._set_params(x) - - def log_likelihood(self): - return (self.dL_dK*self.kernel.K(self.X, self.X2)).sum() - - def _log_likelihood_gradients(self): - raise NotImplementedError, "This needs to be implemented to use the kern_check_model class." - -class Kern_check_dK_dtheta(Kern_check_model): - """This class allows gradient checks for the gradient of a kernel with respect to parameters. """ - def __init__(self, kernel=None, dL_dK=None, X=None, X2=None): - Kern_check_model.__init__(self,kernel=kernel,dL_dK=dL_dK, X=X, X2=X2) - - def _log_likelihood_gradients(self): - return self.kernel.dK_dtheta(self.dL_dK, self.X, self.X2) - -class Kern_check_dKdiag_dtheta(Kern_check_model): - """This class allows gradient checks of the gradient of the diagonal of a kernel with respect to the parameters.""" - def __init__(self, kernel=None, dL_dK=None, X=None): - Kern_check_model.__init__(self,kernel=kernel,dL_dK=dL_dK, X=X, X2=None) - if dL_dK==None: - self.dL_dK = np.ones((self.X.shape[0])) - - def log_likelihood(self): - return (self.dL_dK*self.kernel.Kdiag(self.X)).sum() - - def _log_likelihood_gradients(self): - return self.kernel.dKdiag_dtheta(self.dL_dK, self.X) - -class Kern_check_dK_dX(Kern_check_model): - """This class allows gradient checks for the gradient of a kernel with respect to X. """ - def __init__(self, kernel=None, dL_dK=None, X=None, X2=None): - Kern_check_model.__init__(self,kernel=kernel,dL_dK=dL_dK, X=X, X2=X2) - - def _log_likelihood_gradients(self): - return self.kernel.dK_dX(self.dL_dK, self.X, self.X2).flatten() - - def _get_param_names(self): - return ['X_' +str(i) + ','+str(j) for j in range(self.X.shape[1]) for i in range(self.X.shape[0])] - - def _get_params(self): - return self.X.flatten() - - def _set_params(self, x): - self.X=x.reshape(self.X.shape) - -class Kern_check_dKdiag_dX(Kern_check_model): - """This class allows gradient checks for the gradient of a kernel diagonal with respect to X. """ - def __init__(self, kernel=None, dL_dK=None, X=None, X2=None): - Kern_check_model.__init__(self,kernel=kernel,dL_dK=dL_dK, X=X, X2=None) - if dL_dK==None: - self.dL_dK = np.ones((self.X.shape[0])) - - def log_likelihood(self): - return (self.dL_dK*self.kernel.Kdiag(self.X)).sum() - - def _log_likelihood_gradients(self): - return self.kernel.dKdiag_dX(self.dL_dK, self.X).flatten() - - def _get_param_names(self): - return ['X_' +str(i) + ','+str(j) for j in range(self.X.shape[1]) for i in range(self.X.shape[0])] - - def _get_params(self): - return self.X.flatten() - - def _set_params(self, x): - self.X=x.reshape(self.X.shape) - -def kern_test(kern, X=None, X2=None, output_ind=None, verbose=False, X_positive=False): - """This function runs on kernels to check the correctness of their implementation. It checks that the covariance function is positive definite for a randomly generated data set. - - :param kern: the kernel to be tested. - :type kern: GPy.kern.Kernpart - :param X: X input values to test the covariance function. - :type X: ndarray - :param X2: X2 input values to test the covariance function. - :type X2: ndarray - - """ - pass_checks = True - if X==None: - X = np.random.randn(10, kern.input_dim) - if X_positive: - X = abs(X) - if output_ind is not None: - assert(output_ind=0.,1.,0.) - -class Brownian(Kernpart): - """ - Brownian Motion kernel. - - :param input_dim: the number of input dimensions - :type input_dim: int - :param variance: - :type variance: float - """ - def __init__(self,input_dim,variance=1.): - self.input_dim = input_dim - assert self.input_dim==1, "Brownian motion in 1D only" - self.num_params = 1 - self.name = 'Brownian' - self._set_params(np.array([variance]).flatten()) - - def _get_params(self): - return self.variance - - def _set_params(self,x): - assert x.shape==(1,) - self.variance = x - - def _get_param_names(self): - return ['variance'] - - def K(self,X,X2,target): - if X2 is None: - X2 = X - target += self.variance*np.fmin(X,X2.T) - - def Kdiag(self,X,target): - target += self.variance*X.flatten() - - def dK_dtheta(self,dL_dK,X,X2,target): - if X2 is None: - X2 = X - target += np.sum(np.fmin(X,X2.T)*dL_dK) - - def dKdiag_dtheta(self,dL_dKdiag,X,target): - target += np.dot(X.flatten(), dL_dKdiag) - - def dK_dX(self,dL_dK,X,X2,target): - raise NotImplementedError, "TODO" - #target += self.variance - #target -= self.variance*theta(X-X2.T) - #if X.shape==X2.shape: - #if np.all(X==X2): - #np.add(target[:,:,0],self.variance*np.diag(X2.flatten()-X.flatten()),target[:,:,0]) - - - def dKdiag_dX(self,dL_dKdiag,X,target): - target += self.variance*dL_dKdiag[:,None] - diff --git a/GPy/kern/parts/Matern32.py b/GPy/kern/parts/Matern32.py deleted file mode 100644 index 40da79f0..00000000 --- a/GPy/kern/parts/Matern32.py +++ /dev/null @@ -1,139 +0,0 @@ -# Copyright (c) 2012, GPy authors (see AUTHORS.txt). -# Licensed under the BSD 3-clause license (see LICENSE.txt) - - -from kernpart import Kernpart -import numpy as np -from scipy import integrate - -class Matern32(Kernpart): - """ - Matern 3/2 kernel: - - .. math:: - - k(r) = \\sigma^2 (1 + \\sqrt{3} r) \exp(- \sqrt{3} r) \\ \\ \\ \\ \\text{ where } r = \sqrt{\sum_{i=1}^input_dim \\frac{(x_i-y_i)^2}{\ell_i^2} } - - :param input_dim: the number of input dimensions - :type input_dim: int - :param variance: the variance :math:`\sigma^2` - :type variance: float - :param lengthscale: the vector of lengthscale :math:`\ell_i` - :type lengthscale: array or list of the appropriate size (or float if there is only one lengthscale parameter) - :param ARD: Auto Relevance Determination. If equal to "False", the kernel is isotropic (ie. one single lengthscale parameter \ell), otherwise there is one lengthscale parameter per dimension. - :type ARD: Boolean - :rtype: kernel object - - """ - - def __init__(self, input_dim, variance=1., lengthscale=None, ARD=False): - self.input_dim = input_dim - self.ARD = ARD - if ARD == False: - self.num_params = 2 - self.name = 'Mat32' - if lengthscale is not None: - lengthscale = np.asarray(lengthscale) - assert lengthscale.size == 1, "Only one lengthscale needed for non-ARD kernel" - else: - lengthscale = np.ones(1) - else: - self.num_params = self.input_dim + 1 - self.name = 'Mat32' - if lengthscale is not None: - lengthscale = np.asarray(lengthscale) - assert lengthscale.size == self.input_dim, "bad number of lengthscales" - else: - lengthscale = np.ones(self.input_dim) - self._set_params(np.hstack((variance, lengthscale.flatten()))) - - def _get_params(self): - """return the value of the parameters.""" - return np.hstack((self.variance, self.lengthscale)) - - def _set_params(self, x): - """set the value of the parameters.""" - assert x.size == self.num_params - self.variance = x[0] - self.lengthscale = x[1:] - - def _get_param_names(self): - """return parameter names.""" - if self.num_params == 2: - return ['variance', 'lengthscale'] - else: - return ['variance'] + ['lengthscale_%i' % i for i in range(self.lengthscale.size)] - - def K(self, X, X2, target): - """Compute the covariance matrix between X and X2.""" - if X2 is None: X2 = X - dist = np.sqrt(np.sum(np.square((X[:, None, :] - X2[None, :, :]) / self.lengthscale), -1)) - np.add(self.variance * (1 + np.sqrt(3.) * dist) * np.exp(-np.sqrt(3.) * dist), target, target) - - def Kdiag(self, X, target): - """Compute the diagonal of the covariance matrix associated to X.""" - np.add(target, self.variance, target) - - def dK_dtheta(self, dL_dK, X, X2, target): - """derivative of the covariance matrix with respect to the parameters.""" - if X2 is None: X2 = X - dist = np.sqrt(np.sum(np.square((X[:, None, :] - X2[None, :, :]) / self.lengthscale), -1)) - dvar = (1 + np.sqrt(3.) * dist) * np.exp(-np.sqrt(3.) * dist) - invdist = 1. / np.where(dist != 0., dist, np.inf) - dist2M = np.square(X[:, None, :] - X2[None, :, :]) / self.lengthscale ** 3 - # dl = (self.variance* 3 * dist * np.exp(-np.sqrt(3.)*dist))[:,:,np.newaxis] * dist2M*invdist[:,:,np.newaxis] - target[0] += np.sum(dvar * dL_dK) - if self.ARD == True: - dl = (self.variance * 3 * dist * np.exp(-np.sqrt(3.) * dist))[:, :, np.newaxis] * dist2M * invdist[:, :, np.newaxis] - # dl = self.variance*dvar[:,:,None]*dist2M*invdist[:,:,None] - target[1:] += (dl * dL_dK[:, :, None]).sum(0).sum(0) - else: - dl = (self.variance * 3 * dist * np.exp(-np.sqrt(3.) * dist)) * dist2M.sum(-1) * invdist - # dl = self.variance*dvar*dist2M.sum(-1)*invdist - target[1] += np.sum(dl * dL_dK) - - def dKdiag_dtheta(self, dL_dKdiag, X, target): - """derivative of the diagonal of the covariance matrix with respect to the parameters.""" - target[0] += np.sum(dL_dKdiag) - - def dK_dX(self, dL_dK, X, X2, target): - """derivative of the covariance matrix with respect to X.""" - if X2 is None: - dist = np.sqrt(np.sum(np.square((X[:, None, :] - X[None, :, :]) / self.lengthscale), -1))[:, :, None] - ddist_dX = 2*(X[:, None, :] - X[None, :, :]) / self.lengthscale ** 2 / np.where(dist != 0., dist, np.inf) - - else: - dist = np.sqrt(np.sum(np.square((X[:, None, :] - X2[None, :, :]) / self.lengthscale), -1))[:, :, None] - ddist_dX = (X[:, None, :] - X2[None, :, :]) / self.lengthscale ** 2 / np.where(dist != 0., dist, np.inf) - dK_dX = -np.transpose(3 * self.variance * dist * np.exp(-np.sqrt(3) * dist) * ddist_dX, (1, 0, 2)) - target += np.sum(dK_dX * dL_dK.T[:, :, None], 0) - - def dKdiag_dX(self, dL_dKdiag, X, target): - pass - - def Gram_matrix(self, F, F1, F2, lower, upper): - """ - Return the Gram matrix of the vector of functions F with respect to the RKHS norm. The use of this function is limited to input_dim=1. - - :param F: vector of functions - :type F: np.array - :param F1: vector of derivatives of F - :type F1: np.array - :param F2: vector of second derivatives of F - :type F2: np.array - :param lower,upper: boundaries of the input domain - :type lower,upper: floats - """ - assert self.input_dim == 1 - def L(x, i): - return(3. / self.lengthscale ** 2 * F[i](x) + 2 * np.sqrt(3) / self.lengthscale * F1[i](x) + F2[i](x)) - n = F.shape[0] - G = np.zeros((n, n)) - for i in range(n): - for j in range(i, n): - G[i, j] = G[j, i] = integrate.quad(lambda x : L(x, i) * L(x, j), lower, upper)[0] - Flower = np.array([f(lower) for f in F])[:, None] - F1lower = np.array([f(lower) for f in F1])[:, None] - # print "OLD \n", np.dot(F1lower,F1lower.T), "\n \n" - # return(G) - return(self.lengthscale ** 3 / (12.*np.sqrt(3) * self.variance) * G + 1. / self.variance * np.dot(Flower, Flower.T) + self.lengthscale ** 2 / (3.*self.variance) * np.dot(F1lower, F1lower.T)) diff --git a/GPy/kern/parts/Matern52.py b/GPy/kern/parts/Matern52.py deleted file mode 100644 index 4bf4a1a8..00000000 --- a/GPy/kern/parts/Matern52.py +++ /dev/null @@ -1,145 +0,0 @@ -# Copyright (c) 2012, GPy authors (see AUTHORS.txt). -# Licensed under the BSD 3-clause license (see LICENSE.txt) - - -from kernpart import Kernpart -import numpy as np -import hashlib -from scipy import integrate - -class Matern52(Kernpart): - """ - Matern 5/2 kernel: - - .. math:: - - k(r) = \sigma^2 (1 + \sqrt{5} r + \\frac53 r^2) \exp(- \sqrt{5} r) \ \ \ \ \ \\text{ where } r = \sqrt{\sum_{i=1}^input_dim \\frac{(x_i-y_i)^2}{\ell_i^2} } - - :param input_dim: the number of input dimensions - :type input_dim: int - :param variance: the variance :math:`\sigma^2` - :type variance: float - :param lengthscale: the vector of lengthscale :math:`\ell_i` - :type lengthscale: array or list of the appropriate size (or float if there is only one lengthscale parameter) - :param ARD: Auto Relevance Determination. If equal to "False", the kernel is isotropic (ie. one single lengthscale parameter \ell), otherwise there is one lengthscale parameter per dimension. - :type ARD: Boolean - :rtype: kernel object - - """ - def __init__(self,input_dim,variance=1.,lengthscale=None,ARD=False): - self.input_dim = input_dim - self.ARD = ARD - if ARD == False: - self.num_params = 2 - self.name = 'Mat52' - if lengthscale is not None: - lengthscale = np.asarray(lengthscale) - assert lengthscale.size == 1, "Only one lengthscale needed for non-ARD kernel" - else: - lengthscale = np.ones(1) - else: - self.num_params = self.input_dim + 1 - self.name = 'Mat52' - if lengthscale is not None: - lengthscale = np.asarray(lengthscale) - assert lengthscale.size == self.input_dim, "bad number of lengthscales" - else: - lengthscale = np.ones(self.input_dim) - self._set_params(np.hstack((variance,lengthscale.flatten()))) - - def _get_params(self): - """return the value of the parameters.""" - return np.hstack((self.variance,self.lengthscale)) - - def _set_params(self,x): - """set the value of the parameters.""" - assert x.size == self.num_params - self.variance = x[0] - self.lengthscale = x[1:] - - def _get_param_names(self): - """return parameter names.""" - if self.num_params == 2: - return ['variance','lengthscale'] - else: - return ['variance']+['lengthscale_%i'%i for i in range(self.lengthscale.size)] - - def K(self,X,X2,target): - """Compute the covariance matrix between X and X2.""" - if X2 is None: X2 = X - dist = np.sqrt(np.sum(np.square((X[:,None,:]-X2[None,:,:])/self.lengthscale),-1)) - np.add(self.variance*(1+np.sqrt(5.)*dist+5./3*dist**2)*np.exp(-np.sqrt(5.)*dist), target,target) - - def Kdiag(self,X,target): - """Compute the diagonal of the covariance matrix associated to X.""" - np.add(target,self.variance,target) - - def dK_dtheta(self,dL_dK,X,X2,target): - """derivative of the covariance matrix with respect to the parameters.""" - if X2 is None: X2 = X - dist = np.sqrt(np.sum(np.square((X[:,None,:]-X2[None,:,:])/self.lengthscale),-1)) - invdist = 1./np.where(dist!=0.,dist,np.inf) - dist2M = np.square(X[:,None,:]-X2[None,:,:])/self.lengthscale**3 - dvar = (1+np.sqrt(5.)*dist+5./3*dist**2)*np.exp(-np.sqrt(5.)*dist) - dl = (self.variance * 5./3 * dist * (1 + np.sqrt(5.)*dist ) * np.exp(-np.sqrt(5.)*dist))[:,:,np.newaxis] * dist2M*invdist[:,:,np.newaxis] - target[0] += np.sum(dvar*dL_dK) - if self.ARD: - dl = (self.variance * 5./3 * dist * (1 + np.sqrt(5.)*dist ) * np.exp(-np.sqrt(5.)*dist))[:,:,np.newaxis] * dist2M*invdist[:,:,np.newaxis] - #dl = (self.variance* 3 * dist * np.exp(-np.sqrt(3.)*dist))[:,:,np.newaxis] * dist2M*invdist[:,:,np.newaxis] - target[1:] += (dl*dL_dK[:,:,None]).sum(0).sum(0) - else: - dl = (self.variance * 5./3 * dist * (1 + np.sqrt(5.)*dist ) * np.exp(-np.sqrt(5.)*dist)) * dist2M.sum(-1)*invdist - #dl = (self.variance* 3 * dist * np.exp(-np.sqrt(3.)*dist)) * dist2M.sum(-1)*invdist - target[1] += np.sum(dl*dL_dK) - - def dKdiag_dtheta(self,dL_dKdiag,X,target): - """derivative of the diagonal of the covariance matrix with respect to the parameters.""" - target[0] += np.sum(dL_dKdiag) - - def dK_dX(self,dL_dK,X,X2,target): - """derivative of the covariance matrix with respect to X.""" - if X2 is None: - dist = np.sqrt(np.sum(np.square((X[:,None,:]-X[None,:,:])/self.lengthscale),-1))[:,:,None] - ddist_dX = 2*(X[:,None,:]-X[None,:,:])/self.lengthscale**2/np.where(dist!=0.,dist,np.inf) - else: - dist = np.sqrt(np.sum(np.square((X[:,None,:]-X2[None,:,:])/self.lengthscale),-1))[:,:,None] - ddist_dX = (X[:,None,:]-X2[None,:,:])/self.lengthscale**2/np.where(dist!=0.,dist,np.inf) - dK_dX = - np.transpose(self.variance*5./3*dist*(1+np.sqrt(5)*dist)*np.exp(-np.sqrt(5)*dist)*ddist_dX,(1,0,2)) - target += np.sum(dK_dX*dL_dK.T[:,:,None],0) - - def dKdiag_dX(self,dL_dKdiag,X,target): - pass - - def Gram_matrix(self,F,F1,F2,F3,lower,upper): - """ - Return the Gram matrix of the vector of functions F with respect to the RKHS norm. The use of this function is limited to input_dim=1. - - :param F: vector of functions - :type F: np.array - :param F1: vector of derivatives of F - :type F1: np.array - :param F2: vector of second derivatives of F - :type F2: np.array - :param F3: vector of third derivatives of F - :type F3: np.array - :param lower,upper: boundaries of the input domain - :type lower,upper: floats - """ - assert self.input_dim == 1 - def L(x,i): - return(5*np.sqrt(5)/self.lengthscale**3*F[i](x) + 15./self.lengthscale**2*F1[i](x)+ 3*np.sqrt(5)/self.lengthscale*F2[i](x) + F3[i](x)) - n = F.shape[0] - G = np.zeros((n,n)) - for i in range(n): - for j in range(i,n): - G[i,j] = G[j,i] = integrate.quad(lambda x : L(x,i)*L(x,j),lower,upper)[0] - G_coef = 3.*self.lengthscale**5/(400*np.sqrt(5)) - Flower = np.array([f(lower) for f in F])[:,None] - F1lower = np.array([f(lower) for f in F1])[:,None] - F2lower = np.array([f(lower) for f in F2])[:,None] - orig = 9./8*np.dot(Flower,Flower.T) + 9.*self.lengthscale**4/200*np.dot(F2lower,F2lower.T) - orig2 = 3./5*self.lengthscale**2 * ( np.dot(F1lower,F1lower.T) + 1./8*np.dot(Flower,F2lower.T) + 1./8*np.dot(F2lower,Flower.T)) - return(1./self.variance* (G_coef*G + orig + orig2)) - - - diff --git a/GPy/kern/parts/__init__.py b/GPy/kern/parts/__init__.py deleted file mode 100644 index 672a7802..00000000 --- a/GPy/kern/parts/__init__.py +++ /dev/null @@ -1,31 +0,0 @@ -import bias -import Brownian -import coregionalize -import exponential -import eq_ode1 -import finite_dimensional -import fixed -import gibbs -import hetero -import hierarchical -import independent_outputs -import linear -import Matern32 -import Matern52 -import mlp -# import ODE_1 -# import ODE_UY -import periodic_exponential -import periodic_Matern32 -import periodic_Matern52 -import poly -import prod_orthogonal -import prod -import rational_quadratic -import rbfcos -import rbf -import rbf_inv -import spline -import symmetric -import sympy_helpers -import white diff --git a/GPy/kern/parts/bias.py b/GPy/kern/parts/bias.py deleted file mode 100644 index 2b72e7c9..00000000 --- a/GPy/kern/parts/bias.py +++ /dev/null @@ -1,89 +0,0 @@ -# Copyright (c) 2012, GPy authors (see AUTHORS.txt). -# Licensed under the BSD 3-clause license (see LICENSE.txt) - - -from kernpart import Kernpart -import numpy as np -import hashlib - -class Bias(Kernpart): - def __init__(self,input_dim,variance=1.): - """ - :param input_dim: the number of input dimensions - :type input_dim: int - :param variance: the variance of the kernel - :type variance: float - """ - self.input_dim = input_dim - self.num_params = 1 - self.name = 'bias' - self._set_params(np.array([variance]).flatten()) - - def _get_params(self): - return self.variance - - def _set_params(self,x): - assert x.shape==(1,) - self.variance = x - - def _get_param_names(self): - return ['variance'] - - def K(self,X,X2,target): - target += self.variance - - def Kdiag(self,X,target): - target += self.variance - - def dK_dtheta(self,dL_dKdiag,X,X2,target): - target += dL_dKdiag.sum() - - def dKdiag_dtheta(self,dL_dKdiag,X,target): - target += dL_dKdiag.sum() - - def dK_dX(self, dL_dK,X, X2, target): - pass - - def dKdiag_dX(self,dL_dKdiag,X,target): - pass - - #---------------------------------------# - # PSI statistics # - #---------------------------------------# - - def psi0(self, Z, mu, S, target): - target += self.variance - - def psi1(self, Z, mu, S, target): - self._psi1 = self.variance - target += self._psi1 - - def psi2(self, Z, mu, S, target): - target += self.variance**2 - - def dpsi0_dtheta(self, dL_dpsi0, Z, mu, S, target): - target += dL_dpsi0.sum() - - def dpsi1_dtheta(self, dL_dpsi1, Z, mu, S, target): - target += dL_dpsi1.sum() - - def dpsi2_dtheta(self, dL_dpsi2, Z, mu, S, target): - target += 2.*self.variance*dL_dpsi2.sum() - - def dpsi0_dZ(self, dL_dpsi0, Z, mu, S, target): - pass - - def dpsi0_dmuS(self, dL_dpsi0, Z, mu, S, target_mu, target_S): - pass - - def dpsi1_dZ(self, dL_dpsi1, Z, mu, S, target): - pass - - def dpsi1_dmuS(self, dL_dpsi1, Z, mu, S, target_mu, target_S): - pass - - def dpsi2_dZ(self, dL_dpsi2, Z, mu, S, target): - pass - - def dpsi2_dmuS(self, dL_dpsi2, Z, mu, S, target_mu, target_S): - pass diff --git a/GPy/kern/parts/coregionalize.py b/GPy/kern/parts/coregionalize.py deleted file mode 100644 index 4748d276..00000000 --- a/GPy/kern/parts/coregionalize.py +++ /dev/null @@ -1,165 +0,0 @@ -# Copyright (c) 2012, James Hensman and Ricardo Andrade -# Licensed under the BSD 3-clause license (see LICENSE.txt) - -from kernpart import Kernpart -import numpy as np -from GPy.util.linalg import mdot, pdinv -import pdb -from scipy import weave - -class Coregionalize(Kernpart): - """ - Covariance function for intrinsic/linear coregionalization models - - This covariance has the form: - .. math:: - \mathbf{B} = \mathbf{W}\mathbf{W}^\top + \text{diag}(kappa) - - An intrinsic/linear coregionalization covariance function of the form: - .. math:: - - k_2(x, y)=\mathbf{B} k(x, y) - - it is obtained as the tensor product between a covariance function - k(x,y) and B. - - :param output_dim: number of outputs to coregionalize - :type output_dim: int - :param rank: number of columns of the W matrix (this parameter is ignored if parameter W is not None) - :type rank: int - :param W: a low rank matrix that determines the correlations between the different outputs, together with kappa it forms the coregionalization matrix B - :type W: numpy array of dimensionality (num_outpus, W_columns) - :param kappa: a vector which allows the outputs to behave independently - :type kappa: numpy array of dimensionality (output_dim,) - - .. note: see coregionalization examples in GPy.examples.regression for some usage. - """ - def __init__(self, output_dim, rank=1, W=None, kappa=None): - self.input_dim = 1 - self.name = 'coregion' - self.output_dim = output_dim - self.rank = rank - if self.rank>output_dim-1: - print("Warning: Unusual choice of rank, it should normally be less than the output_dim.") - if W is None: - self.W = 0.5*np.random.randn(self.output_dim,self.rank)/np.sqrt(self.rank) - else: - assert W.shape==(self.output_dim,self.rank) - self.W = W - if kappa is None: - kappa = 0.5*np.ones(self.output_dim) - else: - assert kappa.shape==(self.output_dim,) - self.kappa = kappa - self.num_params = self.output_dim*(self.rank + 1) - self._set_params(np.hstack([self.W.flatten(),self.kappa])) - - def _get_params(self): - return np.hstack([self.W.flatten(),self.kappa]) - - def _set_params(self,x): - assert x.size == self.num_params - self.kappa = x[-self.output_dim:] - self.W = x[:-self.output_dim].reshape(self.output_dim,self.rank) - self.B = np.dot(self.W,self.W.T) + np.diag(self.kappa) - - def _get_param_names(self): - return sum([['W%i_%i'%(i,j) for j in range(self.rank)] for i in range(self.output_dim)],[]) + ['kappa_%i'%i for i in range(self.output_dim)] - - def K(self,index,index2,target): - index = np.asarray(index,dtype=np.int) - - #here's the old code (numpy) - #if index2 is None: - #index2 = index - #else: - #index2 = np.asarray(index2,dtype=np.int) - #false_target = target.copy() - #ii,jj = np.meshgrid(index,index2) - #ii,jj = ii.T, jj.T - #false_target += self.B[ii,jj] - - if index2 is None: - code=""" - for(int i=0;i>> index = np.asarray([0,0,0,1,1,1,2,2,2]) - returns - >>> [[slice(0,3,None)],[slice(3,6,None)],[slice(6,9,None)]] - - or, a more complicated example - >>> index = np.asarray([0,0,1,1,0,2,2,2,1,1]) - returns - >>> [[slice(0,2,None),slice(4,5,None)],[slice(2,4,None),slice(8,10,None)],[slice(5,8,None)]] - """ - - #contruct the return structure - ind = np.asarray(index,dtype=np.int64) - ret = [[] for i in range(ind.max()+1)] - - #find the switchpoints - ind_ = np.hstack((ind,ind[0]+ind[-1]+1)) - switchpoints = np.nonzero(ind_ - np.roll(ind_,+1))[0] - - [ret[ind_i].append(slice(*indexes_i)) for ind_i,indexes_i in zip(ind[switchpoints[:-1]],zip(switchpoints,switchpoints[1:]))] - return ret - -class IndependentOutputs(Kernpart): - """ - A kernel part shich can reopresent several independent functions. - this kernel 'switches off' parts of the matrix where the output indexes are different. - - The index of the functions is given by the last column in the input X - the rest of the columns of X are passed to the kernel for computation (in blocks). - - """ - def __init__(self,k): - self.input_dim = k.input_dim + 1 - self.num_params = k.num_params - self.name = 'iops('+ k.name + ')' - self.k = k - - def _get_params(self): - return self.k._get_params() - - def _set_params(self,x): - self.k._set_params(x) - self.params = x - - def _get_param_names(self): - return self.k._get_param_names() - - def K(self,X,X2,target): - #Sort out the slices from the input data - X,slices = X[:,:-1],index_to_slices(X[:,-1]) - if X2 is None: - X2,slices2 = X,slices - else: - X2,slices2 = X2[:,:-1],index_to_slices(X2[:,-1]) - - [[[self.k.K(X[s],X2[s2],target[s,s2]) for s in slices_i] for s2 in slices_j] for slices_i,slices_j in zip(slices,slices2)] - - def Kdiag(self,X,target): - X,slices = X[:,:-1],index_to_slices(X[:,-1]) - [[self.k.Kdiag(X[s],target[s]) for s in slices_i] for slices_i in slices] - - def dK_dtheta(self,dL_dK,X,X2,target): - X,slices = X[:,:-1],index_to_slices(X[:,-1]) - if X2 is None: - X2,slices2 = X,slices - else: - X2,slices2 = X2[:,:-1],index_to_slices(X2[:,-1]) - [[[self.k.dK_dtheta(dL_dK[s,s2],X[s],X2[s2],target) for s in slices_i] for s2 in slices_j] for slices_i,slices_j in zip(slices,slices2)] - - - def dK_dX(self,dL_dK,X,X2,target): - X,slices = X[:,:-1],index_to_slices(X[:,-1]) - if X2 is None: - X2,slices2 = X,slices - else: - X2,slices2 = X2[:,:-1],index_to_slices(X2[:,-1]) - [[[self.k.dK_dX(dL_dK[s,s2],X[s],X2[s2],target[s,:-1]) for s in slices_i] for s2 in slices_j] for slices_i,slices_j in zip(slices,slices2)] - - def dKdiag_dX(self,dL_dKdiag,X,target): - X,slices = X[:,:-1],index_to_slices(X[:,-1]) - [[self.k.dKdiag_dX(dL_dKdiag[s],X[s],target[s,:-1]) for s in slices_i] for slices_i in slices] - - - def dKdiag_dtheta(self,dL_dKdiag,X,target): - X,slices = X[:,:-1],index_to_slices(X[:,-1]) - [[self.k.dKdiag_dX(dL_dKdiag[s],X[s],target) for s in slices_i] for slices_i in slices] diff --git a/GPy/kern/parts/kernpart.py b/GPy/kern/parts/kernpart.py deleted file mode 100644 index f6777083..00000000 --- a/GPy/kern/parts/kernpart.py +++ /dev/null @@ -1,125 +0,0 @@ -# Copyright (c) 2012, GPy authors (see AUTHORS.txt). -# Licensed under the BSD 3-clause license (see LICENSE.txt) - - -class Kernpart(object): - def __init__(self,input_dim): - """ - The base class for a kernpart: a positive definite function which forms part of a covariance function (kernel). - - :param input_dim: the number of input dimensions to the function - :type input_dim: int - - Do not instantiate. - """ - # the input dimensionality for the covariance - self.input_dim = input_dim - # the number of optimisable parameters - self.num_params = 1 - # the name of the covariance function. - self.name = 'unnamed' - - def _get_params(self): - raise NotImplementedError - def _set_params(self,x): - raise NotImplementedError - def _get_param_names(self): - raise NotImplementedError - def K(self,X,X2,target): - raise NotImplementedError - def Kdiag(self,X,target): - raise NotImplementedError - def dK_dtheta(self,dL_dK,X,X2,target): - raise NotImplementedError - def dKdiag_dtheta(self,dL_dKdiag,X,target): - # In the base case compute this by calling dK_dtheta. Need to - # override for stationary covariances (for example) to save - # time. - for i in range(X.shape[0]): - self.dK_dtheta(dL_dKdiag[i], X[i, :][None, :], X2=None, target=target) - def psi0(self,Z,mu,S,target): - raise NotImplementedError - def dpsi0_dtheta(self,dL_dpsi0,Z,mu,S,target): - raise NotImplementedError - def dpsi0_dmuS(self,dL_dpsi0,Z,mu,S,target_mu,target_S): - raise NotImplementedError - def psi1(self,Z,mu,S,target): - raise NotImplementedError - def dpsi1_dtheta(self,Z,mu,S,target): - raise NotImplementedError - def dpsi1_dZ(self,dL_dpsi1,Z,mu,S,target): - raise NotImplementedError - def dpsi1_dmuS(self,dL_dpsi1,Z,mu,S,target_mu,target_S): - raise NotImplementedError - def psi2(self,Z,mu,S,target): - raise NotImplementedError - def dpsi2_dZ(self,dL_dpsi2,Z,mu,S,target): - raise NotImplementedError - def dpsi2_dtheta(self,dL_dpsi2,Z,mu,S,target): - raise NotImplementedError - def dpsi2_dmuS(self,dL_dpsi2,Z,mu,S,target_mu,target_S): - raise NotImplementedError - def dK_dX(self, dL_dK, X, X2, target): - raise NotImplementedError - def dKdiag_dX(self, dL_dK, X, target): - raise NotImplementedError - - - -class Kernpart_stationary(Kernpart): - def __init__(self, input_dim, lengthscale=None, ARD=False): - self.input_dim = input_dim - self.ARD = ARD - if not ARD: - self.num_params = 2 - if lengthscale is not None: - self.lengthscale = np.asarray(lengthscale) - assert self.lengthscale.size == 1, "Only one lengthscale needed for non-ARD kernel" - else: - self.lengthscale = np.ones(1) - else: - self.num_params = self.input_dim + 1 - if lengthscale is not None: - self.lengthscale = np.asarray(lengthscale) - assert self.lengthscale.size == self.input_dim, "bad number of lengthscales" - else: - self.lengthscale = np.ones(self.input_dim) - - # initialize cache - self._Z, self._mu, self._S = np.empty(shape=(3, 1)) - self._X, self._X2, self._params = np.empty(shape=(3, 1)) - - def _set_params(self, x): - self.lengthscale = x - self.lengthscale2 = np.square(self.lengthscale) - # reset cached results - self._X, self._X2, self._params = np.empty(shape=(3, 1)) - self._Z, self._mu, self._S = np.empty(shape=(3, 1)) # cached versions of Z,mu,S - - - def dKdiag_dtheta(self, dL_dKdiag, X, target): - # For stationary covariances, derivative of diagonal elements - # wrt lengthscale is 0. - target[0] += np.sum(dL_dKdiag) - - def dKdiag_dX(self, dL_dK, X, target): - pass # true for all stationary kernels - - -class Kernpart_inner(Kernpart): - def __init__(self,input_dim): - """ - The base class for a kernpart_inner: a positive definite function which forms part of a kernel that is based on the inner product between inputs. - - :param input_dim: the number of input dimensions to the function - :type input_dim: int - - Do not instantiate. - """ - Kernpart.__init__(self, input_dim) - - # initialize cache - self._Z, self._mu, self._S = np.empty(shape=(3, 1)) - self._X, self._X2, self._params = np.empty(shape=(3, 1)) - - diff --git a/GPy/kern/parts/linear.py b/GPy/kern/parts/linear.py deleted file mode 100644 index ab96bb31..00000000 --- a/GPy/kern/parts/linear.py +++ /dev/null @@ -1,325 +0,0 @@ -# Copyright (c) 2012, GPy authors (see AUTHORS.txt). -# Licensed under the BSD 3-clause license (see LICENSE.txt) - - -from kernpart import Kernpart -import numpy as np -from ...util.linalg import tdot -from ...util.misc import fast_array_equal -from scipy import weave -from ...util.config import * - -class Linear(Kernpart): - """ - Linear kernel - - .. math:: - - k(x,y) = \sum_{i=1}^input_dim \sigma^2_i x_iy_i - - :param input_dim: the number of input dimensions - :type input_dim: int - :param variances: the vector of variances :math:`\sigma^2_i` - :type variances: array or list of the appropriate size (or float if there is only one variance parameter) - :param ARD: Auto Relevance Determination. If equal to "False", the kernel has only one variance parameter \sigma^2, otherwise there is one variance parameter per dimension. - :type ARD: Boolean - :rtype: kernel object - """ - - def __init__(self, input_dim, variances=None, ARD=False): - self.input_dim = input_dim - self.ARD = ARD - if ARD == False: - self.num_params = 1 - self.name = 'linear' - if variances is not None: - variances = np.asarray(variances) - assert variances.size == 1, "Only one variance needed for non-ARD kernel" - else: - variances = np.ones(1) - self._Xcache, self._X2cache = np.empty(shape=(2,)) - else: - self.num_params = self.input_dim - self.name = 'linear' - if variances is not None: - variances = np.asarray(variances) - assert variances.size == self.input_dim, "bad number of lengthscales" - else: - variances = np.ones(self.input_dim) - self._set_params(variances.flatten()) - - # initialize cache - self._Z, self._mu, self._S = np.empty(shape=(3, 1)) - self._X, self._X2, self._params = np.empty(shape=(3, 1)) - - # a set of optional args to pass to weave - weave_options_openmp = {'headers' : [''], - 'extra_compile_args': ['-fopenmp -O3'], - 'extra_link_args' : ['-lgomp'], - 'libraries': ['gomp']} - weave_options_noopenmp = {'extra_compile_args': ['-O3']} - - - if config.getboolean('parallel', 'openmp'): - self.weave_options = weave_options_openmp - self.weave_support_code = """ - #include - #include - """ - else: - self.weave_options = weave_options_noopenmp - self.weave_support_code = """ - #include - """ - - def _get_params(self): - return self.variances - - def _set_params(self, x): - assert x.size == (self.num_params) - self.variances = x - self.variances2 = np.square(self.variances) - - def _get_param_names(self): - if self.num_params == 1: - return ['variance'] - else: - return ['variance_%i' % i for i in range(self.variances.size)] - - def K(self, X, X2, target): - if self.ARD: - XX = X * np.sqrt(self.variances) - if X2 is None: - target += tdot(XX) - else: - XX2 = X2 * np.sqrt(self.variances) - target += np.dot(XX, XX2.T) - else: - self._K_computations(X, X2) - target += self.variances * self._dot_product - - def Kdiag(self, X, target): - np.add(target, np.sum(self.variances * np.square(X), -1), target) - - def dK_dtheta(self, dL_dK, X, X2, target): - if self.ARD: - if X2 is None: - [np.add(target[i:i + 1], np.sum(dL_dK * tdot(X[:, i:i + 1])), target[i:i + 1]) for i in range(self.input_dim)] - else: - product = X[:, None, :] * X2[None, :, :] - target += (dL_dK[:, :, None] * product).sum(0).sum(0) - else: - self._K_computations(X, X2) - target += np.sum(self._dot_product * dL_dK) - - def dKdiag_dtheta(self, dL_dKdiag, X, target): - tmp = dL_dKdiag[:, None] * X ** 2 - if self.ARD: - target += tmp.sum(0) - else: - target += tmp.sum() - - def dK_dX(self, dL_dK, X, X2, target): - if X2 is None: - target += 2*(((X[None,:, :] * self.variances)) * dL_dK[:, :, None]).sum(1) - else: - target += (((X2[None,:, :] * self.variances)) * dL_dK[:, :, None]).sum(1) - - def dKdiag_dX(self,dL_dKdiag,X,target): - target += 2.*self.variances*dL_dKdiag[:,None]*X - - #---------------------------------------# - # PSI statistics # - #---------------------------------------# - - def psi0(self, Z, mu, S, target): - self._psi_computations(Z, mu, S) - target += np.sum(self.variances * self.mu2_S, 1) - - def dpsi0_dtheta(self, dL_dpsi0, Z, mu, S, target): - self._psi_computations(Z, mu, S) - tmp = dL_dpsi0[:, None] * self.mu2_S - if self.ARD: - target += tmp.sum(0) - else: - target += tmp.sum() - - def dpsi0_dmuS(self, dL_dpsi0, Z, mu, S, target_mu, target_S): - target_mu += dL_dpsi0[:, None] * (2.0 * mu * self.variances) - target_S += dL_dpsi0[:, None] * self.variances - - def psi1(self, Z, mu, S, target): - """the variance, it does nothing""" - self._psi1 = self.K(mu, Z, target) - - def dpsi1_dtheta(self, dL_dpsi1, Z, mu, S, target): - """the variance, it does nothing""" - self.dK_dtheta(dL_dpsi1, mu, Z, target) - - def dpsi1_dmuS(self, dL_dpsi1, Z, mu, S, target_mu, target_S): - """Do nothing for S, it does not affect psi1""" - self._psi_computations(Z, mu, S) - target_mu += (dL_dpsi1[:, :, None] * (Z * self.variances)).sum(1) - - def dpsi1_dZ(self, dL_dpsi1, Z, mu, S, target): - self.dK_dX(dL_dpsi1.T, Z, mu, target) - - def psi2(self, Z, mu, S, target): - self._psi_computations(Z, mu, S) - target += self._psi2 - - def psi2_new(self,Z,mu,S,target): - tmp = np.zeros((mu.shape[0], Z.shape[0])) - self.K(mu,Z,tmp) - target += tmp[:,:,None]*tmp[:,None,:] + np.sum(S[:,None,None,:]*self.variances**2*Z[None,:,None,:]*Z[None,None,:,:],-1) - - def dpsi2_dtheta_new(self, dL_dpsi2, Z, mu, S, target): - tmp = np.zeros((mu.shape[0], Z.shape[0])) - self.K(mu,Z,tmp) - self.dK_dtheta(2.*np.sum(dL_dpsi2*tmp[:,None,:],2),mu,Z,target) - result= 2.*(dL_dpsi2[:,:,:,None]*S[:,None,None,:]*self.variances*Z[None,:,None,:]*Z[None,None,:,:]).sum(0).sum(0).sum(0) - if self.ARD: - target += result.sum(0).sum(0).sum(0) - else: - target += result.sum() - - def dpsi2_dtheta(self, dL_dpsi2, Z, mu, S, target): - self._psi_computations(Z, mu, S) - tmp = dL_dpsi2[:, :, :, None] * (self.ZAinner[:, :, None, :] * (2 * Z)[None, None, :, :]) - if self.ARD: - target += tmp.sum(0).sum(0).sum(0) - else: - target += tmp.sum() - - def dpsi2_dmuS_new(self, dL_dpsi2, Z, mu, S, target_mu, target_S): - tmp = np.zeros((mu.shape[0], Z.shape[0])) - self.K(mu,Z,tmp) - self.dK_dX(2.*np.sum(dL_dpsi2*tmp[:,None,:],2),mu,Z,target_mu) - - Zs = Z*self.variances - Zs_sq = Zs[:,None,:]*Zs[None,:,:] - target_S += (dL_dpsi2[:,:,:,None]*Zs_sq[None,:,:,:]).sum(1).sum(1) - - def dpsi2_dmuS(self, dL_dpsi2, Z, mu, S, target_mu, target_S): - """Think N,num_inducing,num_inducing,input_dim """ - self._psi_computations(Z, mu, S) - AZZA = self.ZA.T[:, None, :, None] * self.ZA[None, :, None, :] - AZZA = AZZA + AZZA.swapaxes(1, 2) - AZZA_2 = AZZA/2. - #muAZZA = np.tensordot(mu,AZZA,(-1,0)) - #target_mu_dummy, target_S_dummy = np.zeros_like(target_mu), np.zeros_like(target_S) - #target_mu_dummy += (dL_dpsi2[:, :, :, None] * muAZZA).sum(1).sum(1) - #target_S_dummy += (dL_dpsi2[:, :, :, None] * self.ZA[None, :, None, :] * self.ZA[None, None, :, :]).sum(1).sum(1) - - - if config.getboolean('parallel', 'openmp'): - pragma_string = "#pragma omp parallel for private(m,mm,q,qq,factor,tmp)" - else: - pragma_string = '' - - #Using weave, we can exploiut the symmetry of this problem: - code = """ - int n, m, mm,q,qq; - double factor,tmp; - %s - for(n=0;n' + k2.name - self.k1 = k1 - self.k2 = k2 - self._X, self._X2, self._params = np.empty(shape=(3,1)) - self._set_params(np.hstack((k1._get_params(),k2._get_params()))) - - def _get_params(self): - """return the value of the parameters.""" - return np.hstack((self.k1._get_params(), self.k2._get_params())) - - def _set_params(self,x): - """set the value of the parameters.""" - self.k1._set_params(x[:self.k1.num_params]) - self.k2._set_params(x[self.k1.num_params:]) - - def _get_param_names(self): - """return parameter names.""" - return [self.k1.name + '_' + param_name for param_name in self.k1._get_param_names()] + [self.k2.name + '_' + param_name for param_name in self.k2._get_param_names()] - - def K(self,X,X2,target): - self._K_computations(X,X2) - target += self._K1 * self._K2 - - def dK_dtheta(self,dL_dK,X,X2,target): - """derivative of the covariance matrix with respect to the parameters.""" - self._K_computations(X,X2) - if X2 is None: - self.k1.dK_dtheta(dL_dK*self._K2, X[:,:self.k1.input_dim], None, target[:self.k1.num_params]) - self.k2.dK_dtheta(dL_dK*self._K1, X[:,self.k1.input_dim:], None, target[self.k1.num_params:]) - else: - self.k1.dK_dtheta(dL_dK*self._K2, X[:,:self.k1.input_dim], X2[:,:self.k1.input_dim], target[:self.k1.num_params]) - self.k2.dK_dtheta(dL_dK*self._K1, X[:,self.k1.input_dim:], X2[:,self.k1.input_dim:], target[self.k1.num_params:]) - - def Kdiag(self,X,target): - """Compute the diagonal of the covariance matrix associated to X.""" - target1 = np.zeros(X.shape[0]) - target2 = np.zeros(X.shape[0]) - self.k1.Kdiag(X[:,:self.k1.input_dim],target1) - self.k2.Kdiag(X[:,self.k1.input_dim:],target2) - target += target1 * target2 - - def dKdiag_dtheta(self,dL_dKdiag,X,target): - K1 = np.zeros(X.shape[0]) - K2 = np.zeros(X.shape[0]) - self.k1.Kdiag(X[:,:self.k1.input_dim],K1) - self.k2.Kdiag(X[:,self.k1.input_dim:],K2) - self.k1.dKdiag_dtheta(dL_dKdiag*K2,X[:,:self.k1.input_dim],target[:self.k1.num_params]) - self.k2.dKdiag_dtheta(dL_dKdiag*K1,X[:,self.k1.input_dim:],target[self.k1.num_params:]) - - def dK_dX(self,dL_dK,X,X2,target): - """derivative of the covariance matrix with respect to X.""" - self._K_computations(X,X2) - self.k1.dK_dX(dL_dK*self._K2, X[:,:self.k1.input_dim], X2[:,:self.k1.input_dim], target) - self.k2.dK_dX(dL_dK*self._K1, X[:,self.k1.input_dim:], X2[:,self.k1.input_dim:], target) - - def dKdiag_dX(self, dL_dKdiag, X, target): - K1 = np.zeros(X.shape[0]) - K2 = np.zeros(X.shape[0]) - self.k1.Kdiag(X[:,0:self.k1.input_dim],K1) - self.k2.Kdiag(X[:,self.k1.input_dim:],K2) - - self.k1.dK_dX(dL_dKdiag*K2, X[:,:self.k1.input_dim], target) - self.k2.dK_dX(dL_dKdiag*K1, X[:,self.k1.input_dim:], target) - - def _K_computations(self,X,X2): - if not (np.array_equal(X,self._X) and np.array_equal(X2,self._X2) and np.array_equal(self._params , self._get_params())): - self._X = X.copy() - self._params == self._get_params().copy() - if X2 is None: - self._X2 = None - self._K1 = np.zeros((X.shape[0],X.shape[0])) - self._K2 = np.zeros((X.shape[0],X.shape[0])) - self.k1.K(X[:,:self.k1.input_dim],None,self._K1) - self.k2.K(X[:,self.k1.input_dim:],None,self._K2) - else: - self._X2 = X2.copy() - self._K1 = np.zeros((X.shape[0],X2.shape[0])) - self._K2 = np.zeros((X.shape[0],X2.shape[0])) - self.k1.K(X[:,:self.k1.input_dim],X2[:,:self.k1.input_dim],self._K1) - self.k2.K(X[:,self.k1.input_dim:],X2[:,self.k1.input_dim:],self._K2) - diff --git a/GPy/kern/parts/rational_quadratic.py b/GPy/kern/parts/rational_quadratic.py deleted file mode 100644 index a75a5b11..00000000 --- a/GPy/kern/parts/rational_quadratic.py +++ /dev/null @@ -1,82 +0,0 @@ -# Copyright (c) 2012, GPy authors (see AUTHORS.txt). -# Licensed under the BSD 3-clause license (see LICENSE.txt) - - -from kernpart import Kernpart -import numpy as np - -class RationalQuadratic(Kernpart): - """ - rational quadratic kernel - - .. math:: - - k(r) = \sigma^2 \\bigg( 1 + \\frac{r^2}{2 \ell^2} \\bigg)^{- \\alpha} \ \ \ \ \ \\text{ where } r^2 = (x-y)^2 - - :param input_dim: the number of input dimensions - :type input_dim: int (input_dim=1 is the only value currently supported) - :param variance: the variance :math:`\sigma^2` - :type variance: float - :param lengthscale: the lengthscale :math:`\ell` - :type lengthscale: float - :param power: the power :math:`\\alpha` - :type power: float - :rtype: Kernpart object - - """ - def __init__(self,input_dim,variance=1.,lengthscale=1.,power=1.): - assert input_dim == 1, "For this kernel we assume input_dim=1" - self.input_dim = input_dim - self.num_params = 3 - self.name = 'rat_quad' - self.variance = variance - self.lengthscale = lengthscale - self.power = power - - def _get_params(self): - return np.hstack((self.variance,self.lengthscale,self.power)) - - def _set_params(self,x): - self.variance = x[0] - self.lengthscale = x[1] - self.power = x[2] - - def _get_param_names(self): - return ['variance','lengthscale','power'] - - def K(self,X,X2,target): - if X2 is None: X2 = X - dist2 = np.square((X-X2.T)/self.lengthscale) - target += self.variance*(1 + dist2/2.)**(-self.power) - - def Kdiag(self,X,target): - target += self.variance - - def dK_dtheta(self,dL_dK,X,X2,target): - if X2 is None: X2 = X - dist2 = np.square((X-X2.T)/self.lengthscale) - - dvar = (1 + dist2/2.)**(-self.power) - dl = self.power * self.variance * dist2 / self.lengthscale * (1 + dist2/2.)**(-self.power-1) - dp = - self.variance * np.log(1 + dist2/2.) * (1 + dist2/2.)**(-self.power) - - target[0] += np.sum(dvar*dL_dK) - target[1] += np.sum(dl*dL_dK) - target[2] += np.sum(dp*dL_dK) - - def dKdiag_dtheta(self,dL_dKdiag,X,target): - target[0] += np.sum(dL_dKdiag) - # here self.lengthscale and self.power have no influence on Kdiag so target[1:] are unchanged - - def dK_dX(self,dL_dK,X,X2,target): - """derivative of the covariance matrix with respect to X.""" - if X2 is None: - dist2 = np.square((X-X.T)/self.lengthscale) - dX = -2.*self.variance*self.power * (X-X.T)/self.lengthscale**2 * (1 + dist2/2./self.lengthscale)**(-self.power-1) - else: - dist2 = np.square((X-X2.T)/self.lengthscale) - dX = -self.variance*self.power * (X-X2.T)/self.lengthscale**2 * (1 + dist2/2./self.lengthscale)**(-self.power-1) - target += np.sum(dL_dK*dX,1)[:,np.newaxis] - - def dKdiag_dX(self,dL_dKdiag,X,target): - pass diff --git a/GPy/kern/parts/rbf.py b/GPy/kern/parts/rbf.py deleted file mode 100644 index dbc689d5..00000000 --- a/GPy/kern/parts/rbf.py +++ /dev/null @@ -1,369 +0,0 @@ -# Copyright (c) 2012, GPy authors (see AUTHORS.txt). -# Licensed under the BSD 3-clause license (see LICENSE.txt) - - -from kernpart import Kernpart -import numpy as np -from scipy import weave -from ...util.linalg import tdot -from ...util.misc import fast_array_equal -from ...util.config import * - -class RBF(Kernpart): - """ - Radial Basis Function kernel, aka squared-exponential, exponentiated quadratic or Gaussian kernel: - - .. math:: - - k(r) = \sigma^2 \exp \\bigg(- \\frac{1}{2} r^2 \\bigg) \ \ \ \ \ \\text{ where } r^2 = \sum_{i=1}^d \\frac{ (x_i-x^\prime_i)^2}{\ell_i^2} - - where \ell_i is the lengthscale, \sigma^2 the variance and d the dimensionality of the input. - - :param input_dim: the number of input dimensions - :type input_dim: int - :param variance: the variance of the kernel - :type variance: float - :param lengthscale: the vector of lengthscale of the kernel - :type lengthscale: array or list of the appropriate size (or float if there is only one lengthscale parameter) - :param ARD: Auto Relevance Determination. If equal to "False", the kernel is isotropic (ie. one single lengthscale parameter \ell), otherwise there is one lengthscale parameter per dimension. - :type ARD: Boolean - :rtype: kernel object - - .. Note: this object implements both the ARD and 'spherical' version of the function - """ - - def __init__(self, input_dim, variance=1., lengthscale=None, ARD=False): - self.input_dim = input_dim - self.name = 'rbf' - self.ARD = ARD - if not ARD: - self.num_params = 2 - if lengthscale is not None: - lengthscale = np.asarray(lengthscale) - assert lengthscale.size == 1, "Only one lengthscale needed for non-ARD kernel" - else: - lengthscale = np.ones(1) - else: - self.num_params = self.input_dim + 1 - if lengthscale is not None: - lengthscale = np.asarray(lengthscale) - assert lengthscale.size == self.input_dim, "bad number of lengthscales" - else: - lengthscale = np.ones(self.input_dim) - - self._set_params(np.hstack((variance, lengthscale.flatten()))) - - # initialize cache - self._Z, self._mu, self._S = np.empty(shape=(3, 1)) - self._X, self._X2, self._params = np.empty(shape=(3, 1)) - - # a set of optional args to pass to weave - weave_options_openmp = {'headers' : [''], - 'extra_compile_args': ['-fopenmp -O3'], - 'extra_link_args' : ['-lgomp'], - 'libraries': ['gomp']} - weave_options_noopenmp = {'extra_compile_args': ['-O3']} - - - - if config.getboolean('parallel', 'openmp'): - self.weave_options = weave_options_openmp - self.weave_support_code = """ - #include - #include - """ - else: - self.weave_options = weave_options_noopenmp - self.weave_support_code = """ - #include - """ - - - def _get_params(self): - return np.hstack((self.variance, self.lengthscale)) - - def _set_params(self, x): - assert x.size == (self.num_params) - self.variance = x[0] - self.lengthscale = x[1:] - self.lengthscale2 = np.square(self.lengthscale) - # reset cached results - self._X, self._X2, self._params = np.empty(shape=(3, 1)) - self._Z, self._mu, self._S = np.empty(shape=(3, 1)) # cached versions of Z,mu,S - - def _get_param_names(self): - if self.num_params == 2: - return ['variance', 'lengthscale'] - else: - return ['variance'] + ['lengthscale_%i' % i for i in range(self.lengthscale.size)] - - def K(self, X, X2, target): - self._K_computations(X, X2) - target += self.variance * self._K_dvar - - def Kdiag(self, X, target): - np.add(target, self.variance, target) - - def dK_dtheta(self, dL_dK, X, X2, target): - self._K_computations(X, X2) - target[0] += np.sum(self._K_dvar * dL_dK) - if self.ARD: - dvardLdK = self._K_dvar * dL_dK - var_len3 = self.variance / np.power(self.lengthscale, 3) - if X2 is None: - # save computation for the symmetrical case - dvardLdK = dvardLdK + dvardLdK.T - code = """ - int q,i,j; - double tmp; - for(q=0; q - """ % pragma_string - - N, num_inducing, input_dim = int(N), int(num_inducing), int(input_dim) - weave.inline(code, support_code=support_code, - arg_names=['N', 'num_inducing', 'input_dim', 'mu', 'Zhat', 'mudist_sq', 'mudist', 'lengthscale2', '_psi2_denom', 'psi2_Zdist_sq', 'psi2_exponent', 'half_log_psi2_denom', 'psi2', 'variance_sq'], - type_converters=weave.converters.blitz, **self.weave_options) - - return mudist, mudist_sq, psi2_exponent, psi2 diff --git a/GPy/kern/parts/rbfcos.py b/GPy/kern/parts/rbfcos.py deleted file mode 100644 index 4d09dfdb..00000000 --- a/GPy/kern/parts/rbfcos.py +++ /dev/null @@ -1,117 +0,0 @@ - -# Copyright (c) 2012, James Hensman and Andrew Gordon Wilson -# Licensed under the BSD 3-clause license (see LICENSE.txt) - - -from kernpart import Kernpart -import numpy as np - -class RBFCos(Kernpart): - def __init__(self,input_dim,variance=1.,frequencies=None,bandwidths=None,ARD=False): - self.input_dim = input_dim - self.name = 'rbfcos' - if self.input_dim>10: - print "Warning: the rbfcos kernel requires a lot of memory for high dimensional inputs" - self.ARD = ARD - - #set the default frequencies and bandwidths, appropriate num_params - if ARD: - self.num_params = 2*self.input_dim + 1 - if frequencies is not None: - frequencies = np.asarray(frequencies) - assert frequencies.size == self.input_dim, "bad number of frequencies" - else: - frequencies = np.ones(self.input_dim) - if bandwidths is not None: - bandwidths = np.asarray(bandwidths) - assert bandwidths.size == self.input_dim, "bad number of bandwidths" - else: - bandwidths = np.ones(self.input_dim) - else: - self.num_params = 3 - if frequencies is not None: - frequencies = np.asarray(frequencies) - assert frequencies.size == 1, "Exactly one frequency needed for non-ARD kernel" - else: - frequencies = np.ones(1) - - if bandwidths is not None: - bandwidths = np.asarray(bandwidths) - assert bandwidths.size == 1, "Exactly one bandwidth needed for non-ARD kernel" - else: - bandwidths = np.ones(1) - - #initialise cache - self._X, self._X2, self._params = np.empty(shape=(3,1)) - - self._set_params(np.hstack((variance,frequencies.flatten(),bandwidths.flatten()))) - - - def _get_params(self): - return np.hstack((self.variance,self.frequencies, self.bandwidths)) - - def _set_params(self,x): - assert x.size==(self.num_params) - if self.ARD: - self.variance = x[0] - self.frequencies = x[1:1+self.input_dim] - self.bandwidths = x[1+self.input_dim:] - else: - self.variance, self.frequencies, self.bandwidths = x - - def _get_param_names(self): - if self.num_params == 3: - return ['variance','frequency','bandwidth'] - else: - return ['variance']+['frequency_%i'%i for i in range(self.input_dim)]+['bandwidth_%i'%i for i in range(self.input_dim)] - - def K(self,X,X2,target): - self._K_computations(X,X2) - target += self.variance*self._dvar - - def Kdiag(self,X,target): - np.add(target,self.variance,target) - - def dK_dtheta(self,dL_dK,X,X2,target): - self._K_computations(X,X2) - target[0] += np.sum(dL_dK*self._dvar) - if self.ARD: - for q in xrange(self.input_dim): - target[q+1] += -2.*np.pi*self.variance*np.sum(dL_dK*self._dvar*np.tan(2.*np.pi*self._dist[:,:,q]*self.frequencies[q])*self._dist[:,:,q]) - target[q+1+self.input_dim] += -2.*np.pi**2*self.variance*np.sum(dL_dK*self._dvar*self._dist2[:,:,q]) - else: - target[1] += -2.*np.pi*self.variance*np.sum(dL_dK*self._dvar*np.sum(np.tan(2.*np.pi*self._dist*self.frequencies)*self._dist,-1)) - target[2] += -2.*np.pi**2*self.variance*np.sum(dL_dK*self._dvar*self._dist2.sum(-1)) - - - def dKdiag_dtheta(self,dL_dKdiag,X,target): - target[0] += np.sum(dL_dKdiag) - - def dK_dX(self,dL_dK,X,X2,target): - #TODO!!! - raise NotImplementedError - - def dKdiag_dX(self,dL_dKdiag,X,target): - pass - - def _K_computations(self,X,X2): - if not (np.all(X==self._X) and np.all(X2==self._X2)): - if X2 is None: X2 = X - self._X = X.copy() - self._X2 = X2.copy() - - #do the distances: this will be high memory for large input_dim - #NB: we don't take the abs of the dist because cos is symmetric - self._dist = X[:,None,:] - X2[None,:,:] - self._dist2 = np.square(self._dist) - - #ensure the next section is computed: - self._params = np.empty(self.num_params) - - if not np.all(self._params == self._get_params()): - self._params == self._get_params().copy() - - self._rbf_part = np.exp(-2.*np.pi**2*np.sum(self._dist2*self.bandwidths,-1)) - self._cos_part = np.prod(np.cos(2.*np.pi*self._dist*self.frequencies),-1) - self._dvar = self._rbf_part*self._cos_part - diff --git a/GPy/kern/parts/sympykern.py b/GPy/kern/parts/sympykern.py deleted file mode 100644 index a839437b..00000000 --- a/GPy/kern/parts/sympykern.py +++ /dev/null @@ -1,461 +0,0 @@ -import numpy as np -import sympy as sp -from sympy.utilities.codegen import codegen -from sympy.core.cache import clear_cache -from scipy import weave -import re -import os -import sys -current_dir = os.path.dirname(os.path.abspath(__file__)) -import tempfile -import pdb -import ast -from kernpart import Kernpart -from ...util.config import config - -class spkern(Kernpart): - """ - A kernel object, where all the hard work in done by sympy. - - :param k: the covariance function - :type k: a positive definite sympy function of x_0, z_0, x_1, z_1, x_2, z_2... - - To construct a new sympy kernel, you'll need to define: - - a kernel function using a sympy object. Ensure that the kernel is of the form k(x,z). - - that's it! we'll extract the variables from the function k. - - Note: - - to handle multiple inputs, call them x_1, z_1, etc - - to handle multpile correlated outputs, you'll need to add parameters with an index, such as lengthscale_i and lengthscale_j. - """ - def __init__(self, input_dim, k=None, output_dim=1, name=None, param=None): - if name is None: - self.name='sympykern' - else: - self.name = name - if k is None: - raise ValueError, "You must provide an argument for the covariance function." - self._sp_k = k - sp_vars = [e for e in k.atoms() if e.is_Symbol] - self._sp_x= sorted([e for e in sp_vars if e.name[0:2]=='x_'],key=lambda x:int(x.name[2:])) - self._sp_z= sorted([e for e in sp_vars if e.name[0:2]=='z_'],key=lambda z:int(z.name[2:])) - # Check that variable names make sense. - assert all([x.name=='x_%i'%i for i,x in enumerate(self._sp_x)]) - assert all([z.name=='z_%i'%i for i,z in enumerate(self._sp_z)]) - assert len(self._sp_x)==len(self._sp_z) - self.input_dim = len(self._sp_x) - self._real_input_dim = self.input_dim - if output_dim > 1: - self.input_dim += 1 - assert self.input_dim == input_dim - self.output_dim = output_dim - # extract parameter names - thetas = sorted([e for e in sp_vars if not (e.name[0:2]=='x_' or e.name[0:2]=='z_')],key=lambda e:e.name) - - - # Look for parameters with index. - if self.output_dim>1: - self._sp_theta_i = sorted([e for e in thetas if (e.name[-2:]=='_i')], key=lambda e:e.name) - self._sp_theta_j = sorted([e for e in thetas if (e.name[-2:]=='_j')], key=lambda e:e.name) - # Make sure parameter appears with both indices! - assert len(self._sp_theta_i)==len(self._sp_theta_j) - assert all([theta_i.name[:-2]==theta_j.name[:-2] for theta_i, theta_j in zip(self._sp_theta_i, self._sp_theta_j)]) - - # Extract names of shared parameters - self._sp_theta = [theta for theta in thetas if theta not in self._sp_theta_i and theta not in self._sp_theta_j] - - self.num_split_params = len(self._sp_theta_i) - self._split_theta_names = ["%s"%theta.name[:-2] for theta in self._sp_theta_i] - for theta in self._split_theta_names: - setattr(self, theta, np.ones(self.output_dim)) - - self.num_shared_params = len(self._sp_theta) - self.num_params = self.num_shared_params+self.num_split_params*self.output_dim - - else: - self.num_split_params = 0 - self._split_theta_names = [] - self._sp_theta = thetas - self.num_shared_params = len(self._sp_theta) - self.num_params = self.num_shared_params - - for theta in self._sp_theta: - val = 1.0 - if param is not None: - if param.has_key(theta): - val = param[theta] - setattr(self, theta.name, val) - #deal with param - self._set_params(self._get_params()) - - #Differentiate! - self._sp_dk_dtheta = [sp.diff(k,theta).simplify() for theta in self._sp_theta] - if self.output_dim > 1: - self._sp_dk_dtheta_i = [sp.diff(k,theta).simplify() for theta in self._sp_theta_i] - - self._sp_dk_dx = [sp.diff(k,xi).simplify() for xi in self._sp_x] - - if False: - self.compute_psi_stats() - - self._gen_code() - - if False: - extra_compile_args = ['-ftree-vectorize', '-mssse3', '-ftree-vectorizer-verbose=5'] - else: - extra_compile_args = [] - - self.weave_kwargs = { - 'support_code':self._function_code, - 'include_dirs':[tempfile.gettempdir(), current_dir], - 'headers':['"sympy_helpers.h"'], - 'sources':[os.path.join(current_dir,"sympy_helpers.cpp")], - 'extra_compile_args':extra_compile_args, - 'extra_link_args':[], - 'verbose':True} - if config.getboolean('parallel', 'openmp'): self.weave_kwargs.append('-lgomp') - - def __add__(self,other): - return spkern(self._sp_k+other._sp_k) - - def _gen_code(self): - """Generates the C functions necessary for computing the covariance function using the sympy objects as input.""" - #TODO: maybe generate one C function only to save compile time? Also easier to take that as a basis and hand craft other covariances?? - - #generate c functions from sympy objects - argument_sequence = self._sp_x+self._sp_z+self._sp_theta - code_list = [('k',self._sp_k)] - # gradients with respect to covariance input - code_list += [('dk_d%s'%x.name,dx) for x,dx in zip(self._sp_x,self._sp_dk_dx)] - # gradient with respect to parameters - code_list += [('dk_d%s'%theta.name,dtheta) for theta,dtheta in zip(self._sp_theta,self._sp_dk_dtheta)] - # gradient with respect to multiple output parameters - if self.output_dim > 1: - argument_sequence += self._sp_theta_i + self._sp_theta_j - code_list += [('dk_d%s'%theta.name,dtheta) for theta,dtheta in zip(self._sp_theta_i,self._sp_dk_dtheta_i)] - (foo_c,self._function_code), (foo_h,self._function_header) = \ - codegen(code_list, "C",'foobar',argument_sequence=argument_sequence) - #put the header file where we can find it - f = file(os.path.join(tempfile.gettempdir(),'foobar.h'),'w') - f.write(self._function_header) - f.close() - - # Substitute any known derivatives which sympy doesn't compute - self._function_code = re.sub('DiracDelta\(.+?,.+?\)','0.0',self._function_code) - - - ############################################################ - # This is the basic argument construction for the C code. # - ############################################################ - - arg_list = (["X2(i, %s)"%x.name[2:] for x in self._sp_x] - + ["Z2(j, %s)"%z.name[2:] for z in self._sp_z]) - - # for multiple outputs need to also provide these arguments reversed. - if self.output_dim>1: - reverse_arg_list = list(arg_list) - reverse_arg_list.reverse() - - # Add in any 'shared' parameters to the list. - param_arg_list = [shared_params.name for shared_params in self._sp_theta] - arg_list += param_arg_list - - precompute_list=[] - if self.output_dim > 1: - reverse_arg_list+=list(param_arg_list) - split_param_arg_list = ["%s1(%s)"%(theta.name[:-2].upper(),index) for index in ['ii', 'jj'] for theta in self._sp_theta_i] - split_param_reverse_arg_list = ["%s1(%s)"%(theta.name[:-2].upper(),index) for index in ['jj', 'ii'] for theta in self._sp_theta_i] - arg_list += split_param_arg_list - reverse_arg_list += split_param_reverse_arg_list - # Extract the right output indices from the inputs. - c_define_output_indices = [' '*16 + "int %s=(int)%s(%s, %i);"%(index, var, index2, self.input_dim-1) for index, var, index2 in zip(['ii', 'jj'], ['X2', 'Z2'], ['i', 'j'])] - precompute_list += c_define_output_indices - reverse_arg_string = ", ".join(reverse_arg_list) - arg_string = ", ".join(arg_list) - precompute_string = "\n".join(precompute_list) - - # Code to compute argments string needed when only X is provided. - X_arg_string = re.sub('Z','X',arg_string) - # Code to compute argument string when only diagonal is required. - diag_arg_string = re.sub('int jj','//int jj',X_arg_string) - diag_arg_string = re.sub('j','i',diag_arg_string) - if precompute_string == '': - # if it's not multioutput, the precompute strings are set to zero - diag_precompute_string = '' - diag_precompute_replace = '' - else: - # for multioutput we need to extract the index of the output form the input. - diag_precompute_string = precompute_list[0] - diag_precompute_replace = precompute_list[1] - - - # Here's the code to do the looping for K - self._K_code =\ - """ - // _K_code - // Code for computing the covariance function. - int i; - int j; - int N = target_array->dimensions[0]; - int num_inducing = target_array->dimensions[1]; - int input_dim = X_array->dimensions[1]; - //#pragma omp parallel for private(j) - for (i=0;idimensions[0]; - int num_inducing = target_array->dimensions[1]; - int input_dim = X_array->dimensions[1]; - //#pragma omp parallel for private(j) - for (i=0;idimensions[0]; - int input_dim = X_array->dimensions[1]; - //#pragma omp parallel for - for (i=0;i1: - grad_func_list += c_define_output_indices - grad_func_list += [' '*16 + 'TARGET1(%i+ii) += PARTIAL2(i, j)*dk_d%s(%s);'%(self.num_shared_params+i*self.output_dim, theta.name, arg_string) for i, theta in enumerate(self._sp_theta_i)] - grad_func_list += [' '*16 + 'TARGET1(%i+jj) += PARTIAL2(i, j)*dk_d%s(%s);'%(self.num_shared_params+i*self.output_dim, theta.name, reverse_arg_string) for i, theta in enumerate(self._sp_theta_i)] - grad_func_list += ([' '*16 + 'TARGET1(%i) += PARTIAL2(i, j)*dk_d%s(%s);'%(i,theta.name,arg_string) for i,theta in enumerate(self._sp_theta)]) - grad_func_string = '\n'.join(grad_func_list) - - self._dK_dtheta_code =\ - """ - // _dK_dtheta_code - // Code for computing gradient of covariance with respect to parameters. - int i; - int j; - int N = partial_array->dimensions[0]; - int num_inducing = partial_array->dimensions[1]; - int input_dim = X_array->dimensions[1]; - //#pragma omp parallel for private(j) - for (i=0;idimensions[0]; - int input_dim = X_array->dimensions[1]; - for (i=0;i1: - gradX_func_list += c_define_output_indices - gradX_func_list += ["TARGET2(i, %i) += PARTIAL2(i, j)*dk_dx_%i(%s);"%(q,q,arg_string) for q in range(self._real_input_dim)] - gradX_func_string = "\n".join(gradX_func_list) - - self._dK_dX_code = \ - """ - // _dK_dX_code - // Code for computing gradient of covariance with respect to inputs. - int i; - int j; - int N = partial_array->dimensions[0]; - int num_inducing = partial_array->dimensions[1]; - int input_dim = X_array->dimensions[1]; - //#pragma omp parallel for private(j) - for (i=0;idimensions[0]; - int input_dim = X_array->dimensions[1]; - for (int i=0;i1: - arg_names += self._split_theta_names - arg_names += ['output_dim'] - return arg_names - - def _weave_inline(self, code, X, target, Z=None, partial=None): - output_dim = self.output_dim - for shared_params in self._sp_theta: - locals()[shared_params.name] = getattr(self, shared_params.name) - - # Need to extract parameters first - for split_params in self._split_theta_names: - locals()[split_params] = getattr(self, split_params) - arg_names = self._get_arg_names(Z, partial) - weave.inline(code=code, arg_names=arg_names,**self.weave_kwargs) - - def K(self,X,Z,target): - if Z is None: - self._weave_inline(self._K_code_X, X, target) - else: - self._weave_inline(self._K_code, X, target, Z) - - - def Kdiag(self,X,target): - self._weave_inline(self._Kdiag_code, X, target) - - def dK_dtheta(self,partial,X,Z,target): - if Z is None: - self._weave_inline(self._dK_dtheta_code_X, X, target, Z, partial) - else: - self._weave_inline(self._dK_dtheta_code, X, target, Z, partial) - - def dKdiag_dtheta(self,partial,X,target): - self._weave_inline(self._dKdiag_dtheta_code, X, target, Z=None, partial=partial) - - def dK_dX(self,partial,X,Z,target): - if Z is None: - self._weave_inline(self._dK_dX_code_X, X, target, Z, partial) - else: - self._weave_inline(self._dK_dX_code, X, target, Z, partial) - - def dKdiag_dX(self,partial,X,target): - self._weave_inline(self._dKdiag_dX_code, X, target, Z=None, partial=partial) - - def compute_psi_stats(self): - #define some normal distributions - mus = [sp.var('mu_%i'%i,real=True) for i in range(self.input_dim)] - Ss = [sp.var('S_%i'%i,positive=True) for i in range(self.input_dim)] - normals = [(2*sp.pi*Si)**(-0.5)*sp.exp(-0.5*(xi-mui)**2/Si) for xi, mui, Si in zip(self._sp_x, mus, Ss)] - - #do some integration! - #self._sp_psi0 = ?? - self._sp_psi1 = self._sp_k - for i in range(self.input_dim): - print 'perfoming integrals %i of %i'%(i+1,2*self.input_dim) - sys.stdout.flush() - self._sp_psi1 *= normals[i] - self._sp_psi1 = sp.integrate(self._sp_psi1,(self._sp_x[i],-sp.oo,sp.oo)) - clear_cache() - self._sp_psi1 = self._sp_psi1.simplify() - - #and here's psi2 (eek!) - zprime = [sp.Symbol('zp%i'%i) for i in range(self.input_dim)] - self._sp_psi2 = self._sp_k.copy()*self._sp_k.copy().subs(zip(self._sp_z,zprime)) - for i in range(self.input_dim): - print 'perfoming integrals %i of %i'%(self.input_dim+i+1,2*self.input_dim) - sys.stdout.flush() - self._sp_psi2 *= normals[i] - self._sp_psi2 = sp.integrate(self._sp_psi2,(self._sp_x[i],-sp.oo,sp.oo)) - clear_cache() - self._sp_psi2 = self._sp_psi2.simplify() - - - def _set_params(self,param): - assert param.size == (self.num_params) - for i, shared_params in enumerate(self._sp_theta): - setattr(self, shared_params.name, param[i]) - - if self.output_dim>1: - for i, split_params in enumerate(self._split_theta_names): - start = self.num_shared_params + i*self.output_dim - end = self.num_shared_params + (i+1)*self.output_dim - setattr(self, split_params, param[start:end]) - - - def _get_params(self): - params = np.zeros(0) - for shared_params in self._sp_theta: - params = np.hstack((params, getattr(self, shared_params.name))) - if self.output_dim>1: - for split_params in self._split_theta_names: - params = np.hstack((params, getattr(self, split_params).flatten())) - return params - - def _get_param_names(self): - if self.output_dim>1: - return [x.name for x in self._sp_theta] + [x.name[:-2] + str(i) for x in self._sp_theta_i for i in range(self.output_dim)] - else: - return [x.name for x in self._sp_theta] diff --git a/GPy/kern/parts/white.py b/GPy/kern/parts/white.py deleted file mode 100644 index 49200bd6..00000000 --- a/GPy/kern/parts/white.py +++ /dev/null @@ -1,84 +0,0 @@ -# Copyright (c) 2012, GPy authors (see AUTHORS.txt). -# Licensed under the BSD 3-clause license (see LICENSE.txt) - -from kernpart import Kernpart -import numpy as np - -class White(Kernpart): - """ - White noise kernel. - - :param input_dim: the number of input dimensions - :type input_dim: int - :param variance: - :type variance: float - """ - def __init__(self,input_dim,variance=1.): - self.input_dim = input_dim - self.num_params = 1 - self.name = 'white' - self._set_params(np.array([variance]).flatten()) - self._psi1 = 0 # TODO: more elegance here - - def _get_params(self): - return self.variance - - def _set_params(self,x): - assert x.shape==(1,) - self.variance = x - - def _get_param_names(self): - return ['variance'] - - def K(self,X,X2,target): - if X2 is None: - target += np.eye(X.shape[0])*self.variance - - def Kdiag(self,X,target): - target += self.variance - - def dK_dtheta(self,dL_dK,X,X2,target): - if X2 is None: - target += np.trace(dL_dK) - - def dKdiag_dtheta(self,dL_dKdiag,X,target): - target += np.sum(dL_dKdiag) - - def dK_dX(self,dL_dK,X,X2,target): - pass - - def dKdiag_dX(self,dL_dKdiag,X,target): - pass - - def psi0(self,Z,mu,S,target): - pass # target += self.variance - - def dpsi0_dtheta(self,dL_dpsi0,Z,mu,S,target): - pass # target += dL_dpsi0.sum() - - def dpsi0_dmuS(self,dL_dpsi0,Z,mu,S,target_mu,target_S): - pass - - def psi1(self,Z,mu,S,target): - pass - - def dpsi1_dtheta(self,dL_dpsi1,Z,mu,S,target): - pass - - def dpsi1_dZ(self,dL_dpsi1,Z,mu,S,target): - pass - - def dpsi1_dmuS(self,dL_dpsi1,Z,mu,S,target_mu,target_S): - pass - - def psi2(self,Z,mu,S,target): - pass - - def dpsi2_dZ(self,dL_dpsi2,Z,mu,S,target): - pass - - def dpsi2_dtheta(self,dL_dpsi2,Z,mu,S,target): - pass - - def dpsi2_dmuS(self,dL_dpsi2,Z,mu,S,target_mu,target_S): - pass diff --git a/GPy/likelihoods/__init__.py b/GPy/likelihoods/__init__.py index b46b59ff..28e44541 100644 --- a/GPy/likelihoods/__init__.py +++ b/GPy/likelihoods/__init__.py @@ -1,7 +1,8 @@ -from ep import EP -from laplace import Laplace -from ep_mixed_noise import EP_Mixed_Noise +from bernoulli import Bernoulli +from exponential import Exponential from gaussian import Gaussian -from gaussian_mixed_noise import Gaussian_Mixed_Noise -import noise_models -from noise_model_constructors import * +from gamma import Gamma +from poisson import Poisson +from student_t import StudentT +from likelihood import Likelihood +from mixed_noise import MixedNoise diff --git a/GPy/likelihoods/bernoulli.py b/GPy/likelihoods/bernoulli.py new file mode 100644 index 00000000..596b9dc3 --- /dev/null +++ b/GPy/likelihoods/bernoulli.py @@ -0,0 +1,224 @@ +# Copyright (c) 2012-2014 The GPy authors (see AUTHORS.txt) +# Licensed under the BSD 3-clause license (see LICENSE.txt) + +import numpy as np +from ..util.univariate_Gaussian import std_norm_pdf, std_norm_cdf +import link_functions +from likelihood import Likelihood +from scipy import stats + +class Bernoulli(Likelihood): + """ + Bernoulli likelihood + + .. math:: + p(y_{i}|\\lambda(f_{i})) = \\lambda(f_{i})^{y_{i}}(1-f_{i})^{1-y_{i}} + + .. Note:: + Y takes values in either {-1, 1} or {0, 1}. + link function should have the domain [0, 1], e.g. probit (default) or Heaviside + + .. See also:: + likelihood.py, for the parent class + """ + def __init__(self, gp_link=None): + if gp_link is None: + gp_link = link_functions.Probit() + + super(Bernoulli, self).__init__(gp_link, 'Bernoulli') + + if isinstance(gp_link , (link_functions.Heaviside, link_functions.Probit)): + self.log_concave = True + + def _preprocess_values(self, Y): + """ + Check if the values of the observations correspond to the values + assumed by the likelihood function. + + ..Note:: Binary classification algorithm works better with classes {-1, 1} + """ + Y_prep = Y.copy() + Y1 = Y[Y.flatten()==1].size + Y2 = Y[Y.flatten()==0].size + assert Y1 + Y2 == Y.size, 'Bernoulli likelihood is meant to be used only with outputs in {0, 1}.' + Y_prep[Y.flatten() == 0] = -1 + return Y_prep + + def moments_match_ep(self, Y_i, tau_i, v_i): + """ + Moments match of the marginal approximation in EP algorithm + + :param i: number of observation (int) + :param tau_i: precision of the cavity distribution (float) + :param v_i: mean/variance of the cavity distribution (float) + """ + if Y_i == 1: + sign = 1. + elif Y_i == 0 or Y_i == -1: + sign = -1 + else: + raise ValueError("bad value for Bernoulli observation (0, 1)") + if isinstance(self.gp_link, link_functions.Probit): + z = sign*v_i/np.sqrt(tau_i**2 + tau_i) + Z_hat = std_norm_cdf(z) + phi = std_norm_pdf(z) + mu_hat = v_i/tau_i + sign*phi/(Z_hat*np.sqrt(tau_i**2 + tau_i)) + sigma2_hat = 1./tau_i - (phi/((tau_i**2+tau_i)*Z_hat))*(z+phi/Z_hat) + + elif isinstance(self.gp_link, link_functions.Heaviside): + a = sign*v_i/np.sqrt(tau_i) + Z_hat = std_norm_cdf(a) + N = std_norm_pdf(a) + mu_hat = v_i/tau_i + sign*N/Z_hat/np.sqrt(tau_i) + sigma2_hat = (1. - a*N/Z_hat - np.square(N/Z_hat))/tau_i + else: + #TODO: do we want to revert to numerical quadrature here? + raise ValueError("Exact moment matching not available for link {}".format(self.gp_link.__name__)) + + return Z_hat, mu_hat, sigma2_hat + + def predictive_mean(self, mu, variance, Y_metadata=None): + + if isinstance(self.gp_link, link_functions.Probit): + return stats.norm.cdf(mu/np.sqrt(1+variance)) + + elif isinstance(self.gp_link, link_functions.Heaviside): + return stats.norm.cdf(mu/np.sqrt(variance)) + + else: + raise NotImplementedError + + def predictive_variance(self, mu, variance, pred_mean, Y_metadata=None): + + if isinstance(self.gp_link, link_functions.Heaviside): + return 0. + else: + return np.nan + + def pdf_link(self, inv_link_f, y, Y_metadata=None): + """ + Likelihood function given inverse link of f. + + .. math:: + p(y_{i}|\\lambda(f_{i})) = \\lambda(f_{i})^{y_{i}}(1-f_{i})^{1-y_{i}} + + :param inv_link_f: latent variables inverse link of f. + :type inv_link_f: Nx1 array + :param y: data + :type y: Nx1 array + :param Y_metadata: Y_metadata not used in bernoulli + :returns: likelihood evaluated for this point + :rtype: float + + .. Note: + Each y_i must be in {0, 1} + """ + #objective = (inv_link_f**y) * ((1.-inv_link_f)**(1.-y)) + return np.where(y, inv_link_f, 1.-inv_link_f) + + def logpdf_link(self, inv_link_f, y, Y_metadata=None): + """ + Log Likelihood function given inverse link of f. + + .. math:: + \\ln p(y_{i}|\\lambda(f_{i})) = y_{i}\\log\\lambda(f_{i}) + (1-y_{i})\\log (1-f_{i}) + + :param inv_link_f: latent variables inverse link of f. + :type inv_link_f: Nx1 array + :param y: data + :type y: Nx1 array + :param Y_metadata: Y_metadata not used in bernoulli + :returns: log likelihood evaluated at points inverse link of f. + :rtype: float + """ + #objective = y*np.log(inv_link_f) + (1.-y)*np.log(inv_link_f) + p = np.where(y==1, inv_link_f, 1.-inv_link_f) + return np.log(np.clip(p, 1e-6 ,np.inf)) + + def dlogpdf_dlink(self, inv_link_f, y, Y_metadata=None): + """ + Gradient of the pdf at y, given inverse link of f w.r.t inverse link of f. + + .. math:: + \\frac{d\\ln p(y_{i}|\\lambda(f_{i}))}{d\\lambda(f)} = \\frac{y_{i}}{\\lambda(f_{i})} - \\frac{(1 - y_{i})}{(1 - \\lambda(f_{i}))} + + :param inv_link_f: latent variables inverse link of f. + :type inv_link_f: Nx1 array + :param y: data + :type y: Nx1 array + :param Y_metadata: Y_metadata not used in bernoulli + :returns: gradient of log likelihood evaluated at points inverse link of f. + :rtype: Nx1 array + """ + #grad = (y/inv_link_f) - (1.-y)/(1-inv_link_f) + #grad = np.where(y, 1./inv_link_f, -1./(1-inv_link_f)) + ff = np.clip(inv_link_f, 1e-6, 1-1e-6) + denom = np.where(y, ff, -(1-ff)) + return 1./denom + + def d2logpdf_dlink2(self, inv_link_f, y, Y_metadata=None): + """ + Hessian at y, given inv_link_f, w.r.t inv_link_f the hessian will be 0 unless i == j + i.e. second derivative logpdf at y given inverse link of f_i and inverse link of f_j w.r.t inverse link of f_i and inverse link of f_j. + + + .. math:: + \\frac{d^{2}\\ln p(y_{i}|\\lambda(f_{i}))}{d\\lambda(f)^{2}} = \\frac{-y_{i}}{\\lambda(f)^{2}} - \\frac{(1-y_{i})}{(1-\\lambda(f))^{2}} + + :param inv_link_f: latent variables inverse link of f. + :type inv_link_f: Nx1 array + :param y: data + :type y: Nx1 array + :param Y_metadata: Y_metadata not used in bernoulli + :returns: Diagonal of log hessian matrix (second derivative of log likelihood evaluated at points inverse link of f. + :rtype: Nx1 array + + .. Note:: + Will return diagonal of hessian, since every where else it is 0, as the likelihood factorizes over cases + (the distribution for y_i depends only on inverse link of f_i not on inverse link of f_(j!=i) + """ + #d2logpdf_dlink2 = -y/(inv_link_f**2) - (1-y)/((1-inv_link_f)**2) + #d2logpdf_dlink2 = np.where(y, -1./np.square(inv_link_f), -1./np.square(1.-inv_link_f)) + arg = np.where(y, inv_link_f, 1.-inv_link_f) + ret = -1./np.square(np.clip(arg, 1e-3, np.inf)) + if np.any(np.isinf(ret)): + stop + return ret + + def d3logpdf_dlink3(self, inv_link_f, y, Y_metadata=None): + """ + Third order derivative log-likelihood function at y given inverse link of f w.r.t inverse link of f + + .. math:: + \\frac{d^{3} \\ln p(y_{i}|\\lambda(f_{i}))}{d^{3}\\lambda(f)} = \\frac{2y_{i}}{\\lambda(f)^{3}} - \\frac{2(1-y_{i}}{(1-\\lambda(f))^{3}} + + :param inv_link_f: latent variables passed through inverse link of f. + :type inv_link_f: Nx1 array + :param y: data + :type y: Nx1 array + :param Y_metadata: Y_metadata not used in bernoulli + :returns: third derivative of log likelihood evaluated at points inverse_link(f) + :rtype: Nx1 array + """ + assert np.atleast_1d(inv_link_f).shape == np.atleast_1d(y).shape + #d3logpdf_dlink3 = 2*(y/(inv_link_f**3) - (1-y)/((1-inv_link_f)**3)) + state = np.seterr(divide='ignore') + # TODO check y \in {0, 1} or {-1, 1} + d3logpdf_dlink3 = np.where(y, 2./(inv_link_f**3), -2./((1.-inv_link_f)**3)) + np.seterr(**state) + return d3logpdf_dlink3 + + def samples(self, gp, Y_metadata=None): + """ + Returns a set of samples of observations based on a given value of the latent variable. + + :param gp: latent variable + """ + orig_shape = gp.shape + gp = gp.flatten() + ns = np.ones_like(gp, dtype=int) + Ysim = np.random.binomial(ns, self.gp_link.transf(gp)) + return Ysim.reshape(orig_shape) + + def exact_inference_gradients(self, dL_dKdiag,Y_metadata=None): + pass diff --git a/GPy/likelihoods/ep.py b/GPy/likelihoods/ep.py deleted file mode 100644 index aa106067..00000000 --- a/GPy/likelihoods/ep.py +++ /dev/null @@ -1,392 +0,0 @@ -import numpy as np -from scipy import stats -from ..util.linalg import pdinv,mdot,jitchol,chol_inv,DSYR,tdot,dtrtrs -from likelihood import likelihood - -class EP(likelihood): - def __init__(self,data,noise_model): - """ - Expectation Propagation - - :param data: data to model - :type data: numpy array - :param noise_model: noise distribution - :type noise_model: A GPy noise model - - """ - self.noise_model = noise_model - self.data = data - self.num_data, self.output_dim = self.data.shape - self.is_heteroscedastic = True - self.num_params = 0 - - #Initial values - Likelihood approximation parameters: - #p(y|f) = t(f|tau_tilde,v_tilde) - self.tau_tilde = np.zeros(self.num_data) - self.v_tilde = np.zeros(self.num_data) - - #initial values for the GP variables - self.Y = np.zeros((self.num_data,1)) - self.covariance_matrix = np.eye(self.num_data) - self.precision = np.ones(self.num_data)[:,None] - self.Z = 0 - self.YYT = None - self.V = self.precision * self.Y - self.VVT_factor = self.V - self.trYYT = 0. - - super(EP, self).__init__() - - def restart(self): - self.tau_tilde = np.zeros(self.num_data) - self.v_tilde = np.zeros(self.num_data) - self.Y = np.zeros((self.num_data,1)) - self.covariance_matrix = np.eye(self.num_data) - self.precision = np.ones(self.num_data)[:,None] - self.Z = 0 - self.YYT = None - self.V = self.precision * self.Y - self.VVT_factor = self.V - self.trYYT = 0. - - def predictive_values(self,mu,var,full_cov,**noise_args): - if full_cov: - raise NotImplementedError, "Cannot make correlated predictions with an EP likelihood" - return self.noise_model.predictive_values(mu,var,**noise_args) - - def log_predictive_density(self, y_test, mu_star, var_star): - """ - Calculation of the log predictive density - - .. math: - p(y_{*}|D) = p(y_{*}|f_{*})p(f_{*}|\mu_{*}\\sigma^{2}_{*}) - - :param y_test: test observations (y_{*}) - :type y_test: (Nx1) array - :param mu_star: predictive mean of gaussian p(f_{*}|mu_{*}, var_{*}) - :type mu_star: (Nx1) array - :param var_star: predictive variance of gaussian p(f_{*}|mu_{*}, var_{*}) - :type var_star: (Nx1) array - """ - return self.noise_model.log_predictive_density(y_test, mu_star, var_star) - - def _get_params(self): - #return np.zeros(0) - return self.noise_model._get_params() - - def _get_param_names(self): - #return [] - return self.noise_model._get_param_names() - - def _set_params(self,p): - #pass # TODO: the EP likelihood might want to take some parameters... - self.noise_model._set_params(p) - - def _gradients(self,partial): - #return np.zeros(0) # TODO: the EP likelihood might want to take some parameters... - return self.noise_model._gradients(partial) - - def _compute_GP_variables(self): - #Variables to be called from GP - mu_tilde = self.v_tilde/self.tau_tilde #When calling EP, this variable is used instead of Y in the GP model - sigma_sum = 1./self.tau_ + 1./self.tau_tilde - mu_diff_2 = (self.v_/self.tau_ - mu_tilde)**2 - self.Z = np.sum(np.log(self.Z_hat)) + 0.5*np.sum(np.log(sigma_sum)) + 0.5*np.sum(mu_diff_2/sigma_sum) #Normalization constant, aka Z_ep - self.Z += 0.5*self.num_data*np.log(2*np.pi) - - self.Y = mu_tilde[:,None] - self.YYT = np.dot(self.Y,self.Y.T) - self.covariance_matrix = np.diag(1./self.tau_tilde) - self.precision = self.tau_tilde[:,None] - self.V = self.precision * self.Y - self.VVT_factor = self.V - self.trYYT = np.trace(self.YYT) - - def fit_full(self, K, epsilon=1e-3,power_ep=[1.,1.]): - """ - The expectation-propagation algorithm. - For nomenclature see Rasmussen & Williams 2006. - - :param epsilon: Convergence criterion, maximum squared difference allowed between mean updates to stop iterations (float) - :type epsilon: float - :param power_ep: Power EP parameters - :type power_ep: list of floats - - """ - self.epsilon = epsilon - self.eta, self.delta = power_ep - - #Initial values - Posterior distribution parameters: q(f|X,Y) = N(f|mu,Sigma) - mu = np.zeros(self.num_data) - Sigma = K.copy() - - """ - Initial values - Cavity distribution parameters: - q_(f|mu_,sigma2_) = Product{q_i(f|mu_i,sigma2_i)} - sigma_ = 1./tau_ - mu_ = v_/tau_ - """ - self.tau_ = np.empty(self.num_data,dtype=float) - self.v_ = np.empty(self.num_data,dtype=float) - - #Initial values - Marginal moments - z = np.empty(self.num_data,dtype=float) - self.Z_hat = np.empty(self.num_data,dtype=float) - phi = np.empty(self.num_data,dtype=float) - mu_hat = np.empty(self.num_data,dtype=float) - sigma2_hat = np.empty(self.num_data,dtype=float) - - #Approximation - epsilon_np1 = self.epsilon + 1. - epsilon_np2 = self.epsilon + 1. - self.iterations = 0 - self.np1 = [self.tau_tilde.copy()] - self.np2 = [self.v_tilde.copy()] - while epsilon_np1 > self.epsilon or epsilon_np2 > self.epsilon: - update_order = np.random.permutation(self.num_data) - for i in update_order: - #Cavity distribution parameters - self.tau_[i] = 1./Sigma[i,i] - self.eta*self.tau_tilde[i] - self.v_[i] = mu[i]/Sigma[i,i] - self.eta*self.v_tilde[i] - #Marginal moments - self.Z_hat[i], mu_hat[i], sigma2_hat[i] = self.noise_model.moments_match(self.data[i],self.tau_[i],self.v_[i]) - #Site parameters update - Delta_tau = self.delta/self.eta*(1./sigma2_hat[i] - 1./Sigma[i,i]) - Delta_v = self.delta/self.eta*(mu_hat[i]/sigma2_hat[i] - mu[i]/Sigma[i,i]) - self.tau_tilde[i] += Delta_tau - self.v_tilde[i] += Delta_v - #Posterior distribution parameters update - DSYR(Sigma,Sigma[:,i].copy(), -float(Delta_tau/(1.+ Delta_tau*Sigma[i,i]))) - mu = np.dot(Sigma,self.v_tilde) - self.iterations += 1 - #Sigma recomptutation with Cholesky decompositon - Sroot_tilde_K = np.sqrt(self.tau_tilde)[:,None]*K - B = np.eye(self.num_data) + np.sqrt(self.tau_tilde)[None,:]*Sroot_tilde_K - L = jitchol(B) - V,info = dtrtrs(L,Sroot_tilde_K,lower=1) - Sigma = K - np.dot(V.T,V) - mu = np.dot(Sigma,self.v_tilde) - epsilon_np1 = sum((self.tau_tilde-self.np1[-1])**2)/self.num_data - epsilon_np2 = sum((self.v_tilde-self.np2[-1])**2)/self.num_data - self.np1.append(self.tau_tilde.copy()) - self.np2.append(self.v_tilde.copy()) - - return self._compute_GP_variables() - - def fit_DTC(self, Kmm, Kmn, epsilon=1e-3,power_ep=[1.,1.]): - """ - The expectation-propagation algorithm with sparse pseudo-input. - For nomenclature see ... 2013. - - :param epsilon: Convergence criterion, maximum squared difference allowed between mean updates to stop iterations (float) - :type epsilon: float - :param power_ep: Power EP parameters - :type power_ep: list of floats - - """ - self.epsilon = epsilon - self.eta, self.delta = power_ep - - num_inducing = Kmm.shape[0] - - #TODO: this doesn't work with uncertain inputs! - - """ - Prior approximation parameters: - q(f|X) = int_{df}{N(f|KfuKuu_invu,diag(Kff-Qff)*N(u|0,Kuu)} = N(f|0,Sigma0) - Sigma0 = Qnn = Knm*Kmmi*Kmn - """ - KmnKnm = np.dot(Kmn,Kmn.T) - Lm = jitchol(Kmm) - Lmi = chol_inv(Lm) - Kmmi = np.dot(Lmi.T,Lmi) - KmmiKmn = np.dot(Kmmi,Kmn) - Qnn_diag = np.sum(Kmn*KmmiKmn,-2) - LLT0 = Kmm.copy() - - #Kmmi, Lm, Lmi, Kmm_logdet = pdinv(Kmm) - #KmnKnm = np.dot(Kmn, Kmn.T) - #KmmiKmn = np.dot(Kmmi,Kmn) - #Qnn_diag = np.sum(Kmn*KmmiKmn,-2) - #LLT0 = Kmm.copy() - - """ - Posterior approximation: q(f|y) = N(f| mu, Sigma) - Sigma = Diag + P*R.T*R*P.T + K - mu = w + P*Gamma - """ - mu = np.zeros(self.num_data) - LLT = Kmm.copy() - Sigma_diag = Qnn_diag.copy() - - """ - Initial values - Cavity distribution parameters: - q_(g|mu_,sigma2_) = Product{q_i(g|mu_i,sigma2_i)} - sigma_ = 1./tau_ - mu_ = v_/tau_ - """ - self.tau_ = np.empty(self.num_data,dtype=float) - self.v_ = np.empty(self.num_data,dtype=float) - - #Initial values - Marginal moments - z = np.empty(self.num_data,dtype=float) - self.Z_hat = np.empty(self.num_data,dtype=float) - phi = np.empty(self.num_data,dtype=float) - mu_hat = np.empty(self.num_data,dtype=float) - sigma2_hat = np.empty(self.num_data,dtype=float) - - #Approximation - epsilon_np1 = 1 - epsilon_np2 = 1 - self.iterations = 0 - np1 = [self.tau_tilde.copy()] - np2 = [self.v_tilde.copy()] - while epsilon_np1 > self.epsilon or epsilon_np2 > self.epsilon: - update_order = np.random.permutation(self.num_data) - for i in update_order: - #Cavity distribution parameters - self.tau_[i] = 1./Sigma_diag[i] - self.eta*self.tau_tilde[i] - self.v_[i] = mu[i]/Sigma_diag[i] - self.eta*self.v_tilde[i] - #Marginal moments - self.Z_hat[i], mu_hat[i], sigma2_hat[i] = self.noise_model.moments_match(self.data[i],self.tau_[i],self.v_[i]) - #Site parameters update - Delta_tau = self.delta/self.eta*(1./sigma2_hat[i] - 1./Sigma_diag[i]) - Delta_v = self.delta/self.eta*(mu_hat[i]/sigma2_hat[i] - mu[i]/Sigma_diag[i]) - self.tau_tilde[i] += Delta_tau - self.v_tilde[i] += Delta_v - #Posterior distribution parameters update - DSYR(LLT,Kmn[:,i].copy(),Delta_tau) #LLT = LLT + np.outer(Kmn[:,i],Kmn[:,i])*Delta_tau - L = jitchol(LLT) - #cholUpdate(L,Kmn[:,i]*np.sqrt(Delta_tau)) - V,info = dtrtrs(L,Kmn,lower=1) - Sigma_diag = np.sum(V*V,-2) - si = np.sum(V.T*V[:,i],-1) - mu += (Delta_v-Delta_tau*mu[i])*si - self.iterations += 1 - #Sigma recomputation with Cholesky decompositon - LLT = LLT0 + np.dot(Kmn*self.tau_tilde[None,:],Kmn.T) - L = jitchol(LLT) - V,info = dtrtrs(L,Kmn,lower=1) - V2,info = dtrtrs(L.T,V,lower=0) - Sigma_diag = np.sum(V*V,-2) - Knmv_tilde = np.dot(Kmn,self.v_tilde) - mu = np.dot(V2.T,Knmv_tilde) - epsilon_np1 = sum((self.tau_tilde-np1[-1])**2)/self.num_data - epsilon_np2 = sum((self.v_tilde-np2[-1])**2)/self.num_data - np1.append(self.tau_tilde.copy()) - np2.append(self.v_tilde.copy()) - - self._compute_GP_variables() - - def fit_FITC(self, Kmm, Kmn, Knn_diag, epsilon=1e-3,power_ep=[1.,1.]): - """ - The expectation-propagation algorithm with sparse pseudo-input. - For nomenclature see Naish-Guzman and Holden, 2008. - - :param epsilon: Convergence criterion, maximum squared difference allowed between mean updates to stop iterations (float) - :type epsilon: float - :param power_ep: Power EP parameters - :type power_ep: list of floats - """ - self.epsilon = epsilon - self.eta, self.delta = power_ep - - num_inducing = Kmm.shape[0] - - """ - Prior approximation parameters: - q(f|X) = int_{df}{N(f|KfuKuu_invu,diag(Kff-Qff)*N(u|0,Kuu)} = N(f|0,Sigma0) - Sigma0 = diag(Knn-Qnn) + Qnn, Qnn = Knm*Kmmi*Kmn - """ - Lm = jitchol(Kmm) - Lmi = chol_inv(Lm) - Kmmi = np.dot(Lmi.T,Lmi) - P0 = Kmn.T - KmnKnm = np.dot(P0.T, P0) - KmmiKmn = np.dot(Kmmi,P0.T) - Qnn_diag = np.sum(P0.T*KmmiKmn,-2) - Diag0 = Knn_diag - Qnn_diag - R0 = jitchol(Kmmi).T - - """ - Posterior approximation: q(f|y) = N(f| mu, Sigma) - Sigma = Diag + P*R.T*R*P.T + K - mu = w + P*Gamma - """ - self.w = np.zeros(self.num_data) - self.Gamma = np.zeros(num_inducing) - mu = np.zeros(self.num_data) - P = P0.copy() - R = R0.copy() - Diag = Diag0.copy() - Sigma_diag = Knn_diag - RPT0 = np.dot(R0,P0.T) - - """ - Initial values - Cavity distribution parameters: - q_(g|mu_,sigma2_) = Product{q_i(g|mu_i,sigma2_i)} - sigma_ = 1./tau_ - mu_ = v_/tau_ - """ - self.tau_ = np.empty(self.num_data,dtype=float) - self.v_ = np.empty(self.num_data,dtype=float) - - #Initial values - Marginal moments - z = np.empty(self.num_data,dtype=float) - self.Z_hat = np.empty(self.num_data,dtype=float) - phi = np.empty(self.num_data,dtype=float) - mu_hat = np.empty(self.num_data,dtype=float) - sigma2_hat = np.empty(self.num_data,dtype=float) - - #Approximation - epsilon_np1 = 1 - epsilon_np2 = 1 - self.iterations = 0 - self.np1 = [self.tau_tilde.copy()] - self.np2 = [self.v_tilde.copy()] - while epsilon_np1 > self.epsilon or epsilon_np2 > self.epsilon: - update_order = np.random.permutation(self.num_data) - for i in update_order: - #Cavity distribution parameters - self.tau_[i] = 1./Sigma_diag[i] - self.eta*self.tau_tilde[i] - self.v_[i] = mu[i]/Sigma_diag[i] - self.eta*self.v_tilde[i] - #Marginal moments - self.Z_hat[i], mu_hat[i], sigma2_hat[i] = self.noise_model.moments_match(self.data[i],self.tau_[i],self.v_[i]) - #Site parameters update - Delta_tau = self.delta/self.eta*(1./sigma2_hat[i] - 1./Sigma_diag[i]) - Delta_v = self.delta/self.eta*(mu_hat[i]/sigma2_hat[i] - mu[i]/Sigma_diag[i]) - self.tau_tilde[i] += Delta_tau - self.v_tilde[i] += Delta_v - #Posterior distribution parameters update - dtd1 = Delta_tau*Diag[i] + 1. - dii = Diag[i] - Diag[i] = dii - (Delta_tau * dii**2.)/dtd1 - pi_ = P[i,:].reshape(1,num_inducing) - P[i,:] = pi_ - (Delta_tau*dii)/dtd1 * pi_ - Rp_i = np.dot(R,pi_.T) - RTR = np.dot(R.T,np.dot(np.eye(num_inducing) - Delta_tau/(1.+Delta_tau*Sigma_diag[i]) * np.dot(Rp_i,Rp_i.T),R)) - R = jitchol(RTR).T - self.w[i] += (Delta_v - Delta_tau*self.w[i])*dii/dtd1 - self.Gamma += (Delta_v - Delta_tau*mu[i])*np.dot(RTR,P[i,:].T) - RPT = np.dot(R,P.T) - Sigma_diag = Diag + np.sum(RPT.T*RPT.T,-1) - mu = self.w + np.dot(P,self.Gamma) - self.iterations += 1 - #Sigma recomptutation with Cholesky decompositon - Iplus_Dprod_i = 1./(1.+ Diag0 * self.tau_tilde) - Diag = Diag0 * Iplus_Dprod_i - P = Iplus_Dprod_i[:,None] * P0 - safe_diag = np.where(Diag0 < self.tau_tilde, self.tau_tilde/(1.+Diag0*self.tau_tilde), (1. - Iplus_Dprod_i)/Diag0) - L = jitchol(np.eye(num_inducing) + np.dot(RPT0,safe_diag[:,None]*RPT0.T)) - R,info = dtrtrs(L,R0,lower=1) - RPT = np.dot(R,P.T) - Sigma_diag = Diag + np.sum(RPT.T*RPT.T,-1) - self.w = Diag * self.v_tilde - self.Gamma = np.dot(R.T, np.dot(RPT,self.v_tilde)) - mu = self.w + np.dot(P,self.Gamma) - epsilon_np1 = sum((self.tau_tilde-self.np1[-1])**2)/self.num_data - epsilon_np2 = sum((self.v_tilde-self.np2[-1])**2)/self.num_data - self.np1.append(self.tau_tilde.copy()) - self.np2.append(self.v_tilde.copy()) - - return self._compute_GP_variables() diff --git a/GPy/likelihoods/ep_mixed_noise.py b/GPy/likelihoods/ep_mixed_noise.py deleted file mode 100644 index f5452512..00000000 --- a/GPy/likelihoods/ep_mixed_noise.py +++ /dev/null @@ -1,385 +0,0 @@ -# Copyright (c) 2013, Ricardo Andrade -# Licensed under the BSD 3-clause license (see LICENSE.txt) - - -import numpy as np -from scipy import stats -from ..util.linalg import pdinv,mdot,jitchol,chol_inv,DSYR,tdot,dtrtrs -from likelihood import likelihood - -class EP_Mixed_Noise(likelihood): - def __init__(self,data_list,noise_model_list,epsilon=1e-3,power_ep=[1.,1.]): - """ - Expectation Propagation - - Arguments - --------- - :param data_list: list of outputs - :param noise_model_list: a list of noise models - :param epsilon: Convergence criterion, maximum squared difference allowed between mean updates to stop iterations - :type epsilon: float - :param power_ep: list of power ep parameters - """ - assert len(data_list) == len(noise_model_list) - self.noise_model_list = noise_model_list - n_list = [data.size for data in data_list] - self.n_models = len(data_list) - self.n_params = [noise_model._get_params().size for noise_model in noise_model_list] - self.index = np.vstack([np.repeat(i,n)[:,None] for i,n in zip(range(self.n_models),n_list)]) - self.epsilon = epsilon - self.eta, self.delta = power_ep - self.data = np.vstack(data_list) - self.N, self.output_dim = self.data.shape - self.is_heteroscedastic = True - self.num_params = 0#FIXME - self._transf_data = np.vstack([noise_model._preprocess_values(data) for noise_model,data in zip(noise_model_list,data_list)]) - #TODO non-gaussian index - - #Initial values - Likelihood approximation parameters: - #p(y|f) = t(f|tau_tilde,v_tilde) - self.tau_tilde = np.zeros(self.N) - self.v_tilde = np.zeros(self.N) - - #initial values for the GP variables - self.Y = np.zeros((self.N,1)) - self.covariance_matrix = np.eye(self.N) - self.precision = np.ones(self.N)[:,None] - self.Z = 0 - self.YYT = None - self.V = self.precision * self.Y - self.VVT_factor = self.V - self.trYYT = 0. - - def restart(self): - self.tau_tilde = np.zeros(self.N) - self.v_tilde = np.zeros(self.N) - self.Y = np.zeros((self.N,1)) - self.covariance_matrix = np.eye(self.N) - self.precision = np.ones(self.N)[:,None] - self.Z = 0 - self.YYT = None - self.V = self.precision * self.Y - self.VVT_factor = self.V - self.trYYT = 0. - - def predictive_values(self,mu,var,full_cov,noise_model): - """ - Predicts the output given the GP - - :param mu: GP's mean - :param var: GP's variance - :param full_cov: whether to return the full covariance matrix, or just the diagonal - :type full_cov: False|True - :param noise_model: noise model to use - :type noise_model: integer - """ - if full_cov: - raise NotImplementedError, "Cannot make correlated predictions with an EP likelihood" - #_mu = [] - #_var = [] - #_q1 = [] - #_q2 = [] - #for m,v,o in zip(mu,var,output.flatten()): - # a,b,c,d = self.noise_model_list[int(o)].predictive_values(m,v) - # _mu.append(a) - # _var.append(b) - # _q1.append(c) - # _q2.append(d) - #return np.vstack(_mu),np.vstack(_var),np.vstack(_q1),np.vstack(_q2) - return self.noise_model_list[noise_model].predictive_values(mu,var) - - def _get_params(self): - return np.hstack([noise_model._get_params().flatten() for noise_model in self.noise_model_list]) - - def _get_param_names(self): - names = [] - for noise_model in self.noise_model_list: - names += noise_model._get_param_names() - return names - - def _set_params(self,p): - cs_params = np.cumsum([0]+self.n_params) - for i in range(len(self.n_params)): - self.noise_model_list[i]._set_params(p[cs_params[i]:cs_params[i+1]]) - - def _gradients(self,partial): - #NOTE this is not tested - return np.hstack([noise_model._gradients(partial) for noise_model in self.noise_model_list]) - - def _compute_GP_variables(self): - #Variables to be called from GP - mu_tilde = self.v_tilde/self.tau_tilde #When calling EP, this variable is used instead of Y in the GP model - sigma_sum = 1./self.tau_ + 1./self.tau_tilde - mu_diff_2 = (self.v_/self.tau_ - mu_tilde)**2 - self.Z = np.sum(np.log(self.Z_hat)) + 0.5*np.sum(np.log(sigma_sum)) + 0.5*np.sum(mu_diff_2/sigma_sum) #Normalization constant, aka Z_ep - - self.Y = mu_tilde[:,None] - self.YYT = np.dot(self.Y,self.Y.T) - self.covariance_matrix = np.diag(1./self.tau_tilde) - self.precision = self.tau_tilde[:,None] - self.V = self.precision * self.Y - self.VVT_factor = self.V - self.trYYT = np.trace(self.YYT) - - def fit_full(self,K): - """ - The expectation-propagation algorithm. - For nomenclature see Rasmussen & Williams 2006. - """ - #Initial values - Posterior distribution parameters: q(f|X,Y) = N(f|mu,Sigma) - mu = np.zeros(self.N) - Sigma = K.copy() - - """ - Initial values - Cavity distribution parameters: - q_(f|mu_,sigma2_) = Product{q_i(f|mu_i,sigma2_i)} - sigma_ = 1./tau_ - mu_ = v_/tau_ - """ - self.tau_ = np.empty(self.N,dtype=float) - self.v_ = np.empty(self.N,dtype=float) - - #Initial values - Marginal moments - z = np.empty(self.N,dtype=float) - self.Z_hat = np.empty(self.N,dtype=float) - phi = np.empty(self.N,dtype=float) - mu_hat = np.empty(self.N,dtype=float) - sigma2_hat = np.empty(self.N,dtype=float) - - #Approximation - epsilon_np1 = self.epsilon + 1. - epsilon_np2 = self.epsilon + 1. - self.iterations = 0 - self.np1 = [self.tau_tilde.copy()] - self.np2 = [self.v_tilde.copy()] - while epsilon_np1 > self.epsilon or epsilon_np2 > self.epsilon: - update_order = np.random.permutation(self.N) - for i in update_order: - #Cavity distribution parameters - self.tau_[i] = 1./Sigma[i,i] - self.eta*self.tau_tilde[i] - self.v_[i] = mu[i]/Sigma[i,i] - self.eta*self.v_tilde[i] - #Marginal moments - self.Z_hat[i], mu_hat[i], sigma2_hat[i] = self.noise_model_list[self.index[i]].moments_match(self._transf_data[i],self.tau_[i],self.v_[i]) - #Site parameters update - Delta_tau = self.delta/self.eta*(1./sigma2_hat[i] - 1./Sigma[i,i]) - Delta_v = self.delta/self.eta*(mu_hat[i]/sigma2_hat[i] - mu[i]/Sigma[i,i]) - self.tau_tilde[i] += Delta_tau - self.v_tilde[i] += Delta_v - #Posterior distribution parameters update - DSYR(Sigma,Sigma[:,i].copy(), -float(Delta_tau/(1.+ Delta_tau*Sigma[i,i]))) - mu = np.dot(Sigma,self.v_tilde) - self.iterations += 1 - #Sigma recomptutation with Cholesky decompositon - Sroot_tilde_K = np.sqrt(self.tau_tilde)[:,None]*K - B = np.eye(self.N) + np.sqrt(self.tau_tilde)[None,:]*Sroot_tilde_K - L = jitchol(B) - V,info = dtrtrs(L,Sroot_tilde_K,lower=1) - Sigma = K - np.dot(V.T,V) - mu = np.dot(Sigma,self.v_tilde) - epsilon_np1 = sum((self.tau_tilde-self.np1[-1])**2)/self.N - epsilon_np2 = sum((self.v_tilde-self.np2[-1])**2)/self.N - self.np1.append(self.tau_tilde.copy()) - self.np2.append(self.v_tilde.copy()) - - return self._compute_GP_variables() - - def fit_DTC(self, Kmm, Kmn): - """ - The expectation-propagation algorithm with sparse pseudo-input. - For nomenclature see ... 2013. - """ - num_inducing = Kmm.shape[0] - - #TODO: this doesn't work with uncertain inputs! - - """ - Prior approximation parameters: - q(f|X) = int_{df}{N(f|KfuKuu_invu,diag(Kff-Qff)*N(u|0,Kuu)} = N(f|0,Sigma0) - Sigma0 = Qnn = Knm*Kmmi*Kmn - """ - KmnKnm = np.dot(Kmn,Kmn.T) - Lm = jitchol(Kmm) - Lmi = chol_inv(Lm) - Kmmi = np.dot(Lmi.T,Lmi) - KmmiKmn = np.dot(Kmmi,Kmn) - Qnn_diag = np.sum(Kmn*KmmiKmn,-2) - LLT0 = Kmm.copy() - - #Kmmi, Lm, Lmi, Kmm_logdet = pdinv(Kmm) - #KmnKnm = np.dot(Kmn, Kmn.T) - #KmmiKmn = np.dot(Kmmi,Kmn) - #Qnn_diag = np.sum(Kmn*KmmiKmn,-2) - #LLT0 = Kmm.copy() - - """ - Posterior approximation: q(f|y) = N(f| mu, Sigma) - Sigma = Diag + P*R.T*R*P.T + K - mu = w + P*Gamma - """ - mu = np.zeros(self.N) - LLT = Kmm.copy() - Sigma_diag = Qnn_diag.copy() - - """ - Initial values - Cavity distribution parameters: - q_(g|mu_,sigma2_) = Product{q_i(g|mu_i,sigma2_i)} - sigma_ = 1./tau_ - mu_ = v_/tau_ - """ - self.tau_ = np.empty(self.N,dtype=float) - self.v_ = np.empty(self.N,dtype=float) - - #Initial values - Marginal moments - z = np.empty(self.N,dtype=float) - self.Z_hat = np.empty(self.N,dtype=float) - phi = np.empty(self.N,dtype=float) - mu_hat = np.empty(self.N,dtype=float) - sigma2_hat = np.empty(self.N,dtype=float) - - #Approximation - epsilon_np1 = 1 - epsilon_np2 = 1 - self.iterations = 0 - np1 = [self.tau_tilde.copy()] - np2 = [self.v_tilde.copy()] - while epsilon_np1 > self.epsilon or epsilon_np2 > self.epsilon: - update_order = np.random.permutation(self.N) - for i in update_order: - #Cavity distribution parameters - self.tau_[i] = 1./Sigma_diag[i] - self.eta*self.tau_tilde[i] - self.v_[i] = mu[i]/Sigma_diag[i] - self.eta*self.v_tilde[i] - #Marginal moments - self.Z_hat[i], mu_hat[i], sigma2_hat[i] = self.noise_model_list[self.index[i]].moments_match(self._transf_data[i],self.tau_[i],self.v_[i]) - #Site parameters update - Delta_tau = self.delta/self.eta*(1./sigma2_hat[i] - 1./Sigma_diag[i]) - Delta_v = self.delta/self.eta*(mu_hat[i]/sigma2_hat[i] - mu[i]/Sigma_diag[i]) - self.tau_tilde[i] += Delta_tau - self.v_tilde[i] += Delta_v - #Posterior distribution parameters update - DSYR(LLT,Kmn[:,i].copy(),Delta_tau) #LLT = LLT + np.outer(Kmn[:,i],Kmn[:,i])*Delta_tau - L = jitchol(LLT) - #cholUpdate(L,Kmn[:,i]*np.sqrt(Delta_tau)) - V,info = dtrtrs(L,Kmn,lower=1) - Sigma_diag = np.sum(V*V,-2) - si = np.sum(V.T*V[:,i],-1) - mu += (Delta_v-Delta_tau*mu[i])*si - self.iterations += 1 - #Sigma recomputation with Cholesky decompositon - LLT = LLT0 + np.dot(Kmn*self.tau_tilde[None,:],Kmn.T) - L = jitchol(LLT) - V,info = dtrtrs(L,Kmn,lower=1) - V2,info = dtrtrs(L.T,V,lower=0) - Sigma_diag = np.sum(V*V,-2) - Knmv_tilde = np.dot(Kmn,self.v_tilde) - mu = np.dot(V2.T,Knmv_tilde) - epsilon_np1 = sum((self.tau_tilde-np1[-1])**2)/self.N - epsilon_np2 = sum((self.v_tilde-np2[-1])**2)/self.N - np1.append(self.tau_tilde.copy()) - np2.append(self.v_tilde.copy()) - - self._compute_GP_variables() - - def fit_FITC(self, Kmm, Kmn, Knn_diag): - """ - The expectation-propagation algorithm with sparse pseudo-input. - For nomenclature see Naish-Guzman and Holden, 2008. - """ - num_inducing = Kmm.shape[0] - - """ - Prior approximation parameters: - q(f|X) = int_{df}{N(f|KfuKuu_invu,diag(Kff-Qff)*N(u|0,Kuu)} = N(f|0,Sigma0) - Sigma0 = diag(Knn-Qnn) + Qnn, Qnn = Knm*Kmmi*Kmn - """ - Lm = jitchol(Kmm) - Lmi = chol_inv(Lm) - Kmmi = np.dot(Lmi.T,Lmi) - P0 = Kmn.T - KmnKnm = np.dot(P0.T, P0) - KmmiKmn = np.dot(Kmmi,P0.T) - Qnn_diag = np.sum(P0.T*KmmiKmn,-2) - Diag0 = Knn_diag - Qnn_diag - R0 = jitchol(Kmmi).T - - """ - Posterior approximation: q(f|y) = N(f| mu, Sigma) - Sigma = Diag + P*R.T*R*P.T + K - mu = w + P*Gamma - """ - self.w = np.zeros(self.N) - self.Gamma = np.zeros(num_inducing) - mu = np.zeros(self.N) - P = P0.copy() - R = R0.copy() - Diag = Diag0.copy() - Sigma_diag = Knn_diag - RPT0 = np.dot(R0,P0.T) - - """ - Initial values - Cavity distribution parameters: - q_(g|mu_,sigma2_) = Product{q_i(g|mu_i,sigma2_i)} - sigma_ = 1./tau_ - mu_ = v_/tau_ - """ - self.tau_ = np.empty(self.N,dtype=float) - self.v_ = np.empty(self.N,dtype=float) - - #Initial values - Marginal moments - z = np.empty(self.N,dtype=float) - self.Z_hat = np.empty(self.N,dtype=float) - phi = np.empty(self.N,dtype=float) - mu_hat = np.empty(self.N,dtype=float) - sigma2_hat = np.empty(self.N,dtype=float) - - #Approximation - epsilon_np1 = 1 - epsilon_np2 = 1 - self.iterations = 0 - self.np1 = [self.tau_tilde.copy()] - self.np2 = [self.v_tilde.copy()] - while epsilon_np1 > self.epsilon or epsilon_np2 > self.epsilon: - update_order = np.random.permutation(self.N) - for i in update_order: - #Cavity distribution parameters - self.tau_[i] = 1./Sigma_diag[i] - self.eta*self.tau_tilde[i] - self.v_[i] = mu[i]/Sigma_diag[i] - self.eta*self.v_tilde[i] - #Marginal moments - self.Z_hat[i], mu_hat[i], sigma2_hat[i] = self.noise_model_list[self.index[i]].moments_match(self._transf_data[i],self.tau_[i],self.v_[i]) - #Site parameters update - Delta_tau = self.delta/self.eta*(1./sigma2_hat[i] - 1./Sigma_diag[i]) - Delta_v = self.delta/self.eta*(mu_hat[i]/sigma2_hat[i] - mu[i]/Sigma_diag[i]) - self.tau_tilde[i] += Delta_tau - self.v_tilde[i] += Delta_v - #Posterior distribution parameters update - dtd1 = Delta_tau*Diag[i] + 1. - dii = Diag[i] - Diag[i] = dii - (Delta_tau * dii**2.)/dtd1 - pi_ = P[i,:].reshape(1,num_inducing) - P[i,:] = pi_ - (Delta_tau*dii)/dtd1 * pi_ - Rp_i = np.dot(R,pi_.T) - RTR = np.dot(R.T,np.dot(np.eye(num_inducing) - Delta_tau/(1.+Delta_tau*Sigma_diag[i]) * np.dot(Rp_i,Rp_i.T),R)) - R = jitchol(RTR).T - self.w[i] += (Delta_v - Delta_tau*self.w[i])*dii/dtd1 - self.Gamma += (Delta_v - Delta_tau*mu[i])*np.dot(RTR,P[i,:].T) - RPT = np.dot(R,P.T) - Sigma_diag = Diag + np.sum(RPT.T*RPT.T,-1) - mu = self.w + np.dot(P,self.Gamma) - self.iterations += 1 - #Sigma recomptutation with Cholesky decompositon - Iplus_Dprod_i = 1./(1.+ Diag0 * self.tau_tilde) - Diag = Diag0 * Iplus_Dprod_i - P = Iplus_Dprod_i[:,None] * P0 - safe_diag = np.where(Diag0 < self.tau_tilde, self.tau_tilde/(1.+Diag0*self.tau_tilde), (1. - Iplus_Dprod_i)/Diag0) - L = jitchol(np.eye(num_inducing) + np.dot(RPT0,safe_diag[:,None]*RPT0.T)) - R,info = dtrtrs(L,R0,lower=1) - RPT = np.dot(R,P.T) - Sigma_diag = Diag + np.sum(RPT.T*RPT.T,-1) - self.w = Diag * self.v_tilde - self.Gamma = np.dot(R.T, np.dot(RPT,self.v_tilde)) - mu = self.w + np.dot(P,self.Gamma) - epsilon_np1 = sum((self.tau_tilde-self.np1[-1])**2)/self.N - epsilon_np2 = sum((self.v_tilde-self.np2[-1])**2)/self.N - self.np1.append(self.tau_tilde.copy()) - self.np2.append(self.v_tilde.copy()) - - return self._compute_GP_variables() diff --git a/GPy/likelihoods/noise_models/exponential_noise.py b/GPy/likelihoods/exponential.py similarity index 74% rename from GPy/likelihoods/noise_models/exponential_noise.py rename to GPy/likelihoods/exponential.py index 602ccea5..8110c7d4 100644 --- a/GPy/likelihoods/noise_models/exponential_noise.py +++ b/GPy/likelihoods/exponential.py @@ -1,15 +1,14 @@ -# Copyright (c) 2012, 2013 Ricardo Andrade +# Copyright (c) 2012-2014 GPy Authors # Licensed under the BSD 3-clause license (see LICENSE.txt) import numpy as np from scipy import stats,special import scipy as sp -from GPy.util.univariate_Gaussian import std_norm_pdf,std_norm_cdf -import gp_transformations -from noise_distributions import NoiseDistribution +import link_functions +from likelihood import Likelihood -class Exponential(NoiseDistribution): +class Exponential(Likelihood): """ Expoential likelihood Y is expected to take values in {0,1,2,...} @@ -18,13 +17,12 @@ class Exponential(NoiseDistribution): L(x) = \exp(\lambda) * \lambda**Y_i / Y_i! $$ """ - def __init__(self,gp_link=None,analytical_mean=False,analytical_variance=False): - super(Exponential, self).__init__(gp_link,analytical_mean,analytical_variance) + def __init__(self,gp_link=None): + if gp_link is None: + gp_link = link_functions.Log() + super(Exponential, self).__init__(gp_link, 'ExpLikelihood') - def _preprocess_values(self,Y): - return Y - - def pdf_link(self, link_f, y, extra_data=None): + def pdf_link(self, link_f, y, Y_metadata=None): """ Likelihood function given link(f) @@ -35,16 +33,15 @@ class Exponential(NoiseDistribution): :type link_f: Nx1 array :param y: data :type y: Nx1 array - :param extra_data: extra_data which is not used in exponential distribution + :param Y_metadata: Y_metadata which is not used in exponential distribution :returns: likelihood evaluated for this point :rtype: float """ assert np.atleast_1d(link_f).shape == np.atleast_1d(y).shape log_objective = link_f*np.exp(-y*link_f) return np.exp(np.sum(np.log(log_objective))) - #return np.exp(np.sum(-y/link_f - np.log(link_f) )) - def logpdf_link(self, link_f, y, extra_data=None): + def logpdf_link(self, link_f, y, Y_metadata=None): """ Log Likelihood Function given link(f) @@ -55,17 +52,16 @@ class Exponential(NoiseDistribution): :type link_f: Nx1 array :param y: data :type y: Nx1 array - :param extra_data: extra_data which is not used in exponential distribution + :param Y_metadata: Y_metadata which is not used in exponential distribution :returns: likelihood evaluated for this point :rtype: float """ assert np.atleast_1d(link_f).shape == np.atleast_1d(y).shape log_objective = np.log(link_f) - y*link_f - #logpdf_link = np.sum(-np.log(link_f) - y/link_f) return np.sum(log_objective) - def dlogpdf_dlink(self, link_f, y, extra_data=None): + def dlogpdf_dlink(self, link_f, y, Y_metadata=None): """ Gradient of the log likelihood function at y, given link(f) w.r.t link(f) @@ -76,7 +72,7 @@ class Exponential(NoiseDistribution): :type link_f: Nx1 array :param y: data :type y: Nx1 array - :param extra_data: extra_data which is not used in exponential distribution + :param Y_metadata: Y_metadata which is not used in exponential distribution :returns: gradient of likelihood evaluated at points :rtype: Nx1 array @@ -86,7 +82,7 @@ class Exponential(NoiseDistribution): #grad = y/(link_f**2) - 1./link_f return grad - def d2logpdf_dlink2(self, link_f, y, extra_data=None): + def d2logpdf_dlink2(self, link_f, y, Y_metadata=None): """ Hessian at y, given link(f), w.r.t link(f) i.e. second derivative logpdf at y given link(f_i) and link(f_j) w.r.t link(f_i) and link(f_j) @@ -99,7 +95,7 @@ class Exponential(NoiseDistribution): :type link_f: Nx1 array :param y: data :type y: Nx1 array - :param extra_data: extra_data which is not used in exponential distribution + :param Y_metadata: Y_metadata which is not used in exponential distribution :returns: Diagonal of hessian matrix (second derivative of likelihood evaluated at points f) :rtype: Nx1 array @@ -112,7 +108,7 @@ class Exponential(NoiseDistribution): #hess = -2*y/(link_f**3) + 1/(link_f**2) return hess - def d3logpdf_dlink3(self, link_f, y, extra_data=None): + def d3logpdf_dlink3(self, link_f, y, Y_metadata=None): """ Third order derivative log-likelihood function at y given link(f) w.r.t link(f) @@ -123,7 +119,7 @@ class Exponential(NoiseDistribution): :type link_f: Nx1 array :param y: data :type y: Nx1 array - :param extra_data: extra_data which is not used in exponential distribution + :param Y_metadata: Y_metadata which is not used in exponential distribution :returns: third derivative of likelihood evaluated at points f :rtype: Nx1 array """ @@ -132,18 +128,6 @@ class Exponential(NoiseDistribution): #d3lik_dlink3 = 6*y/(link_f**4) - 2./(link_f**3) return d3lik_dlink3 - def _mean(self,gp): - """ - Mass (or density) function - """ - return self.gp_link.transf(gp) - - def _variance(self,gp): - """ - Mass (or density) function - """ - return self.gp_link.transf(gp)**2 - def samples(self, gp): """ Returns a set of samples of observations based on a given value of the latent variable. diff --git a/GPy/likelihoods/noise_models/gamma_noise.py b/GPy/likelihoods/gamma.py similarity index 79% rename from GPy/likelihoods/noise_models/gamma_noise.py rename to GPy/likelihoods/gamma.py index 2be3106a..c79e196c 100644 --- a/GPy/likelihoods/noise_models/gamma_noise.py +++ b/GPy/likelihoods/gamma.py @@ -1,15 +1,15 @@ -# Copyright (c) 2012, 2013 Ricardo Andrade +# Copyright (c) 2012 - 2014, GPy authors (see AUTHORS.txt). # Licensed under the BSD 3-clause license (see LICENSE.txt) import numpy as np from scipy import stats,special import scipy as sp -from GPy.util.univariate_Gaussian import std_norm_pdf,std_norm_cdf -import gp_transformations -from noise_distributions import NoiseDistribution +from ..core.parameterization import Param +import link_functions +from likelihood import Likelihood -class Gamma(NoiseDistribution): +class Gamma(Likelihood): """ Gamma likelihood @@ -18,14 +18,16 @@ class Gamma(NoiseDistribution): \\alpha_{i} = \\beta y_{i} """ - def __init__(self,gp_link=None,analytical_mean=False,analytical_variance=False,beta=1.): - self.beta = beta - super(Gamma, self).__init__(gp_link,analytical_mean,analytical_variance) + def __init__(self,gp_link=None,beta=1.): + if gp_link is None: + gp_link = link_functions.Log() + super(Gamma, self).__init__(gp_link, 'Gamma') - def _preprocess_values(self,Y): - return Y + self.beta = Param('beta', beta) + self.link_parameter(self.beta) + self.beta.fix()#TODO: gradients! - def pdf_link(self, link_f, y, extra_data=None): + def pdf_link(self, link_f, y, Y_metadata=None): """ Likelihood function given link(f) @@ -37,7 +39,7 @@ class Gamma(NoiseDistribution): :type link_f: Nx1 array :param y: data :type y: Nx1 array - :param extra_data: extra_data which is not used in poisson distribution + :param Y_metadata: Y_metadata which is not used in poisson distribution :returns: likelihood evaluated for this point :rtype: float """ @@ -47,7 +49,7 @@ class Gamma(NoiseDistribution): objective = (y**(alpha - 1.) * np.exp(-self.beta*y) * self.beta**alpha)/ special.gamma(alpha) return np.exp(np.sum(np.log(objective))) - def logpdf_link(self, link_f, y, extra_data=None): + def logpdf_link(self, link_f, y, Y_metadata=None): """ Log Likelihood Function given link(f) @@ -59,7 +61,7 @@ class Gamma(NoiseDistribution): :type link_f: Nx1 array :param y: data :type y: Nx1 array - :param extra_data: extra_data which is not used in poisson distribution + :param Y_metadata: Y_metadata which is not used in poisson distribution :returns: likelihood evaluated for this point :rtype: float @@ -71,7 +73,7 @@ class Gamma(NoiseDistribution): log_objective = alpha*np.log(self.beta) - np.log(special.gamma(alpha)) + (alpha - 1)*np.log(y) - self.beta*y return np.sum(log_objective) - def dlogpdf_dlink(self, link_f, y, extra_data=None): + def dlogpdf_dlink(self, link_f, y, Y_metadata=None): """ Gradient of the log likelihood function at y, given link(f) w.r.t link(f) @@ -83,7 +85,7 @@ class Gamma(NoiseDistribution): :type link_f: Nx1 array :param y: data :type y: Nx1 array - :param extra_data: extra_data which is not used in gamma distribution + :param Y_metadata: Y_metadata which is not used in gamma distribution :returns: gradient of likelihood evaluated at points :rtype: Nx1 array @@ -94,7 +96,7 @@ class Gamma(NoiseDistribution): #return -self.gp_link.dtransf_df(gp)*self.beta*np.log(obs) + special.psi(self.gp_link.transf(gp)*self.beta) * self.gp_link.dtransf_df(gp)*self.beta return grad - def d2logpdf_dlink2(self, link_f, y, extra_data=None): + def d2logpdf_dlink2(self, link_f, y, Y_metadata=None): """ Hessian at y, given link(f), w.r.t link(f) i.e. second derivative logpdf at y given link(f_i) and link(f_j) w.r.t link(f_i) and link(f_j) @@ -108,7 +110,7 @@ class Gamma(NoiseDistribution): :type link_f: Nx1 array :param y: data :type y: Nx1 array - :param extra_data: extra_data which is not used in gamma distribution + :param Y_metadata: Y_metadata which is not used in gamma distribution :returns: Diagonal of hessian matrix (second derivative of likelihood evaluated at points f) :rtype: Nx1 array @@ -122,7 +124,7 @@ class Gamma(NoiseDistribution): #return -self.gp_link.d2transf_df2(gp)*self.beta*np.log(obs) + special.polygamma(1,self.gp_link.transf(gp)*self.beta)*(self.gp_link.dtransf_df(gp)*self.beta)**2 + special.psi(self.gp_link.transf(gp)*self.beta)*self.gp_link.d2transf_df2(gp)*self.beta return hess - def d3logpdf_dlink3(self, link_f, y, extra_data=None): + def d3logpdf_dlink3(self, link_f, y, Y_metadata=None): """ Third order derivative log-likelihood function at y given link(f) w.r.t link(f) @@ -134,22 +136,10 @@ class Gamma(NoiseDistribution): :type link_f: Nx1 array :param y: data :type y: Nx1 array - :param extra_data: extra_data which is not used in gamma distribution + :param Y_metadata: Y_metadata which is not used in gamma distribution :returns: third derivative of likelihood evaluated at points f :rtype: Nx1 array """ assert np.atleast_1d(link_f).shape == np.atleast_1d(y).shape d3lik_dlink3 = -special.polygamma(2, self.beta*link_f)*(self.beta**3) return d3lik_dlink3 - - def _mean(self,gp): - """ - Mass (or density) function - """ - return self.gp_link.transf(gp) - - def _variance(self,gp): - """ - Mass (or density) function - """ - return self.gp_link.transf(gp)/self.beta diff --git a/GPy/likelihoods/gaussian.py b/GPy/likelihoods/gaussian.py index c12d8e6d..125f306f 100644 --- a/GPy/likelihoods/gaussian.py +++ b/GPy/likelihoods/gaussian.py @@ -1,114 +1,318 @@ +# Copyright (c) 2012-2014 The GPy authors (see AUTHORS.txt) +# Licensed under the BSD 3-clause license (see LICENSE.txt) +#TODO +""" +A lot of this code assumes that the link function is the identity. + +I think laplace code is okay, but I'm quite sure that the EP moments will only work if the link is identity. + +Furthermore, exact Guassian inference can only be done for the identity link, so we should be asserting so for all calls which relate to that. + +James 11/12/13 +""" + import numpy as np -from likelihood import likelihood -from ..util.linalg import jitchol +from scipy import stats, special +import link_functions +from likelihood import Likelihood +from ..core.parameterization import Param +from ..core.parameterization.transformations import Logexp +from scipy import stats - -class Gaussian(likelihood): +class Gaussian(Likelihood): """ - Likelihood class for doing Expectation propagation + Gaussian likelihood - :param data: observed output - :type data: Nx1 numpy.darray - :param variance: noise parameter - :param normalize: whether to normalize the data before computing (predictions will be in original scales) - :type normalize: False|True + .. math:: + \\ln p(y_{i}|\\lambda(f_{i})) = -\\frac{N \\ln 2\\pi}{2} - \\frac{\\ln |K|}{2} - \\frac{(y_{i} - \\lambda(f_{i}))^{T}\\sigma^{-2}(y_{i} - \\lambda(f_{i}))}{2} + + :param variance: variance value of the Gaussian distribution + :param N: Number of data points + :type N: int """ - def __init__(self, data, variance=1., normalize=False): - self.is_heteroscedastic = False - self.num_params = 1 - self.Z = 0. # a correction factor which accounts for the approximation made - N, self.output_dim = data.shape + def __init__(self, gp_link=None, variance=1., name='Gaussian_noise'): + if gp_link is None: + gp_link = link_functions.Identity() - # normalization - if normalize: - self._offset = data.mean(0)[None, :] - self._scale = data.std(0)[None, :] - # Don't scale outputs which have zero variance to zero. - self._scale[np.nonzero(self._scale == 0.)] = 1.0e-3 - else: - self._offset = np.zeros((1, self.output_dim)) - self._scale = np.ones((1, self.output_dim)) + assert isinstance(gp_link, link_functions.Identity), "the likelihood only implemented for the identity link" - self.set_data(data) + super(Gaussian, self).__init__(gp_link, name=name) - self._variance = np.asarray(variance) + 1. - self._set_params(np.asarray(variance)) + self.variance = Param('variance', variance, Logexp()) + self.link_parameter(self.variance) - super(Gaussian, self).__init__() + if isinstance(gp_link, link_functions.Identity): + self.log_concave = True - def set_data(self, data): - self.data = data - self.N, D = data.shape - assert D == self.output_dim - self.Y = (self.data - self._offset) / self._scale - if D > self.N: - self.YYT = np.dot(self.Y, self.Y.T) - self.trYYT = np.trace(self.YYT) - self.YYT_factor = jitchol(self.YYT) - else: - self.YYT = None - self.trYYT = np.sum(np.square(self.Y)) - self.YYT_factor = self.Y + def betaY(self,Y,Y_metadata=None): + #TODO: ~Ricardo this does not live here + return Y/self.gaussian_variance(Y_metadata) - def _get_params(self): - return np.asarray(self._variance) + def gaussian_variance(self, Y_metadata=None): + return self.variance - def _get_param_names(self): - return ["noise_variance"] + def update_gradients(self, grad): + self.variance.gradient = grad - def _set_params(self, x): - x = np.float64(x) - if np.all(self._variance != x): - if x == 0.:#special case of zero noise - self.precision = np.inf - self.V = None - else: - self.precision = 1. / x - self.V = (self.precision) * self.Y - self.VVT_factor = self.precision * self.YYT_factor - self.covariance_matrix = np.eye(self.N) * x - self._variance = x + def exact_inference_gradients(self, dL_dKdiag,Y_metadata=None): + return dL_dKdiag.sum() - def predictive_values(self, mu, var, full_cov, **likelihood_args): + def _preprocess_values(self, Y): """ - Un-normalize the prediction and add the likelihood variance, then return the 5%, 95% interval + Check if the values of the observations correspond to the values + assumed by the likelihood function. """ - mean = mu * self._scale + self._offset + return Y + + def _moments_match_ep(self, data_i, tau_i, v_i): + """ + Moments match of the marginal approximation in EP algorithm + + :param i: number of observation (int) + :param tau_i: precision of the cavity distribution (float) + :param v_i: mean/variance of the cavity distribution (float) + """ + sigma2_hat = 1./(1./self.variance + tau_i) + mu_hat = sigma2_hat*(data_i/self.variance + v_i) + sum_var = self.variance + 1./tau_i + Z_hat = 1./np.sqrt(2.*np.pi*sum_var)*np.exp(-.5*(data_i - v_i/tau_i)**2./sum_var) + return Z_hat, mu_hat, sigma2_hat + + def predictive_values(self, mu, var, full_cov=False, Y_metadata=None): if full_cov: - if self.output_dim > 1: - raise NotImplementedError, "TODO" - # Note. for output_dim>1, we need to re-normalise all the outputs independently. - # This will mess up computations of diag(true_var), below. - # note that the upper, lower quantiles should be the same shape as mean - # Augment the output variance with the likelihood variance and rescale. - true_var = (var + np.eye(var.shape[0]) * self._variance) * self._scale ** 2 - _5pc = mean - 2.*np.sqrt(np.diag(true_var)) - _95pc = mean + 2.*np.sqrt(np.diag(true_var)) + if var.ndim == 2: + var += np.eye(var.shape[0])*self.variance + if var.ndim == 3: + var += np.atleast_3d(np.eye(var.shape[0])*self.variance) else: - true_var = (var + self._variance) * self._scale ** 2 - _5pc = mean - 2.*np.sqrt(true_var) - _95pc = mean + 2.*np.sqrt(true_var) - return mean, true_var, _5pc, _95pc + var += self.variance + return mu, var + + def predictive_mean(self, mu, sigma): + return mu + + def predictive_variance(self, mu, sigma, predictive_mean=None): + return self.variance + sigma**2 + + def predictive_quantiles(self, mu, var, quantiles, Y_metadata=None): + return [stats.norm.ppf(q/100.)*np.sqrt(var + self.variance) + mu for q in quantiles] + + def pdf_link(self, link_f, y, Y_metadata=None): + """ + Likelihood function given link(f) + + .. math:: + \\ln p(y_{i}|\\lambda(f_{i})) = -\\frac{N \\ln 2\\pi}{2} - \\frac{\\ln |K|}{2} - \\frac{(y_{i} - \\lambda(f_{i}))^{T}\\sigma^{-2}(y_{i} - \\lambda(f_{i}))}{2} + + :param link_f: latent variables link(f) + :type link_f: Nx1 array + :param y: data + :type y: Nx1 array + :param Y_metadata: Y_metadata not used in gaussian + :returns: likelihood evaluated for this point + :rtype: float + """ + #Assumes no covariance, exp, sum, log for numerical stability + return np.exp(np.sum(np.log(stats.norm.pdf(y, link_f, np.sqrt(self.variance))))) + + def logpdf_link(self, link_f, y, Y_metadata=None): + """ + Log likelihood function given link(f) + + .. math:: + \\ln p(y_{i}|\\lambda(f_{i})) = -\\frac{N \\ln 2\\pi}{2} - \\frac{\\ln |K|}{2} - \\frac{(y_{i} - \\lambda(f_{i}))^{T}\\sigma^{-2}(y_{i} - \\lambda(f_{i}))}{2} + + :param link_f: latent variables link(f) + :type link_f: Nx1 array + :param y: data + :type y: Nx1 array + :param Y_metadata: Y_metadata not used in gaussian + :returns: log likelihood evaluated for this point + :rtype: float + """ + assert np.asarray(link_f).shape == np.asarray(y).shape + N = y.shape[0] + ln_det_cov = N*np.log(self.variance) + + return -0.5*(np.sum((y-link_f)**2/self.variance) + ln_det_cov + N*np.log(2.*np.pi)) + + def dlogpdf_dlink(self, link_f, y, Y_metadata=None): + """ + Gradient of the pdf at y, given link(f) w.r.t link(f) + + .. math:: + \\frac{d \\ln p(y_{i}|\\lambda(f_{i}))}{d\\lambda(f)} = \\frac{1}{\\sigma^{2}}(y_{i} - \\lambda(f_{i})) + + :param link_f: latent variables link(f) + :type link_f: Nx1 array + :param y: data + :type y: Nx1 array + :param Y_metadata: Y_metadata not used in gaussian + :returns: gradient of log likelihood evaluated at points link(f) + :rtype: Nx1 array + """ + assert np.asarray(link_f).shape == np.asarray(y).shape + s2_i = (1.0/self.variance) + grad = s2_i*y - s2_i*link_f + return grad + + def d2logpdf_dlink2(self, link_f, y, Y_metadata=None): + """ + Hessian at y, given link_f, w.r.t link_f. + i.e. second derivative logpdf at y given link(f_i) link(f_j) w.r.t link(f_i) and link(f_j) + + The hessian will be 0 unless i == j + + .. math:: + \\frac{d^{2} \\ln p(y_{i}|\\lambda(f_{i}))}{d^{2}f} = -\\frac{1}{\\sigma^{2}} + + :param link_f: latent variables link(f) + :type link_f: Nx1 array + :param y: data + :type y: Nx1 array + :param Y_metadata: Y_metadata not used in gaussian + :returns: Diagonal of log hessian matrix (second derivative of log likelihood evaluated at points link(f)) + :rtype: Nx1 array + + .. Note:: + Will return diagonal of hessian, since every where else it is 0, as the likelihood factorizes over cases + (the distribution for y_i depends only on link(f_i) not on link(f_(j!=i)) + """ + assert np.asarray(link_f).shape == np.asarray(y).shape + N = y.shape[0] + hess = -(1.0/self.variance)*np.ones((N, 1)) + return hess + + def d3logpdf_dlink3(self, link_f, y, Y_metadata=None): + """ + Third order derivative log-likelihood function at y given link(f) w.r.t link(f) + + .. math:: + \\frac{d^{3} \\ln p(y_{i}|\\lambda(f_{i}))}{d^{3}\\lambda(f)} = 0 + + :param link_f: latent variables link(f) + :type link_f: Nx1 array + :param y: data + :type y: Nx1 array + :param Y_metadata: Y_metadata not used in gaussian + :returns: third derivative of log likelihood evaluated at points link(f) + :rtype: Nx1 array + """ + assert np.asarray(link_f).shape == np.asarray(y).shape + N = y.shape[0] + d3logpdf_dlink3 = np.zeros((N,1)) + return d3logpdf_dlink3 + + def dlogpdf_link_dvar(self, link_f, y, Y_metadata=None): + """ + Gradient of the log-likelihood function at y given link(f), w.r.t variance parameter (noise_variance) + + .. math:: + \\frac{d \\ln p(y_{i}|\\lambda(f_{i}))}{d\\sigma^{2}} = -\\frac{N}{2\\sigma^{2}} + \\frac{(y_{i} - \\lambda(f_{i}))^{2}}{2\\sigma^{4}} + + :param link_f: latent variables link(f) + :type link_f: Nx1 array + :param y: data + :type y: Nx1 array + :param Y_metadata: Y_metadata not used in gaussian + :returns: derivative of log likelihood evaluated at points link(f) w.r.t variance parameter + :rtype: float + """ + assert np.asarray(link_f).shape == np.asarray(y).shape + e = y - link_f + s_4 = 1.0/(self.variance**2) + N = y.shape[0] + dlik_dsigma = -0.5*N/self.variance + 0.5*s_4*np.sum(np.square(e)) + return np.sum(dlik_dsigma) # Sure about this sum? + + def dlogpdf_dlink_dvar(self, link_f, y, Y_metadata=None): + """ + Derivative of the dlogpdf_dlink w.r.t variance parameter (noise_variance) + + .. math:: + \\frac{d}{d\\sigma^{2}}(\\frac{d \\ln p(y_{i}|\\lambda(f_{i}))}{d\\lambda(f)}) = \\frac{1}{\\sigma^{4}}(-y_{i} + \\lambda(f_{i})) + + :param link_f: latent variables link(f) + :type link_f: Nx1 array + :param y: data + :type y: Nx1 array + :param Y_metadata: Y_metadata not used in gaussian + :returns: derivative of log likelihood evaluated at points link(f) w.r.t variance parameter + :rtype: Nx1 array + """ + assert np.asarray(link_f).shape == np.asarray(y).shape + s_4 = 1.0/(self.variance**2) + dlik_grad_dsigma = -s_4*y + s_4*link_f + return dlik_grad_dsigma + + def d2logpdf_dlink2_dvar(self, link_f, y, Y_metadata=None): + """ + Gradient of the hessian (d2logpdf_dlink2) w.r.t variance parameter (noise_variance) + + .. math:: + \\frac{d}{d\\sigma^{2}}(\\frac{d^{2} \\ln p(y_{i}|\\lambda(f_{i}))}{d^{2}\\lambda(f)}) = \\frac{1}{\\sigma^{4}} + + :param link_f: latent variables link(f) + :type link_f: Nx1 array + :param y: data + :type y: Nx1 array + :param Y_metadata: Y_metadata not used in gaussian + :returns: derivative of log hessian evaluated at points link(f_i) and link(f_j) w.r.t variance parameter + :rtype: Nx1 array + """ + assert np.asarray(link_f).shape == np.asarray(y).shape + s_4 = 1.0/(self.variance**2) + N = y.shape[0] + d2logpdf_dlink2_dvar = np.ones((N,1))*s_4 + return d2logpdf_dlink2_dvar + + def dlogpdf_link_dtheta(self, f, y, Y_metadata=None): + dlogpdf_dvar = self.dlogpdf_link_dvar(f, y, Y_metadata=Y_metadata) + return np.asarray([[dlogpdf_dvar]]) + + def dlogpdf_dlink_dtheta(self, f, y, Y_metadata=None): + dlogpdf_dlink_dvar = self.dlogpdf_dlink_dvar(f, y, Y_metadata=Y_metadata) + return dlogpdf_dlink_dvar + + def d2logpdf_dlink2_dtheta(self, f, y, Y_metadata=None): + d2logpdf_dlink2_dvar = self.d2logpdf_dlink2_dvar(f, y, Y_metadata=Y_metadata) + return d2logpdf_dlink2_dvar + + def _mean(self, gp): + """ + Expected value of y under the Mass (or density) function p(y|f) + + .. math:: + E_{p(y|f)}[y] + """ + return self.gp_link.transf(gp) + + def _variance(self, gp): + """ + Variance of y under the Mass (or density) function p(y|f) + + .. math:: + Var_{p(y|f)}[y] + """ + return self.variance + + def samples(self, gp, Y_metadata=None): + """ + Returns a set of samples of observations based on a given value of the latent variable. + + :param gp: latent variable + """ + orig_shape = gp.shape + gp = gp.flatten() + #orig_shape = gp.shape + gp = gp.flatten() + Ysim = np.array([np.random.normal(self.gp_link.transf(gpj), scale=np.sqrt(self.variance), size=1) for gpj in gp]) + return Ysim.reshape(orig_shape) def log_predictive_density(self, y_test, mu_star, var_star): """ - Calculation of the log predictive density - - .. math: - p(y_{*}|D) = p(y_{*}|f_{*})p(f_{*}|\mu_{*}\\sigma^{2}_{*}) - - :param y_test: test observations (y_{*}) - :type y_test: (Nx1) array - :param mu_star: predictive mean of gaussian p(f_{*}|mu_{*}, var_{*}) - :type mu_star: (Nx1) array - :param var_star: predictive variance of gaussian p(f_{*}|mu_{*}, var_{*}) - :type var_star: (Nx1) array - - .. Note: - Works as if each test point was provided individually, i.e. not full_cov + assumes independence """ - y_rescaled = (y_test - self._offset)/self._scale - return -0.5*np.log(2*np.pi) -0.5*np.log(var_star + self._variance) -0.5*(np.square(y_rescaled - mu_star))/(var_star + self._variance) + v = var_star + self.variance + return -0.5*np.log(2*np.pi) -0.5*np.log(v) - 0.5*np.square(y_test - mu_star)/v - def _gradients(self, partial): - return np.sum(partial) diff --git a/GPy/likelihoods/gaussian_mixed_noise.py b/GPy/likelihoods/gaussian_mixed_noise.py deleted file mode 100644 index 696867c0..00000000 --- a/GPy/likelihoods/gaussian_mixed_noise.py +++ /dev/null @@ -1,108 +0,0 @@ -# Copyright (c) 2013, Ricardo Andrade -# Licensed under the BSD 3-clause license (see LICENSE.txt) - - -import numpy as np -from scipy import stats -from ..util.linalg import pdinv,mdot,jitchol,chol_inv,DSYR,tdot,dtrtrs -from likelihood import likelihood -from . import Gaussian - - -class Gaussian_Mixed_Noise(likelihood): - """ - Gaussian Likelihood for multiple outputs - - This is a wrapper around likelihood.Gaussian class - - :param data_list: data observations - :type data_list: list of numpy arrays (num_data_output_i x 1), one array per output - :param noise_params: noise parameters of each output - :type noise_params: list of floats, one per output - :param normalize: whether to normalize the data before computing (predictions will be in original scales) - :type normalize: False|True - """ - def __init__(self, data_list, noise_params=None, normalize=True): - self.num_params = len(data_list) - self.n_list = [data.size for data in data_list] - self.index = np.vstack([np.repeat(i,n)[:,None] for i,n in zip(range(self.num_params),self.n_list)]) - - if noise_params is None: - noise_params = [1.] * self.num_params - else: - assert self.num_params == len(noise_params), 'Number of noise parameters does not match the number of noise models.' - - self.noise_model_list = [Gaussian(Y,variance=v,normalize = normalize) for Y,v in zip(data_list,noise_params)] - self.n_params = [noise_model._get_params().size for noise_model in self.noise_model_list] - self.data = np.vstack(data_list) - self.N, self.output_dim = self.data.shape - self._offset = np.zeros((1, self.output_dim)) - self._scale = np.ones((1, self.output_dim)) - - self.is_heteroscedastic = True - self.Z = 0. # a correction factor which accounts for the approximation made - - self.set_data(data_list) - self._set_params(np.asarray(noise_params)) - - super(Gaussian_Mixed_Noise, self).__init__() - - def set_data(self, data_list): - self.data = np.vstack(data_list) - self.N, D = self.data.shape - assert D == self.output_dim - self.Y = (self.data - self._offset) / self._scale - if D > self.N: - raise NotImplementedError - #self.YYT = np.dot(self.Y, self.Y.T) - #self.trYYT = np.trace(self.YYT) - #self.YYT_factor = jitchol(self.YYT) - else: - self.YYT = None - self.trYYT = np.sum(np.square(self.Y)) - self.YYT_factor = self.Y - - def predictive_values(self,mu,var,full_cov,noise_model): - """ - Predicts the output given the GP - - :param mu: GP's mean - :param var: GP's variance - :param full_cov: whether to return the full covariance matrix, or just the diagonal - :type full_cov: False|True - :param noise_model: noise model to use - :type noise_model: integer - """ - if full_cov: - raise NotImplementedError, "Cannot make correlated predictions with an EP likelihood" - return self.noise_model_list[noise_model].predictive_values(mu,var,full_cov) - - def _get_params(self): - return np.hstack([noise_model._get_params().flatten() for noise_model in self.noise_model_list]) - - def _get_param_names(self): - if len(self.noise_model_list) == 1: - names = self.noise_model_list[0]._get_param_names() - else: - names = [] - for noise_model,i in zip(self.noise_model_list,range(len(self.n_list))): - names.append(''.join(noise_model._get_param_names() + ['_%s' %i])) - return names - - def _set_params(self,p): - cs_params = np.cumsum([0]+self.n_params) - - for i in range(len(self.n_params)): - self.noise_model_list[i]._set_params(p[cs_params[i]:cs_params[i+1]]) - self.precision = np.hstack([np.repeat(noise_model.precision,n) for noise_model,n in zip(self.noise_model_list,self.n_list)])[:,None] - - self.V = self.precision * self.Y - self.VVT_factor = self.precision * self.YYT_factor - self.covariance_matrix = np.eye(self.N) * 1./self.precision - - def _gradients(self,partial): - gradients = [] - aux = np.cumsum([0]+self.n_list) - for ai,af,noise_model in zip(aux[:-1],aux[1:],self.noise_model_list): - gradients += [noise_model._gradients(partial[ai:af])] - return np.hstack(gradients) diff --git a/GPy/likelihoods/likelihood.py b/GPy/likelihoods/likelihood.py index 5e7c8c68..203439d6 100644 --- a/GPy/likelihoods/likelihood.py +++ b/GPy/likelihoods/likelihood.py @@ -1,60 +1,77 @@ +# Copyright (c) 2012-2014 The GPy authors (see AUTHORS.txt) +# Licensed under the BSD 3-clause license (see LICENSE.txt) + import numpy as np -import copy -from ..core.parameterized import Parameterized +from scipy import stats,special +import scipy as sp +import link_functions +from ..util.misc import chain_1, chain_2, chain_3 +from scipy.integrate import quad +import warnings +from ..core.parameterization import Parameterized -class likelihood(Parameterized): +class Likelihood(Parameterized): """ - The atom for a likelihood class + Likelihood base class, used to defing p(y|f). - This object interfaces the GP and the data. The most basic likelihood - (Gaussian) inherits directly from this, as does the EP algorithm + All instances use _inverse_ link functions, which can be swapped out. It is + expected that inheriting classes define a default inverse link function - Some things must be defined for this to work properly: + To use this class, inherit and define missing functionality. - - self.Y : the effective Gaussian target of the GP - - self.N, self.D : Y.shape - - self.covariance_matrix : the effective (noise) covariance of the GP targets - - self.Z : a factor which gets added to the likelihood (0 for a Gaussian, Z_EP for EP) - - self.is_heteroscedastic : enables significant computational savings in GP - - self.precision : a scalar or vector representation of the effective target precision - - self.YYT : (optional) = np.dot(self.Y, self.Y.T) enables computational savings for D>N - - self.V : self.precision * self.Y + Inheriting classes *must* implement: + pdf_link : a bound method which turns the output of the link function into the pdf + logpdf_link : the logarithm of the above + + To enable use with EP, inheriting classes *must* define: + TODO: a suitable derivative function for any parameters of the class + It is also desirable to define: + moments_match_ep : a function to compute the EP moments If this isn't defined, the moments will be computed using 1D quadrature. + + To enable use with Laplace approximation, inheriting classes *must* define: + Some derivative functions *AS TODO* + + For exact Gaussian inference, define *JH TODO* """ - def __init__(self): - Parameterized.__init__(self) - self.dZ_dK = 0 + def __init__(self, gp_link, name): + super(Likelihood, self).__init__(name) + assert isinstance(gp_link,link_functions.GPTransformation), "gp_link is not a valid GPTransformation." + self.gp_link = gp_link + self.log_concave = False - def _get_params(self): + def _gradients(self,partial): + return np.zeros(0) + + def update_gradients(self, partial): + if self.size > 0: + raise NotImplementedError('Must be implemented for likelihoods with parameters to be optimized') + + def _preprocess_values(self,Y): + """ + In case it is needed, this function assess the output values or makes any pertinent transformation on them. + + :param Y: observed output + :type Y: Nx1 numpy.darray + + """ + return Y + + def conditional_mean(self, gp): + """ + The mean of the random variable conditioned on one value of the GP + """ raise NotImplementedError - def _get_param_names(self): - raise NotImplementedError - - def _set_params(self, x): - raise NotImplementedError - - def fit_full(self, K): + def conditional_variance(self, gp): """ - No approximations needed by default + The variance of the random variable conditioned on one value of the GP """ - pass - - def restart(self): - """ - No need to restart if not an approximation - """ - pass - - def _gradients(self, partial): - raise NotImplementedError - - def predictive_values(self, mu, var): raise NotImplementedError def log_predictive_density(self, y_test, mu_star, var_star): """ - Calculation of the predictive density + Calculation of the log predictive density .. math: p(y_{*}|D) = p(y_{*}|f_{*})p(f_{*}|\mu_{*}\\sigma^{2}_{*}) @@ -66,4 +83,391 @@ class likelihood(Parameterized): :param var_star: predictive variance of gaussian p(f_{*}|mu_{*}, var_{*}) :type var_star: (Nx1) array """ + assert y_test.shape==mu_star.shape + assert y_test.shape==var_star.shape + assert y_test.shape[1] == 1 + def integral_generator(y, m, v): + """Generate a function which can be integrated to give p(Y*|Y) = int p(Y*|f*)p(f*|Y) df*""" + def f(f_star): + return self.pdf(f_star, y)*np.exp(-(1./(2*v))*np.square(m-f_star)) + return f + + scaled_p_ystar, accuracy = zip(*[quad(integral_generator(y, m, v), -np.inf, np.inf) for y, m, v in zip(y_test.flatten(), mu_star.flatten(), var_star.flatten())]) + scaled_p_ystar = np.array(scaled_p_ystar).reshape(-1,1) + p_ystar = scaled_p_ystar/np.sqrt(2*np.pi*var_star) + return np.log(p_ystar) + + def _moments_match_ep(self,obs,tau,v): + """ + Calculation of moments using quadrature + + :param obs: observed output + :param tau: cavity distribution 1st natural parameter (precision) + :param v: cavity distribution 2nd natural paramenter (mu*precision) + """ + #Compute first integral for zeroth moment. + #NOTE constant np.sqrt(2*pi/tau) added at the end of the function + mu = v/tau + def int_1(f): + return self.pdf(f, obs)*np.exp(-0.5*tau*np.square(mu-f)) + z_scaled, accuracy = quad(int_1, -np.inf, np.inf) + + #Compute second integral for first moment + def int_2(f): + return f*self.pdf(f, obs)*np.exp(-0.5*tau*np.square(mu-f)) + mean, accuracy = quad(int_2, -np.inf, np.inf) + mean /= z_scaled + + #Compute integral for variance + def int_3(f): + return (f**2)*self.pdf(f, obs)*np.exp(-0.5*tau*np.square(mu-f)) + Ef2, accuracy = quad(int_3, -np.inf, np.inf) + Ef2 /= z_scaled + variance = Ef2 - mean**2 + + #Add constant to the zeroth moment + #NOTE: this constant is not needed in the other moments because it cancells out. + z = z_scaled/np.sqrt(2*np.pi/tau) + + return z, mean, variance + + def variational_expectations(self, Y, m, v, gh_points=None): + """ + Use Gauss-Hermite Quadrature to compute + + E_p(f) [ log p(y|f) ] + d/dm E_p(f) [ log p(y|f) ] + d/dv E_p(f) [ log p(y|f) ] + + where p(f) is a Gaussian with mean m and variance v. The shapes of Y, m and v should match. + + if no gh_points are passed, we construct them using defualt options + """ + + if gh_points is None: + gh_x, gh_w = np.polynomial.hermite.hermgauss(12) + else: + gh_x, gh_w = gh_points + + shape = m.shape + m,v,Y = m.flatten(), v.flatten(), Y.flatten() + + #make a grid of points + X = gh_x[None,:]*np.sqrt(2.*v[:,None]) + m[:,None] + + #evaluate the likelhood for the grid. First ax indexes the data (and mu, var) and the second indexes the grid. + # broadcast needs to be handled carefully. + logp = self.logpdf(X,Y[:,None]) + dlogp_dx = self.dlogpdf_df(X, Y[:,None]) + d2logp_dx2 = self.d2logpdf_df2(X, Y[:,None]) + + #clipping for numerical stability + logp = np.clip(logp,-1e6,1e6) + dlogp_dx = np.clip(dlogp_dx,-1e6,1e6) + d2logp_dx2 = np.clip(d2logp_dx2,-1e6,1e6) + + #average over the gird to get derivatives of the Gaussian's parameters + F = np.dot(logp, gh_w) + dF_dm = np.dot(dlogp_dx, gh_w) + dF_dv = np.dot(d2logp_dx2, gh_w)/2. + + if np.any(np.isnan(dF_dv)) or np.any(np.isinf(dF_dv)): + stop + if np.any(np.isnan(dF_dm)) or np.any(np.isinf(dF_dm)): + stop + + return F.reshape(*shape), dF_dm.reshape(*shape), dF_dv.reshape(*shape) + + + + + def predictive_mean(self, mu, variance, Y_metadata=None): + """ + Quadrature calculation of the predictive mean: E(Y_star|Y) = E( E(Y_star|f_star, Y) ) + + :param mu: mean of posterior + :param sigma: standard deviation of posterior + + """ + #conditional_mean: the edpected value of y given some f, under this likelihood + def int_mean(f,m,v): + p = np.exp(-(0.5/v)*np.square(f - m)) + #If p is zero then conditional_mean will overflow + if p < 1e-10: + return 0. + else: + return self.conditional_mean(f)*p + scaled_mean = [quad(int_mean, -np.inf, np.inf,args=(mj,s2j))[0] for mj,s2j in zip(mu,variance)] + mean = np.array(scaled_mean)[:,None] / np.sqrt(2*np.pi*(variance)) + + return mean + + def _conditional_mean(self, f): + """Quadrature calculation of the conditional mean: E(Y_star|f)""" + raise NotImplementedError, "implement this function to make predictions" + + def predictive_variance(self, mu,variance, predictive_mean=None, Y_metadata=None): + """ + Approximation to the predictive variance: V(Y_star) + + The following variance decomposition is used: + V(Y_star) = E( V(Y_star|f_star) ) + V( E(Y_star|f_star) ) + + :param mu: mean of posterior + :param sigma: standard deviation of posterior + :predictive_mean: output's predictive mean, if None _predictive_mean function will be called. + + """ + #sigma2 = sigma**2 + normalizer = np.sqrt(2*np.pi*variance) + + # E( V(Y_star|f_star) ) + def int_var(f,m,v): + p = np.exp(-(0.5/v)*np.square(f - m)) + #If p is zero then conditional_variance will overflow + if p < 1e-10: + return 0. + else: + return self.conditional_variance(f)*p + scaled_exp_variance = [quad(int_var, -np.inf, np.inf,args=(mj,s2j))[0] for mj,s2j in zip(mu,variance)] + exp_var = np.array(scaled_exp_variance)[:,None] / normalizer + + #V( E(Y_star|f_star) ) = E( E(Y_star|f_star)**2 ) - E( E(Y_star|f_star) )**2 + + #E( E(Y_star|f_star) )**2 + if predictive_mean is None: + predictive_mean = self.predictive_mean(mu,variance) + predictive_mean_sq = predictive_mean**2 + + #E( E(Y_star|f_star)**2 ) + def int_pred_mean_sq(f,m,v,predictive_mean_sq): + p = np.exp(-(0.5/v)*np.square(f - m)) + #If p is zero then conditional_mean**2 will overflow + if p < 1e-10: + return 0. + else: + return self.conditional_mean(f)**2*p + + scaled_exp_exp2 = [quad(int_pred_mean_sq, -np.inf, np.inf,args=(mj,s2j,pm2j))[0] for mj,s2j,pm2j in zip(mu,variance,predictive_mean_sq)] + exp_exp2 = np.array(scaled_exp_exp2)[:,None] / normalizer + + var_exp = exp_exp2 - predictive_mean_sq + + # V(Y_star) = E[ V(Y_star|f_star) ] + V[ E(Y_star|f_star) ] + # V(Y_star) = E[ V(Y_star|f_star) ] + E(Y_star**2|f_star) - E[Y_star|f_star]**2 + return exp_var + var_exp + + def pdf_link(self, inv_link_f, y, Y_metadata=None): + raise NotImplementedError + + def logpdf_link(self, inv_link_f, y, Y_metadata=None): + raise NotImplementedError + + def dlogpdf_dlink(self, inv_link_f, y, Y_metadata=None): + raise NotImplementedError + + def d2logpdf_dlink2(self, inv_link_f, y, Y_metadata=None): + raise NotImplementedError + + def d3logpdf_dlink3(self, inv_link_f, y, Y_metadata=None): + raise NotImplementedError + + def dlogpdf_link_dtheta(self, inv_link_f, y, Y_metadata=None): + raise NotImplementedError + + def dlogpdf_dlink_dtheta(self, inv_link_f, y, Y_metadata=None): + raise NotImplementedError + + def d2logpdf_dlink2_dtheta(self, inv_link_f, y, Y_metadata=None): + raise NotImplementedError + + def pdf(self, f, y, Y_metadata=None): + """ + Evaluates the link function link(f) then computes the likelihood (pdf) using it + + .. math: + p(y|\\lambda(f)) + + :param f: latent variables f + :type f: Nx1 array + :param y: data + :type y: Nx1 array + :param Y_metadata: Y_metadata which is not used in student t distribution - not used + :returns: likelihood evaluated for this point + :rtype: float + """ + inv_link_f = self.gp_link.transf(f) + return self.pdf_link(inv_link_f, y, Y_metadata=Y_metadata) + + def logpdf(self, f, y, Y_metadata=None): + """ + Evaluates the link function link(f) then computes the log likelihood (log pdf) using it + + .. math: + \\log p(y|\\lambda(f)) + + :param f: latent variables f + :type f: Nx1 array + :param y: data + :type y: Nx1 array + :param Y_metadata: Y_metadata which is not used in student t distribution - not used + :returns: log likelihood evaluated for this point + :rtype: float + """ + inv_link_f = self.gp_link.transf(f) + return self.logpdf_link(inv_link_f, y, Y_metadata=Y_metadata) + + def dlogpdf_df(self, f, y, Y_metadata=None): + """ + Evaluates the link function link(f) then computes the derivative of log likelihood using it + Uses the Faa di Bruno's formula for the chain rule + + .. math:: + \\frac{d\\log p(y|\\lambda(f))}{df} = \\frac{d\\log p(y|\\lambda(f))}{d\\lambda(f)}\\frac{d\\lambda(f)}{df} + + :param f: latent variables f + :type f: Nx1 array + :param y: data + :type y: Nx1 array + :param Y_metadata: Y_metadata which is not used in student t distribution - not used + :returns: derivative of log likelihood evaluated for this point + :rtype: 1xN array + """ + inv_link_f = self.gp_link.transf(f) + dlogpdf_dlink = self.dlogpdf_dlink(inv_link_f, y, Y_metadata=Y_metadata) + dlink_df = self.gp_link.dtransf_df(f) + return chain_1(dlogpdf_dlink, dlink_df) + + def d2logpdf_df2(self, f, y, Y_metadata=None): + """ + Evaluates the link function link(f) then computes the second derivative of log likelihood using it + Uses the Faa di Bruno's formula for the chain rule + + .. math:: + \\frac{d^{2}\\log p(y|\\lambda(f))}{df^{2}} = \\frac{d^{2}\\log p(y|\\lambda(f))}{d^{2}\\lambda(f)}\\left(\\frac{d\\lambda(f)}{df}\\right)^{2} + \\frac{d\\log p(y|\\lambda(f))}{d\\lambda(f)}\\frac{d^{2}\\lambda(f)}{df^{2}} + + :param f: latent variables f + :type f: Nx1 array + :param y: data + :type y: Nx1 array + :param Y_metadata: Y_metadata which is not used in student t distribution - not used + :returns: second derivative of log likelihood evaluated for this point (diagonal only) + :rtype: 1xN array + """ + inv_link_f = self.gp_link.transf(f) + d2logpdf_dlink2 = self.d2logpdf_dlink2(inv_link_f, y, Y_metadata=Y_metadata) + dlink_df = self.gp_link.dtransf_df(f) + dlogpdf_dlink = self.dlogpdf_dlink(inv_link_f, y, Y_metadata=Y_metadata) + d2link_df2 = self.gp_link.d2transf_df2(f) + return chain_2(d2logpdf_dlink2, dlink_df, dlogpdf_dlink, d2link_df2) + + def d3logpdf_df3(self, f, y, Y_metadata=None): + """ + Evaluates the link function link(f) then computes the third derivative of log likelihood using it + Uses the Faa di Bruno's formula for the chain rule + + .. math:: + \\frac{d^{3}\\log p(y|\\lambda(f))}{df^{3}} = \\frac{d^{3}\\log p(y|\\lambda(f)}{d\\lambda(f)^{3}}\\left(\\frac{d\\lambda(f)}{df}\\right)^{3} + 3\\frac{d^{2}\\log p(y|\\lambda(f)}{d\\lambda(f)^{2}}\\frac{d\\lambda(f)}{df}\\frac{d^{2}\\lambda(f)}{df^{2}} + \\frac{d\\log p(y|\\lambda(f)}{d\\lambda(f)}\\frac{d^{3}\\lambda(f)}{df^{3}} + + :param f: latent variables f + :type f: Nx1 array + :param y: data + :type y: Nx1 array + :param Y_metadata: Y_metadata which is not used in student t distribution - not used + :returns: third derivative of log likelihood evaluated for this point + :rtype: float + """ + inv_link_f = self.gp_link.transf(f) + d3logpdf_dlink3 = self.d3logpdf_dlink3(inv_link_f, y, Y_metadata=Y_metadata) + dlink_df = self.gp_link.dtransf_df(f) + d2logpdf_dlink2 = self.d2logpdf_dlink2(inv_link_f, y, Y_metadata=Y_metadata) + d2link_df2 = self.gp_link.d2transf_df2(f) + dlogpdf_dlink = self.dlogpdf_dlink(inv_link_f, y, Y_metadata=Y_metadata) + d3link_df3 = self.gp_link.d3transf_df3(f) + return chain_3(d3logpdf_dlink3, dlink_df, d2logpdf_dlink2, d2link_df2, dlogpdf_dlink, d3link_df3) + + def dlogpdf_dtheta(self, f, y, Y_metadata=None): + """ + TODO: Doc strings + """ + if self.size > 0: + inv_link_f = self.gp_link.transf(f) + return self.dlogpdf_link_dtheta(inv_link_f, y, Y_metadata=Y_metadata) + else: + # There are no parameters so return an empty array for derivatives + return np.zeros([1, 0]) + + def dlogpdf_df_dtheta(self, f, y, Y_metadata=None): + """ + TODO: Doc strings + """ + if self.size > 0: + inv_link_f = self.gp_link.transf(f) + dlink_df = self.gp_link.dtransf_df(f) + dlogpdf_dlink_dtheta = self.dlogpdf_dlink_dtheta(inv_link_f, y, Y_metadata=Y_metadata) + return chain_1(dlogpdf_dlink_dtheta, dlink_df) + else: + # There are no parameters so return an empty array for derivatives + return np.zeros([f.shape[0], 0]) + + def d2logpdf_df2_dtheta(self, f, y, Y_metadata=None): + """ + TODO: Doc strings + """ + if self.size > 0: + inv_link_f = self.gp_link.transf(f) + dlink_df = self.gp_link.dtransf_df(f) + d2link_df2 = self.gp_link.d2transf_df2(f) + d2logpdf_dlink2_dtheta = self.d2logpdf_dlink2_dtheta(inv_link_f, y, Y_metadata=Y_metadata) + dlogpdf_dlink_dtheta = self.dlogpdf_dlink_dtheta(inv_link_f, y, Y_metadata=Y_metadata) + return chain_2(d2logpdf_dlink2_dtheta, dlink_df, dlogpdf_dlink_dtheta, d2link_df2) + else: + # There are no parameters so return an empty array for derivatives + return np.zeros([f.shape[0], 0]) + + def _laplace_gradients(self, f, y, Y_metadata=None): + dlogpdf_dtheta = self.dlogpdf_dtheta(f, y, Y_metadata=Y_metadata) + dlogpdf_df_dtheta = self.dlogpdf_df_dtheta(f, y, Y_metadata=Y_metadata) + d2logpdf_df2_dtheta = self.d2logpdf_df2_dtheta(f, y, Y_metadata=Y_metadata) + + #Parameters are stacked vertically. Must be listed in same order as 'get_param_names' + # ensure we have gradients for every parameter we want to optimize + assert len(dlogpdf_dtheta) == self.size #1 x num_param array + assert dlogpdf_df_dtheta.shape[1] == self.size #f x num_param matrix + assert d2logpdf_df2_dtheta.shape[1] == self.size #f x num_param matrix + + return dlogpdf_dtheta, dlogpdf_df_dtheta, d2logpdf_df2_dtheta + + def predictive_values(self, mu, var, full_cov=False, Y_metadata=None): + """ + Compute mean, variance of the predictive distibution. + + :param mu: mean of the latent variable, f, of posterior + :param var: variance of the latent variable, f, of posterior + :param full_cov: whether to use the full covariance or just the diagonal + :type full_cov: Boolean + """ + + pred_mean = self.predictive_mean(mu, var, Y_metadata) + pred_var = self.predictive_variance(mu, var, pred_mean, Y_metadata) + + return pred_mean, pred_var + + def predictive_quantiles(self, mu, var, quantiles, Y_metadata=None): + #compute the quantiles by sampling!!! + N_samp = 1000 + s = np.random.randn(mu.shape[0], N_samp)*np.sqrt(var) + mu + #ss_f = s.flatten() + #ss_y = self.samples(ss_f, Y_metadata) + ss_y = self.samples(s, Y_metadata) + #ss_y = ss_y.reshape(mu.shape[0], N_samp) + + return [np.percentile(ss_y ,q, axis=1)[:,None] for q in quantiles] + + def samples(self, gp, Y_metadata=None): + """ + Returns a set of samples of observations based on a given value of the latent variable. + + :param gp: latent variable + """ raise NotImplementedError diff --git a/GPy/likelihoods/noise_models/gp_transformations.py b/GPy/likelihoods/link_functions.py similarity index 78% rename from GPy/likelihoods/noise_models/gp_transformations.py rename to GPy/likelihoods/link_functions.py index 5155a69d..a4ddc760 100644 --- a/GPy/likelihoods/noise_models/gp_transformations.py +++ b/GPy/likelihoods/link_functions.py @@ -1,13 +1,14 @@ -# Copyright (c) 2012, 2013 Ricardo Andrade +# Copyright (c) 2012-2014 The GPy authors (see AUTHORS.txt) # Licensed under the BSD 3-clause license (see LICENSE.txt) - import numpy as np from scipy import stats import scipy as sp -import pylab as pb from GPy.util.univariate_Gaussian import std_norm_pdf,std_norm_cdf,inv_std_norm_cdf +_exp_lim_val = np.finfo(np.float64).max +_lim_val = np.log(_exp_lim_val) + class GPTransformation(object): """ Link function class for doing non-Gaussian likelihoods approximation @@ -69,7 +70,7 @@ class Probit(GPTransformation): .. math:: g(f) = \\Phi^{-1} (mu) - + """ def transf(self,f): return std_norm_cdf(f) @@ -86,6 +87,34 @@ class Probit(GPTransformation): f2 = f**2 return -(1/(np.sqrt(2*np.pi)))*np.exp(-0.5*(f2))*(1-f2) + +class Cloglog(GPTransformation): + """ + Complementary log-log link + .. math:: + + p(f) = 1 - e^{-e^f} + + or + + f = \log (-\log(1-p)) + + """ + def transf(self,f): + return 1-np.exp(-np.exp(f)) + + def dtransf_df(self,f): + return np.exp(f-np.exp(f)) + + def d2transf_df2(self,f): + ef = np.exp(f) + return -np.exp(f-ef)*(ef-1.) + + def d3transf_df3(self,f): + ef = np.exp(f) + return np.exp(f-ef)*(1.-3*ef + ef**2) + + class Log(GPTransformation): """ .. math:: @@ -94,16 +123,16 @@ class Log(GPTransformation): """ def transf(self,f): - return np.exp(f) + return np.exp(np.clip(f, -_lim_val, _lim_val)) def dtransf_df(self,f): - return np.exp(f) + return np.exp(np.clip(f, -_lim_val, _lim_val)) def d2transf_df2(self,f): - return np.exp(f) + return np.exp(np.clip(f, -_lim_val, _lim_val)) def d3transf_df3(self,f): - return np.exp(f) + return np.exp(np.clip(f, -_lim_val, _lim_val)) class Log_ex_1(GPTransformation): """ diff --git a/GPy/likelihoods/mixed_noise.py b/GPy/likelihoods/mixed_noise.py new file mode 100644 index 00000000..8c56f45b --- /dev/null +++ b/GPy/likelihoods/mixed_noise.py @@ -0,0 +1,82 @@ +# Copyright (c) 2012-2014 The GPy authors (see AUTHORS.txt) +# Licensed under the BSD 3-clause license (see LICENSE.txt) + +import numpy as np +from scipy import stats, special +import link_functions +from likelihood import Likelihood +from gaussian import Gaussian +from ..core.parameterization import Param +from ..core.parameterization.transformations import Logexp +from ..core.parameterization import Parameterized +import itertools + +class MixedNoise(Likelihood): + def __init__(self, likelihoods_list, name='mixed_noise'): + #NOTE at the moment this likelihood only works for using a list of gaussians + super(Likelihood, self).__init__(name=name) + + self.link_parameters(*likelihoods_list) + self.likelihoods_list = likelihoods_list + self.log_concave = False + + def gaussian_variance(self, Y_metadata): + assert all([isinstance(l, Gaussian) for l in self.likelihoods_list]) + ind = Y_metadata['output_index'].flatten() + variance = np.zeros(ind.size) + for lik, j in zip(self.likelihoods_list, range(len(self.likelihoods_list))): + variance[ind==j] = lik.variance + return variance + + def betaY(self,Y,Y_metadata): + #TODO not here. + return Y/self.gaussian_variance(Y_metadata=Y_metadata)[:,None] + + def update_gradients(self, gradients): + self.gradient = gradients + + def exact_inference_gradients(self, dL_dKdiag, Y_metadata): + assert all([isinstance(l, Gaussian) for l in self.likelihoods_list]) + ind = Y_metadata['output_index'].flatten() + return np.array([dL_dKdiag[ind==i].sum() for i in range(len(self.likelihoods_list))]) + + def predictive_values(self, mu, var, full_cov=False, Y_metadata=None): + ind = Y_metadata['output_index'].flatten() + _variance = np.array([self.likelihoods_list[j].variance for j in ind ]) + if full_cov: + var += np.eye(var.shape[0])*_variance + else: + var += _variance + return mu, var + + def predictive_variance(self, mu, sigma, Y_metadata): + _variance = self.gaussian_variance(Y_metadata) + return _variance + sigma**2 + + def predictive_quantiles(self, mu, var, quantiles, Y_metadata): + ind = Y_metadata['output_index'].flatten() + outputs = np.unique(ind) + Q = np.zeros( (mu.size,len(quantiles)) ) + for j in outputs: + q = self.likelihoods_list[j].predictive_quantiles(mu[ind==j,:], + var[ind==j,:],quantiles,Y_metadata=None) + Q[ind==j,:] = np.hstack(q) + return [q[:,None] for q in Q.T] + + def samples(self, gp, Y_metadata): + """ + Returns a set of samples of observations based on a given value of the latent variable. + + :param gp: latent variable + """ + N1, N2 = gp.shape + Ysim = np.zeros((N1,N2)) + ind = Y_metadata['output_index'].flatten() + for j in np.unique(ind): + flt = ind==j + gp_filtered = gp[flt,:] + n1 = gp_filtered.shape[0] + lik = self.likelihoods_list[j] + _ysim = np.array([np.random.normal(lik.gp_link.transf(gpj), scale=np.sqrt(lik.variance), size=1) for gpj in gp_filtered.flatten()]) + Ysim[flt,:] = _ysim.reshape(n1,N2) + return Ysim diff --git a/GPy/likelihoods/noise_model_constructors.py b/GPy/likelihoods/noise_model_constructors.py deleted file mode 100644 index e626c6a3..00000000 --- a/GPy/likelihoods/noise_model_constructors.py +++ /dev/null @@ -1,121 +0,0 @@ -# Copyright (c) 2013, GPy authors (see AUTHORS.txt). -# Licensed under the BSD 3-clause license (see LICENSE.txt) - -import numpy as np -import noise_models - -def bernoulli(gp_link=None): - """ - Construct a bernoulli likelihood - - :param gp_link: a GPy gp_link function - """ - if gp_link is None: - gp_link = noise_models.gp_transformations.Probit() - #else: - # assert isinstance(gp_link,noise_models.gp_transformations.GPTransformation), 'gp_link function is not valid.' - - if isinstance(gp_link,noise_models.gp_transformations.Probit): - analytical_mean = True - analytical_variance = False - - elif isinstance(gp_link,noise_models.gp_transformations.Heaviside): - analytical_mean = True - analytical_variance = True - - else: - analytical_mean = False - analytical_variance = False - - return noise_models.bernoulli_noise.Bernoulli(gp_link,analytical_mean,analytical_variance) - -def exponential(gp_link=None): - - """ - Construct a exponential likelihood - - :param gp_link: a GPy gp_link function - """ - if gp_link is None: - gp_link = noise_models.gp_transformations.Log_ex_1() - - analytical_mean = False - analytical_variance = False - return noise_models.exponential_noise.Exponential(gp_link,analytical_mean,analytical_variance) - -def gaussian_ep(gp_link=None,variance=1.): - """ - Construct a gaussian likelihood - - :param gp_link: a GPy gp_link function - :param variance: scalar - """ - if gp_link is None: - gp_link = noise_models.gp_transformations.Identity() - #else: - # assert isinstance(gp_link,noise_models.gp_transformations.GPTransformation), 'gp_link function is not valid.' - - analytical_mean = False - analytical_variance = False - return noise_models.gaussian_noise.Gaussian(gp_link,analytical_mean,analytical_variance,variance) - -def poisson(gp_link=None): - """ - Construct a Poisson likelihood - - :param gp_link: a GPy gp_link function - """ - if gp_link is None: - gp_link = noise_models.gp_transformations.Log_ex_1() - #else: - # assert isinstance(gp_link,noise_models.gp_transformations.GPTransformation), 'gp_link function is not valid.' - analytical_mean = False - analytical_variance = False - return noise_models.poisson_noise.Poisson(gp_link,analytical_mean,analytical_variance) - -def gamma(gp_link=None,beta=1.): - """ - Construct a Gamma likelihood - - :param gp_link: a GPy gp_link function - :param beta: scalar - """ - if gp_link is None: - gp_link = noise_models.gp_transformations.Log_ex_1() - analytical_mean = False - analytical_variance = False - return noise_models.gamma_noise.Gamma(gp_link,analytical_mean,analytical_variance,beta) - -def gaussian(gp_link=None, variance=2, D=None, N=None): - """ - Construct a Gaussian likelihood - - :param gp_link: a GPy gp_link function - :param variance: variance - :type variance: scalar - :returns: Gaussian noise model: - """ - if gp_link is None: - gp_link = noise_models.gp_transformations.Identity() - analytical_mean = True - analytical_variance = True # ? - return noise_models.gaussian_noise.Gaussian(gp_link, analytical_mean, - analytical_variance, variance=variance, D=D, N=N) - -def student_t(gp_link=None, deg_free=5, sigma2=2): - """ - Construct a Student t likelihood - - :param gp_link: a GPy gp_link function - :param deg_free: degrees of freedom of student-t - :type deg_free: scalar - :param sigma2: variance - :type sigma2: scalar - :returns: Student-T noise model - """ - if gp_link is None: - gp_link = noise_models.gp_transformations.Identity() - analytical_mean = True - analytical_variance = True - return noise_models.student_t_noise.StudentT(gp_link, analytical_mean, - analytical_variance,deg_free, sigma2) diff --git a/GPy/likelihoods/noise_models/__init__.py b/GPy/likelihoods/noise_models/__init__.py deleted file mode 100644 index d1d134dc..00000000 --- a/GPy/likelihoods/noise_models/__init__.py +++ /dev/null @@ -1,8 +0,0 @@ -import noise_distributions -import bernoulli_noise -import exponential_noise -import gaussian_noise -import gamma_noise -import poisson_noise -import student_t_noise -import gp_transformations diff --git a/GPy/likelihoods/noise_models/gaussian_noise.py b/GPy/likelihoods/noise_models/gaussian_noise.py deleted file mode 100644 index 3da6bcc8..00000000 --- a/GPy/likelihoods/noise_models/gaussian_noise.py +++ /dev/null @@ -1,300 +0,0 @@ -# Copyright (c) 2012, 2013 Ricardo Andrade -# Licensed under the BSD 3-clause license (see LICENSE.txt) - -import numpy as np -from scipy import stats,special -import scipy as sp -from GPy.util.univariate_Gaussian import std_norm_pdf,std_norm_cdf -import gp_transformations -from noise_distributions import NoiseDistribution - -class Gaussian(NoiseDistribution): - """ - Gaussian likelihood - - .. math:: - \\ln p(y_{i}|\\lambda(f_{i})) = -\\frac{N \\ln 2\\pi}{2} - \\frac{\\ln |K|}{2} - \\frac{(y_{i} - \\lambda(f_{i}))^{T}\\sigma^{-2}(y_{i} - \\lambda(f_{i}))}{2} - - :param variance: variance value of the Gaussian distribution - :param N: Number of data points - :type N: int - """ - def __init__(self,gp_link=None,analytical_mean=False,analytical_variance=False,variance=1., D=None, N=None): - self.variance = variance - self.N = N - self._set_params(np.asarray(variance)) - super(Gaussian, self).__init__(gp_link,analytical_mean,analytical_variance) - if isinstance(gp_link , gp_transformations.Identity): - self.log_concave = True - - def _get_params(self): - return np.array([self.variance]) - - def _get_param_names(self): - return ['noise_model_variance'] - - def _set_params(self, p): - self.variance = float(p) - self.I = np.eye(self.N) - self.covariance_matrix = self.I * self.variance - self.Ki = self.I*(1.0 / self.variance) - #self.ln_det_K = np.sum(np.log(np.diag(self.covariance_matrix))) - self.ln_det_K = self.N*np.log(self.variance) - - def _gradients(self,partial): - return np.zeros(1) - #return np.sum(partial) - - def _preprocess_values(self,Y): - """ - Check if the values of the observations correspond to the values - assumed by the likelihood function. - """ - return Y - - def _moments_match_analytical(self,data_i,tau_i,v_i): - """ - Moments match of the marginal approximation in EP algorithm - - :param i: number of observation (int) - :param tau_i: precision of the cavity distribution (float) - :param v_i: mean/variance of the cavity distribution (float) - """ - sigma2_hat = 1./(1./self.variance + tau_i) - mu_hat = sigma2_hat*(data_i/self.variance + v_i) - sum_var = self.variance + 1./tau_i - Z_hat = 1./np.sqrt(2.*np.pi*sum_var)*np.exp(-.5*(data_i - v_i/tau_i)**2./sum_var) - return Z_hat, mu_hat, sigma2_hat - - def _predictive_mean_analytical(self,mu,sigma): - new_sigma2 = self.predictive_variance(mu,sigma) - return new_sigma2*(mu/sigma**2 + self.gp_link.transf(mu)/self.variance) - - def _predictive_variance_analytical(self,mu,sigma,predictive_mean=None): - return 1./(1./self.variance + 1./sigma**2) - - def _mass(self, link_f, y, extra_data=None): - NotImplementedError("Deprecated, now doing chain in noise_model.py for link function evaluation\ - Please negate your function and use pdf in noise_model.py, if implementing a likelihood\ - rederivate the derivative without doing the chain and put in logpdf, dlogpdf_dlink or\ - its derivatives") - def _nlog_mass(self, link_f, y, extra_data=None): - NotImplementedError("Deprecated, now doing chain in noise_model.py for link function evaluation\ - Please negate your function and use logpdf in noise_model.py, if implementing a likelihood\ - rederivate the derivative without doing the chain and put in logpdf, dlogpdf_dlink or\ - its derivatives") - - def _dnlog_mass_dgp(self, link_f, y, extra_data=None): - NotImplementedError("Deprecated, now doing chain in noise_model.py for link function evaluation\ - Please negate your function and use dlogpdf_df in noise_model.py, if implementing a likelihood\ - rederivate the derivative without doing the chain and put in logpdf, dlogpdf_dlink or\ - its derivatives") - - def _d2nlog_mass_dgp2(self, link_f, y, extra_data=None): - NotImplementedError("Deprecated, now doing chain in noise_model.py for link function evaluation\ - Please negate your function and use d2logpdf_df2 in noise_model.py, if implementing a likelihood\ - rederivate the derivative without doing the chain and put in logpdf, dlogpdf_dlink or\ - its derivatives") - - def pdf_link(self, link_f, y, extra_data=None): - """ - Likelihood function given link(f) - - .. math:: - \\ln p(y_{i}|\\lambda(f_{i})) = -\\frac{N \\ln 2\\pi}{2} - \\frac{\\ln |K|}{2} - \\frac{(y_{i} - \\lambda(f_{i}))^{T}\\sigma^{-2}(y_{i} - \\lambda(f_{i}))}{2} - - :param link_f: latent variables link(f) - :type link_f: Nx1 array - :param y: data - :type y: Nx1 array - :param extra_data: extra_data not used in gaussian - :returns: likelihood evaluated for this point - :rtype: float - """ - #Assumes no covariance, exp, sum, log for numerical stability - return np.exp(np.sum(np.log(stats.norm.pdf(y, link_f, np.sqrt(self.variance))))) - - def logpdf_link(self, link_f, y, extra_data=None): - """ - Log likelihood function given link(f) - - .. math:: - \\ln p(y_{i}|\\lambda(f_{i})) = -\\frac{N \\ln 2\\pi}{2} - \\frac{\\ln |K|}{2} - \\frac{(y_{i} - \\lambda(f_{i}))^{T}\\sigma^{-2}(y_{i} - \\lambda(f_{i}))}{2} - - :param link_f: latent variables link(f) - :type link_f: Nx1 array - :param y: data - :type y: Nx1 array - :param extra_data: extra_data not used in gaussian - :returns: log likelihood evaluated for this point - :rtype: float - """ - assert np.asarray(link_f).shape == np.asarray(y).shape - return -0.5*(np.sum((y-link_f)**2/self.variance) + self.ln_det_K + self.N*np.log(2.*np.pi)) - - def dlogpdf_dlink(self, link_f, y, extra_data=None): - """ - Gradient of the pdf at y, given link(f) w.r.t link(f) - - .. math:: - \\frac{d \\ln p(y_{i}|\\lambda(f_{i}))}{d\\lambda(f)} = \\frac{1}{\\sigma^{2}}(y_{i} - \\lambda(f_{i})) - - :param link_f: latent variables link(f) - :type link_f: Nx1 array - :param y: data - :type y: Nx1 array - :param extra_data: extra_data not used in gaussian - :returns: gradient of log likelihood evaluated at points link(f) - :rtype: Nx1 array - """ - assert np.asarray(link_f).shape == np.asarray(y).shape - s2_i = (1.0/self.variance) - grad = s2_i*y - s2_i*link_f - return grad - - def d2logpdf_dlink2(self, link_f, y, extra_data=None): - """ - Hessian at y, given link_f, w.r.t link_f. - i.e. second derivative logpdf at y given link(f_i) link(f_j) w.r.t link(f_i) and link(f_j) - - The hessian will be 0 unless i == j - - .. math:: - \\frac{d^{2} \\ln p(y_{i}|\\lambda(f_{i}))}{d^{2}f} = -\\frac{1}{\\sigma^{2}} - - :param link_f: latent variables link(f) - :type link_f: Nx1 array - :param y: data - :type y: Nx1 array - :param extra_data: extra_data not used in gaussian - :returns: Diagonal of log hessian matrix (second derivative of log likelihood evaluated at points link(f)) - :rtype: Nx1 array - - .. Note:: - Will return diagonal of hessian, since every where else it is 0, as the likelihood factorizes over cases - (the distribution for y_i depends only on link(f_i) not on link(f_(j!=i)) - """ - assert np.asarray(link_f).shape == np.asarray(y).shape - hess = -(1.0/self.variance)*np.ones((self.N, 1)) - return hess - - def d3logpdf_dlink3(self, link_f, y, extra_data=None): - """ - Third order derivative log-likelihood function at y given link(f) w.r.t link(f) - - .. math:: - \\frac{d^{3} \\ln p(y_{i}|\\lambda(f_{i}))}{d^{3}\\lambda(f)} = 0 - - :param link_f: latent variables link(f) - :type link_f: Nx1 array - :param y: data - :type y: Nx1 array - :param extra_data: extra_data not used in gaussian - :returns: third derivative of log likelihood evaluated at points link(f) - :rtype: Nx1 array - """ - assert np.asarray(link_f).shape == np.asarray(y).shape - d3logpdf_dlink3 = np.diagonal(0*self.I)[:, None] - return d3logpdf_dlink3 - - def dlogpdf_link_dvar(self, link_f, y, extra_data=None): - """ - Gradient of the log-likelihood function at y given link(f), w.r.t variance parameter (noise_variance) - - .. math:: - \\frac{d \\ln p(y_{i}|\\lambda(f_{i}))}{d\\sigma^{2}} = -\\frac{N}{2\\sigma^{2}} + \\frac{(y_{i} - \\lambda(f_{i}))^{2}}{2\\sigma^{4}} - - :param link_f: latent variables link(f) - :type link_f: Nx1 array - :param y: data - :type y: Nx1 array - :param extra_data: extra_data not used in gaussian - :returns: derivative of log likelihood evaluated at points link(f) w.r.t variance parameter - :rtype: float - """ - assert np.asarray(link_f).shape == np.asarray(y).shape - e = y - link_f - s_4 = 1.0/(self.variance**2) - dlik_dsigma = -0.5*self.N/self.variance + 0.5*s_4*np.sum(np.square(e)) - return np.sum(dlik_dsigma) # Sure about this sum? - - def dlogpdf_dlink_dvar(self, link_f, y, extra_data=None): - """ - Derivative of the dlogpdf_dlink w.r.t variance parameter (noise_variance) - - .. math:: - \\frac{d}{d\\sigma^{2}}(\\frac{d \\ln p(y_{i}|\\lambda(f_{i}))}{d\\lambda(f)}) = \\frac{1}{\\sigma^{4}}(-y_{i} + \\lambda(f_{i})) - - :param link_f: latent variables link(f) - :type link_f: Nx1 array - :param y: data - :type y: Nx1 array - :param extra_data: extra_data not used in gaussian - :returns: derivative of log likelihood evaluated at points link(f) w.r.t variance parameter - :rtype: Nx1 array - """ - assert np.asarray(link_f).shape == np.asarray(y).shape - s_4 = 1.0/(self.variance**2) - dlik_grad_dsigma = -s_4*y + s_4*link_f - return dlik_grad_dsigma - - def d2logpdf_dlink2_dvar(self, link_f, y, extra_data=None): - """ - Gradient of the hessian (d2logpdf_dlink2) w.r.t variance parameter (noise_variance) - - .. math:: - \\frac{d}{d\\sigma^{2}}(\\frac{d^{2} \\ln p(y_{i}|\\lambda(f_{i}))}{d^{2}\\lambda(f)}) = \\frac{1}{\\sigma^{4}} - - :param link_f: latent variables link(f) - :type link_f: Nx1 array - :param y: data - :type y: Nx1 array - :param extra_data: extra_data not used in gaussian - :returns: derivative of log hessian evaluated at points link(f_i) and link(f_j) w.r.t variance parameter - :rtype: Nx1 array - """ - assert np.asarray(link_f).shape == np.asarray(y).shape - s_4 = 1.0/(self.variance**2) - d2logpdf_dlink2_dvar = np.diag(s_4*self.I)[:, None] - return d2logpdf_dlink2_dvar - - def dlogpdf_link_dtheta(self, f, y, extra_data=None): - dlogpdf_dvar = self.dlogpdf_link_dvar(f, y, extra_data=extra_data) - return np.asarray([[dlogpdf_dvar]]) - - def dlogpdf_dlink_dtheta(self, f, y, extra_data=None): - dlogpdf_dlink_dvar = self.dlogpdf_dlink_dvar(f, y, extra_data=extra_data) - return dlogpdf_dlink_dvar - - def d2logpdf_dlink2_dtheta(self, f, y, extra_data=None): - d2logpdf_dlink2_dvar = self.d2logpdf_dlink2_dvar(f, y, extra_data=extra_data) - return d2logpdf_dlink2_dvar - - def _mean(self,gp): - """ - Expected value of y under the Mass (or density) function p(y|f) - - .. math:: - E_{p(y|f)}[y] - """ - return self.gp_link.transf(gp) - - def _variance(self,gp): - """ - Variance of y under the Mass (or density) function p(y|f) - - .. math:: - Var_{p(y|f)}[y] - """ - return self.variance - - def samples(self, gp): - """ - Returns a set of samples of observations based on a given value of the latent variable. - - :param gp: latent variable - """ - orig_shape = gp.shape - gp = gp.flatten() - Ysim = np.array([np.random.normal(self.gp_link.transf(gpj), scale=np.sqrt(self.variance), size=1) for gpj in gp]) - return Ysim.reshape(orig_shape) diff --git a/GPy/likelihoods/noise_models/noise_distributions.py b/GPy/likelihoods/noise_models/noise_distributions.py deleted file mode 100644 index b65b7750..00000000 --- a/GPy/likelihoods/noise_models/noise_distributions.py +++ /dev/null @@ -1,434 +0,0 @@ -# Copyright (c) 2012, 2013 Ricardo Andrade -# Licensed under the BSD 3-clause license (see LICENSE.txt) - - -import numpy as np -from scipy import stats,special -import scipy as sp -import pylab as pb -from GPy.util.plot import gpplot -from GPy.util.univariate_Gaussian import std_norm_pdf,std_norm_cdf -import gp_transformations -from GPy.util.misc import chain_1, chain_2, chain_3 -from scipy.integrate import quad -import warnings - -class NoiseDistribution(object): - """ - Likelihood class for doing approximations - """ - def __init__(self,gp_link,analytical_mean=False,analytical_variance=False): - assert isinstance(gp_link,gp_transformations.GPTransformation), "gp_link is not a valid GPTransformation." - self.gp_link = gp_link - self.analytical_mean = analytical_mean - self.analytical_variance = analytical_variance - if self.analytical_mean: - self.moments_match = self._moments_match_analytical - self.predictive_mean = self._predictive_mean_analytical - else: - self.moments_match = self._moments_match_numerical - self.predictive_mean = self._predictive_mean_numerical - if self.analytical_variance: - self.predictive_variance = self._predictive_variance_analytical - else: - self.predictive_variance = self._predictive_variance_numerical - - self.log_concave = False - - def _get_params(self): - return np.zeros(0) - - def _get_param_names(self): - return [] - - def _set_params(self,p): - pass - - def _gradients(self,partial): - return np.zeros(0) - - def _preprocess_values(self,Y): - """ - In case it is needed, this function assess the output values or makes any pertinent transformation on them. - - :param Y: observed output - :type Y: Nx1 numpy.darray - - """ - return Y - - def _moments_match_analytical(self,obs,tau,v): - """ - If available, this function computes the moments analytically. - """ - raise NotImplementedError - - def log_predictive_density(self, y_test, mu_star, var_star): - """ - Calculation of the log predictive density - - .. math: - p(y_{*}|D) = p(y_{*}|f_{*})p(f_{*}|\mu_{*}\\sigma^{2}_{*}) - - :param y_test: test observations (y_{*}) - :type y_test: (Nx1) array - :param mu_star: predictive mean of gaussian p(f_{*}|mu_{*}, var_{*}) - :type mu_star: (Nx1) array - :param var_star: predictive variance of gaussian p(f_{*}|mu_{*}, var_{*}) - :type var_star: (Nx1) array - """ - assert y_test.shape==mu_star.shape - assert y_test.shape==var_star.shape - assert y_test.shape[1] == 1 - def integral_generator(y, m, v): - """Generate a function which can be integrated to give p(Y*|Y) = int p(Y*|f*)p(f*|Y) df*""" - def f(f_star): - return self.pdf(f_star, y)*np.exp(-(1./(2*v))*np.square(m-f_star)) - return f - - scaled_p_ystar, accuracy = zip(*[quad(integral_generator(y, m, v), -np.inf, np.inf) for y, m, v in zip(y_test.flatten(), mu_star.flatten(), var_star.flatten())]) - scaled_p_ystar = np.array(scaled_p_ystar).reshape(-1,1) - p_ystar = scaled_p_ystar/np.sqrt(2*np.pi*var_star) - return np.log(p_ystar) - - def _moments_match_numerical(self,obs,tau,v): - """ - Calculation of moments using quadrature - - :param obs: observed output - :param tau: cavity distribution 1st natural parameter (precision) - :param v: cavity distribution 2nd natural paramenter (mu*precision) - """ - #Compute first integral for zeroth moment. - #NOTE constant np.sqrt(2*pi/tau) added at the end of the function - mu = v/tau - def int_1(f): - return self.pdf(f, obs)*np.exp(-0.5*tau*np.square(mu-f)) - z_scaled, accuracy = quad(int_1, -np.inf, np.inf) - - #Compute second integral for first moment - def int_2(f): - return f*self.pdf(f, obs)*np.exp(-0.5*tau*np.square(mu-f)) - mean, accuracy = quad(int_2, -np.inf, np.inf) - mean /= z_scaled - - #Compute integral for variance - def int_3(f): - return (f**2)*self.pdf(f, obs)*np.exp(-0.5*tau*np.square(mu-f)) - Ef2, accuracy = quad(int_3, -np.inf, np.inf) - Ef2 /= z_scaled - variance = Ef2 - mean**2 - - #Add constant to the zeroth moment - #NOTE: this constant is not needed in the other moments because it cancells out. - z = z_scaled/np.sqrt(2*np.pi/tau) - - return z, mean, variance - - def _predictive_mean_analytical(self,mu,sigma): - """ - Predictive mean - .. math:: - E(Y^{*}|Y) = E( E(Y^{*}|f^{*}, Y) ) - - If available, this function computes the predictive mean analytically. - """ - raise NotImplementedError - - def _predictive_variance_analytical(self,mu,sigma): - """ - Predictive variance - .. math:: - V(Y^{*}| Y) = E( V(Y^{*}|f^{*}, Y) ) + V( E(Y^{*}|f^{*}, Y) ) - - If available, this function computes the predictive variance analytically. - """ - raise NotImplementedError - - def _predictive_mean_numerical(self,mu,variance): - """ - Quadrature calculation of the predictive mean: E(Y_star|Y) = E( E(Y_star|f_star, Y) ) - - :param mu: mean of posterior - :param sigma: standard deviation of posterior - - """ - #import ipdb; ipdb.set_trace() - def int_mean(f,m,v): - return self._mean(f)*np.exp(-(0.5/v)*np.square(f - m)) - #scaled_mean = [quad(int_mean, -np.inf, np.inf,args=(mj,s2j))[0] for mj,s2j in zip(mu,variance)] - scaled_mean = [quad(int_mean, mj-6*np.sqrt(s2j), mj+6*np.sqrt(s2j), args=(mj,s2j))[0] for mj,s2j in zip(mu,variance)] - mean = np.array(scaled_mean)[:,None] / np.sqrt(2*np.pi*(variance)) - - return mean - - def _predictive_variance_numerical(self,mu,variance,predictive_mean=None): - """ - Numerical approximation to the predictive variance: V(Y_star) - - The following variance decomposition is used: - V(Y_star) = E( V(Y_star|f_star) ) + V( E(Y_star|f_star) ) - - :param mu: mean of posterior - :param sigma: standard deviation of posterior - :predictive_mean: output's predictive mean, if None _predictive_mean function will be called. - - """ - normalizer = np.sqrt(2*np.pi*variance) - - # E( V(Y_star|f_star) ) - def int_var(f,m,v): - return self._variance(f)*np.exp(-(0.5/v)*np.square(f - m)) - #Most of the weight is within 6 stds and this avoids some negative infinity and infinity problems of taking f^2 - scaled_exp_variance = [quad(int_var, mj-6*np.sqrt(s2j), mj+6*np.sqrt(s2j), args=(mj,s2j))[0] for mj,s2j in zip(mu,variance)] - exp_var = np.array(scaled_exp_variance)[:,None] / normalizer - - #V( E(Y_star|f_star) ) = E( E(Y_star|f_star)**2 ) - E( E(Y_star|f_star) )**2 - - #E( E(Y_star|f_star) )**2 - if predictive_mean is None: - predictive_mean = self.predictive_mean(mu,variance) - predictive_mean_sq = predictive_mean**2 - - #E( E(Y_star|f_star)**2 ) - def int_pred_mean_sq(f,m,v): - return self._mean(f)**2*np.exp(-(0.5/v)*np.square(f - m)) - scaled_exp_exp2 = [quad(int_pred_mean_sq, mj-6*np.sqrt(s2j), mj+6*np.sqrt(s2j), args=(mj,s2j))[0] for mj,s2j in zip(mu,variance)] - exp_exp2 = np.array(scaled_exp_exp2)[:,None] / normalizer - - var_exp = exp_exp2 - predictive_mean_sq - - # V(Y_star) = E( V(Y_star|f_star) ) + V( E(Y_star|f_star) ) - return exp_var + var_exp - - def pdf_link(self, link_f, y, extra_data=None): - raise NotImplementedError - - def logpdf_link(self, link_f, y, extra_data=None): - raise NotImplementedError - - def dlogpdf_dlink(self, link_f, y, extra_data=None): - raise NotImplementedError - - def d2logpdf_dlink2(self, link_f, y, extra_data=None): - raise NotImplementedError - - def d3logpdf_dlink3(self, link_f, y, extra_data=None): - raise NotImplementedError - - def dlogpdf_link_dtheta(self, link_f, y, extra_data=None): - raise NotImplementedError - - def dlogpdf_dlink_dtheta(self, link_f, y, extra_data=None): - raise NotImplementedError - - def d2logpdf_dlink2_dtheta(self, link_f, y, extra_data=None): - raise NotImplementedError - - def pdf(self, f, y, extra_data=None): - """ - Evaluates the link function link(f) then computes the likelihood (pdf) using it - - .. math: - p(y|\\lambda(f)) - - :param f: latent variables f - :type f: Nx1 array - :param y: data - :type y: Nx1 array - :param extra_data: extra_data which is not used in student t distribution - not used - :returns: likelihood evaluated for this point - :rtype: float - """ - link_f = self.gp_link.transf(f) - return self.pdf_link(link_f, y, extra_data=extra_data) - - def logpdf(self, f, y, extra_data=None): - """ - Evaluates the link function link(f) then computes the log likelihood (log pdf) using it - - .. math: - \\log p(y|\\lambda(f)) - - :param f: latent variables f - :type f: Nx1 array - :param y: data - :type y: Nx1 array - :param extra_data: extra_data which is not used in student t distribution - not used - :returns: log likelihood evaluated for this point - :rtype: float - """ - link_f = self.gp_link.transf(f) - return self.logpdf_link(link_f, y, extra_data=extra_data) - - def dlogpdf_df(self, f, y, extra_data=None): - """ - Evaluates the link function link(f) then computes the derivative of log likelihood using it - Uses the Faa di Bruno's formula for the chain rule - - .. math:: - \\frac{d\\log p(y|\\lambda(f))}{df} = \\frac{d\\log p(y|\\lambda(f))}{d\\lambda(f)}\\frac{d\\lambda(f)}{df} - - :param f: latent variables f - :type f: Nx1 array - :param y: data - :type y: Nx1 array - :param extra_data: extra_data which is not used in student t distribution - not used - :returns: derivative of log likelihood evaluated for this point - :rtype: 1xN array - """ - link_f = self.gp_link.transf(f) - dlogpdf_dlink = self.dlogpdf_dlink(link_f, y, extra_data=extra_data) - dlink_df = self.gp_link.dtransf_df(f) - return chain_1(dlogpdf_dlink, dlink_df) - - def d2logpdf_df2(self, f, y, extra_data=None): - """ - Evaluates the link function link(f) then computes the second derivative of log likelihood using it - Uses the Faa di Bruno's formula for the chain rule - - .. math:: - \\frac{d^{2}\\log p(y|\\lambda(f))}{df^{2}} = \\frac{d^{2}\\log p(y|\\lambda(f))}{d^{2}\\lambda(f)}\\left(\\frac{d\\lambda(f)}{df}\\right)^{2} + \\frac{d\\log p(y|\\lambda(f))}{d\\lambda(f)}\\frac{d^{2}\\lambda(f)}{df^{2}} - - :param f: latent variables f - :type f: Nx1 array - :param y: data - :type y: Nx1 array - :param extra_data: extra_data which is not used in student t distribution - not used - :returns: second derivative of log likelihood evaluated for this point (diagonal only) - :rtype: 1xN array - """ - link_f = self.gp_link.transf(f) - d2logpdf_dlink2 = self.d2logpdf_dlink2(link_f, y, extra_data=extra_data) - dlink_df = self.gp_link.dtransf_df(f) - dlogpdf_dlink = self.dlogpdf_dlink(link_f, y, extra_data=extra_data) - d2link_df2 = self.gp_link.d2transf_df2(f) - return chain_2(d2logpdf_dlink2, dlink_df, dlogpdf_dlink, d2link_df2) - - def d3logpdf_df3(self, f, y, extra_data=None): - """ - Evaluates the link function link(f) then computes the third derivative of log likelihood using it - Uses the Faa di Bruno's formula for the chain rule - - .. math:: - \\frac{d^{3}\\log p(y|\\lambda(f))}{df^{3}} = \\frac{d^{3}\\log p(y|\\lambda(f)}{d\\lambda(f)^{3}}\\left(\\frac{d\\lambda(f)}{df}\\right)^{3} + 3\\frac{d^{2}\\log p(y|\\lambda(f)}{d\\lambda(f)^{2}}\\frac{d\\lambda(f)}{df}\\frac{d^{2}\\lambda(f)}{df^{2}} + \\frac{d\\log p(y|\\lambda(f)}{d\\lambda(f)}\\frac{d^{3}\\lambda(f)}{df^{3}} - - :param f: latent variables f - :type f: Nx1 array - :param y: data - :type y: Nx1 array - :param extra_data: extra_data which is not used in student t distribution - not used - :returns: third derivative of log likelihood evaluated for this point - :rtype: float - """ - link_f = self.gp_link.transf(f) - d3logpdf_dlink3 = self.d3logpdf_dlink3(link_f, y, extra_data=extra_data) - dlink_df = self.gp_link.dtransf_df(f) - d2logpdf_dlink2 = self.d2logpdf_dlink2(link_f, y, extra_data=extra_data) - d2link_df2 = self.gp_link.d2transf_df2(f) - dlogpdf_dlink = self.dlogpdf_dlink(link_f, y, extra_data=extra_data) - d3link_df3 = self.gp_link.d3transf_df3(f) - return chain_3(d3logpdf_dlink3, dlink_df, d2logpdf_dlink2, d2link_df2, dlogpdf_dlink, d3link_df3) - - def dlogpdf_dtheta(self, f, y, extra_data=None): - """ - TODO: Doc strings - """ - if len(self._get_param_names()) > 0: - link_f = self.gp_link.transf(f) - return self.dlogpdf_link_dtheta(link_f, y, extra_data=extra_data) - else: - #Is no parameters so return an empty array for its derivatives - return np.empty([1, 0]) - - def dlogpdf_df_dtheta(self, f, y, extra_data=None): - """ - TODO: Doc strings - """ - if len(self._get_param_names()) > 0: - link_f = self.gp_link.transf(f) - dlink_df = self.gp_link.dtransf_df(f) - dlogpdf_dlink_dtheta = self.dlogpdf_dlink_dtheta(link_f, y, extra_data=extra_data) - return chain_1(dlogpdf_dlink_dtheta, dlink_df) - else: - #Is no parameters so return an empty array for its derivatives - return np.empty([f.shape[0], 0]) - - def d2logpdf_df2_dtheta(self, f, y, extra_data=None): - """ - TODO: Doc strings - """ - if len(self._get_param_names()) > 0: - link_f = self.gp_link.transf(f) - dlink_df = self.gp_link.dtransf_df(f) - d2link_df2 = self.gp_link.d2transf_df2(f) - d2logpdf_dlink2_dtheta = self.d2logpdf_dlink2_dtheta(link_f, y, extra_data=extra_data) - dlogpdf_dlink_dtheta = self.dlogpdf_dlink_dtheta(link_f, y, extra_data=extra_data) - return chain_2(d2logpdf_dlink2_dtheta, dlink_df, dlogpdf_dlink_dtheta, d2link_df2) - else: - #Is no parameters so return an empty array for its derivatives - return np.empty([f.shape[0], 0]) - - def _laplace_gradients(self, f, y, extra_data=None): - dlogpdf_dtheta = self.dlogpdf_dtheta(f, y, extra_data=extra_data) - dlogpdf_df_dtheta = self.dlogpdf_df_dtheta(f, y, extra_data=extra_data) - d2logpdf_df2_dtheta = self.d2logpdf_df2_dtheta(f, y, extra_data=extra_data) - - #Parameters are stacked vertically. Must be listed in same order as 'get_param_names' - # ensure we have gradients for every parameter we want to optimize - assert dlogpdf_dtheta.shape[1] == len(self._get_param_names()) - assert dlogpdf_df_dtheta.shape[1] == len(self._get_param_names()) - assert d2logpdf_df2_dtheta.shape[1] == len(self._get_param_names()) - return dlogpdf_dtheta, dlogpdf_df_dtheta, d2logpdf_df2_dtheta - - def predictive_values(self, mu, var, full_cov=False, sampling=False, num_samples=10000): - """ - Compute mean, variance and conficence interval (percentiles 5 and 95) of the prediction. - - :param mu: mean of the latent variable, f, of posterior - :param var: variance of the latent variable, f, of posterior - :param full_cov: whether to use the full covariance or just the diagonal - :type full_cov: Boolean - :param num_samples: number of samples to use in computing quantiles and - possibly mean variance - :type num_samples: integer - :param sampling: Whether to use samples for mean and variances anyway - :type sampling: Boolean - - """ - - if sampling: - #Get gp_samples f* using posterior mean and variance - if not full_cov: - gp_samples = np.random.multivariate_normal(mu.flatten(), np.diag(var.flatten()), - size=num_samples).T - else: - gp_samples = np.random.multivariate_normal(mu.flatten(), var, - size=num_samples).T - #Push gp samples (f*) through likelihood to give p(y*|f*) - samples = self.samples(gp_samples) - axis=-1 - - #Calculate mean, variance and precentiles from samples - warnings.warn("Using sampling to calculate mean, variance and predictive quantiles.") - pred_mean = np.mean(samples, axis=axis)[:,None] - pred_var = np.var(samples, axis=axis)[:,None] - q1 = np.percentile(samples, 2.5, axis=axis)[:,None] - q3 = np.percentile(samples, 97.5, axis=axis)[:,None] - - else: - pred_mean = self.predictive_mean(mu, var) - pred_var = self.predictive_variance(mu, var, pred_mean) - warnings.warn("Predictive quantiles are only computed when sampling.") - q1 = np.repeat(np.nan,pred_mean.size)[:,None] - q3 = q1.copy() - - return pred_mean, pred_var, q1, q3 - - def samples(self, gp): - """ - Returns a set of samples of observations based on a given value of the latent variable. - - :param gp: latent variable - """ - raise NotImplementedError diff --git a/GPy/likelihoods/noise_models/poisson_noise.py b/GPy/likelihoods/poisson.py similarity index 77% rename from GPy/likelihoods/noise_models/poisson_noise.py rename to GPy/likelihoods/poisson.py index b0300704..ea9b2d10 100644 --- a/GPy/likelihoods/noise_models/poisson_noise.py +++ b/GPy/likelihoods/poisson.py @@ -1,15 +1,14 @@ from __future__ import division -# Copyright (c) 2012, 2013 Ricardo Andrade +# Copyright (c) 2012-2014 Ricardo Andrade, Alan Saul # Licensed under the BSD 3-clause license (see LICENSE.txt) import numpy as np from scipy import stats,special import scipy as sp -from GPy.util.univariate_Gaussian import std_norm_pdf,std_norm_cdf -import gp_transformations -from noise_distributions import NoiseDistribution +import link_functions +from likelihood import Likelihood -class Poisson(NoiseDistribution): +class Poisson(Likelihood): """ Poisson likelihood @@ -19,13 +18,19 @@ class Poisson(NoiseDistribution): .. Note:: Y is expected to take values in {0,1,2,...} """ - def __init__(self,gp_link=None,analytical_mean=False,analytical_variance=False): - super(Poisson, self).__init__(gp_link,analytical_mean,analytical_variance) + def __init__(self, gp_link=None): + if gp_link is None: + gp_link = link_functions.Log() - def _preprocess_values(self,Y): #TODO - return Y + super(Poisson, self).__init__(gp_link, name='Poisson') - def pdf_link(self, link_f, y, extra_data=None): + def _conditional_mean(self, f): + """ + the expected value of y given a value of f + """ + return self.gp_link.transf(gp) + + def pdf_link(self, link_f, y, Y_metadata=None): """ Likelihood function given link(f) @@ -36,14 +41,14 @@ class Poisson(NoiseDistribution): :type link_f: Nx1 array :param y: data :type y: Nx1 array - :param extra_data: extra_data which is not used in poisson distribution + :param Y_metadata: Y_metadata which is not used in poisson distribution :returns: likelihood evaluated for this point :rtype: float """ assert np.atleast_1d(link_f).shape == np.atleast_1d(y).shape return np.prod(stats.poisson.pmf(y,link_f)) - def logpdf_link(self, link_f, y, extra_data=None): + def logpdf_link(self, link_f, y, Y_metadata=None): """ Log Likelihood Function given link(f) @@ -54,7 +59,7 @@ class Poisson(NoiseDistribution): :type link_f: Nx1 array :param y: data :type y: Nx1 array - :param extra_data: extra_data which is not used in poisson distribution + :param Y_metadata: Y_metadata which is not used in poisson distribution :returns: likelihood evaluated for this point :rtype: float @@ -62,7 +67,7 @@ class Poisson(NoiseDistribution): assert np.atleast_1d(link_f).shape == np.atleast_1d(y).shape return np.sum(-link_f + y*np.log(link_f) - special.gammaln(y+1)) - def dlogpdf_dlink(self, link_f, y, extra_data=None): + def dlogpdf_dlink(self, link_f, y, Y_metadata=None): """ Gradient of the log likelihood function at y, given link(f) w.r.t link(f) @@ -73,7 +78,7 @@ class Poisson(NoiseDistribution): :type link_f: Nx1 array :param y: data :type y: Nx1 array - :param extra_data: extra_data which is not used in poisson distribution + :param Y_metadata: Y_metadata which is not used in poisson distribution :returns: gradient of likelihood evaluated at points :rtype: Nx1 array @@ -81,7 +86,7 @@ class Poisson(NoiseDistribution): assert np.atleast_1d(link_f).shape == np.atleast_1d(y).shape return y/link_f - 1 - def d2logpdf_dlink2(self, link_f, y, extra_data=None): + def d2logpdf_dlink2(self, link_f, y, Y_metadata=None): """ Hessian at y, given link(f), w.r.t link(f) i.e. second derivative logpdf at y given link(f_i) and link(f_j) w.r.t link(f_i) and link(f_j) @@ -94,7 +99,7 @@ class Poisson(NoiseDistribution): :type link_f: Nx1 array :param y: data :type y: Nx1 array - :param extra_data: extra_data which is not used in poisson distribution + :param Y_metadata: Y_metadata which is not used in poisson distribution :returns: Diagonal of hessian matrix (second derivative of likelihood evaluated at points f) :rtype: Nx1 array @@ -109,7 +114,7 @@ class Poisson(NoiseDistribution): #transf = self.gp_link.transf(gp) #return obs * ((self.gp_link.dtransf_df(gp)/transf)**2 - d2_df/transf) + d2_df - def d3logpdf_dlink3(self, link_f, y, extra_data=None): + def d3logpdf_dlink3(self, link_f, y, Y_metadata=None): """ Third order derivative log-likelihood function at y given link(f) w.r.t link(f) @@ -120,7 +125,7 @@ class Poisson(NoiseDistribution): :type link_f: Nx1 array :param y: data :type y: Nx1 array - :param extra_data: extra_data which is not used in poisson distribution + :param Y_metadata: Y_metadata which is not used in poisson distribution :returns: third derivative of likelihood evaluated at points f :rtype: Nx1 array """ @@ -128,19 +133,19 @@ class Poisson(NoiseDistribution): d3lik_dlink3 = 2*y/(link_f)**3 return d3lik_dlink3 - def _mean(self,gp): + def conditional_mean(self,gp): """ - Mass (or density) function + The mean of the random variable conditioned on one value of the GP """ return self.gp_link.transf(gp) - def _variance(self,gp): + def conditional_variance(self,gp): """ - Mass (or density) function + The variance of the random variable conditioned on one value of the GP """ return self.gp_link.transf(gp) - def samples(self, gp): + def samples(self, gp, Y_metadata=None): """ Returns a set of samples of observations based on a given value of the latent variable. diff --git a/GPy/likelihoods/student_t.py b/GPy/likelihoods/student_t.py new file mode 100644 index 00000000..855f6b40 --- /dev/null +++ b/GPy/likelihoods/student_t.py @@ -0,0 +1,279 @@ +# Copyright (c) 2012-2014 Ricardo Andrade, Alan Saul +# Licensed under the BSD 3-clause license (see LICENSE.txt) + +import numpy as np +from scipy import stats, special +import scipy as sp +import link_functions +from scipy import stats, integrate +from scipy.special import gammaln, gamma +from likelihood import Likelihood +from ..core.parameterization import Param +from ..core.parameterization.transformations import Logexp + +class StudentT(Likelihood): + """ + Student T likelihood + + For nomanclature see Bayesian Data Analysis 2003 p576 + + .. math:: + p(y_{i}|\\lambda(f_{i})) = \\frac{\\Gamma\\left(\\frac{v+1}{2}\\right)}{\\Gamma\\left(\\frac{v}{2}\\right)\\sqrt{v\\pi\\sigma^{2}}}\\left(1 + \\frac{1}{v}\\left(\\frac{(y_{i} - f_{i})^{2}}{\\sigma^{2}}\\right)\\right)^{\\frac{-v+1}{2}} + + """ + def __init__(self,gp_link=None, deg_free=5, sigma2=2): + if gp_link is None: + gp_link = link_functions.Identity() + + super(StudentT, self).__init__(gp_link, name='Student_T') + # sigma2 is not a noise parameter, it is a squared scale. + self.sigma2 = Param('t_scale2', float(sigma2), Logexp()) + self.v = Param('deg_free', float(deg_free)) + self.link_parameter(self.sigma2) + self.link_parameter(self.v) + self.v.constrain_fixed() + + self.log_concave = False + + def parameters_changed(self): + self.variance = (self.v / float(self.v - 2)) * self.sigma2 + + def update_gradients(self, grads): + """ + Pull out the gradients, be careful as the order must match the order + in which the parameters are added + """ + self.sigma2.gradient = grads[0] + self.v.gradient = grads[1] + + def pdf_link(self, inv_link_f, y, Y_metadata=None): + """ + Likelihood function given link(f) + + .. math:: + p(y_{i}|\\lambda(f_{i})) = \\frac{\\Gamma\\left(\\frac{v+1}{2}\\right)}{\\Gamma\\left(\\frac{v}{2}\\right)\\sqrt{v\\pi\\sigma^{2}}}\\left(1 + \\frac{1}{v}\\left(\\frac{(y_{i} - \\lambda(f_{i}))^{2}}{\\sigma^{2}}\\right)\\right)^{\\frac{-v+1}{2}} + + :param inv_link_f: latent variables link(f) + :type inv_link_f: Nx1 array + :param y: data + :type y: Nx1 array + :param Y_metadata: Y_metadata which is not used in student t distribution + :returns: likelihood evaluated for this point + :rtype: float + """ + assert np.atleast_1d(inv_link_f).shape == np.atleast_1d(y).shape + e = y - inv_link_f + #Careful gamma(big_number) is infinity! + objective = ((np.exp(gammaln((self.v + 1)*0.5) - gammaln(self.v * 0.5)) + / (np.sqrt(self.v * np.pi * self.sigma2))) + * ((1 + (1./float(self.v))*((e**2)/float(self.sigma2)))**(-0.5*(self.v + 1))) + ) + return np.prod(objective) + + def logpdf_link(self, inv_link_f, y, Y_metadata=None): + """ + Log Likelihood Function given link(f) + + .. math:: + \\ln p(y_{i}|\lambda(f_{i})) = \\ln \\Gamma\\left(\\frac{v+1}{2}\\right) - \\ln \\Gamma\\left(\\frac{v}{2}\\right) - \\ln \\sqrt{v \\pi\\sigma^{2}} - \\frac{v+1}{2}\\ln \\left(1 + \\frac{1}{v}\\left(\\frac{(y_{i} - \lambda(f_{i}))^{2}}{\\sigma^{2}}\\right)\\right) + + :param inv_link_f: latent variables (link(f)) + :type inv_link_f: Nx1 array + :param y: data + :type y: Nx1 array + :param Y_metadata: Y_metadata which is not used in student t distribution + :returns: likelihood evaluated for this point + :rtype: float + + """ + assert np.atleast_1d(inv_link_f).shape == np.atleast_1d(y).shape + e = y - inv_link_f + #FIXME: + #Why does np.log(1 + (1/self.v)*((y-inv_link_f)**2)/self.sigma2) suppress the divide by zero?! + #But np.log(1 + (1/float(self.v))*((y-inv_link_f)**2)/self.sigma2) throws it correctly + #print - 0.5*(self.v + 1)*np.log(1 + (1/np.float(self.v))*((e**2)/self.sigma2)) + objective = (+ gammaln((self.v + 1) * 0.5) + - gammaln(self.v * 0.5) + - 0.5*np.log(self.sigma2 * self.v * np.pi) + - 0.5*(self.v + 1)*np.log(1 + (1/np.float(self.v))*((e**2)/self.sigma2)) + ) + return np.sum(objective) + + def dlogpdf_dlink(self, inv_link_f, y, Y_metadata=None): + """ + Gradient of the log likelihood function at y, given link(f) w.r.t link(f) + + .. math:: + \\frac{d \\ln p(y_{i}|\lambda(f_{i}))}{d\\lambda(f)} = \\frac{(v+1)(y_{i}-\lambda(f_{i}))}{(y_{i}-\lambda(f_{i}))^{2} + \\sigma^{2}v} + + :param inv_link_f: latent variables (f) + :type inv_link_f: Nx1 array + :param y: data + :type y: Nx1 array + :param Y_metadata: Y_metadata which is not used in student t distribution + :returns: gradient of likelihood evaluated at points + :rtype: Nx1 array + + """ + assert np.atleast_1d(inv_link_f).shape == np.atleast_1d(y).shape + e = y - inv_link_f + grad = ((self.v + 1) * e) / (self.v * self.sigma2 + (e**2)) + return grad + + def d2logpdf_dlink2(self, inv_link_f, y, Y_metadata=None): + """ + Hessian at y, given link(f), w.r.t link(f) + i.e. second derivative logpdf at y given link(f_i) and link(f_j) w.r.t link(f_i) and link(f_j) + The hessian will be 0 unless i == j + + .. math:: + \\frac{d^{2} \\ln p(y_{i}|\lambda(f_{i}))}{d^{2}\\lambda(f)} = \\frac{(v+1)((y_{i}-\lambda(f_{i}))^{2} - \\sigma^{2}v)}{((y_{i}-\lambda(f_{i}))^{2} + \\sigma^{2}v)^{2}} + + :param inv_link_f: latent variables inv_link(f) + :type inv_link_f: Nx1 array + :param y: data + :type y: Nx1 array + :param Y_metadata: Y_metadata which is not used in student t distribution + :returns: Diagonal of hessian matrix (second derivative of likelihood evaluated at points f) + :rtype: Nx1 array + + .. Note:: + Will return diagonal of hessian, since every where else it is 0, as the likelihood factorizes over cases + (the distribution for y_i depends only on link(f_i) not on link(f_(j!=i)) + """ + assert np.atleast_1d(inv_link_f).shape == np.atleast_1d(y).shape + e = y - inv_link_f + hess = ((self.v + 1)*(e**2 - self.v*self.sigma2)) / ((self.sigma2*self.v + e**2)**2) + return hess + + def d3logpdf_dlink3(self, inv_link_f, y, Y_metadata=None): + """ + Third order derivative log-likelihood function at y given link(f) w.r.t link(f) + + .. math:: + \\frac{d^{3} \\ln p(y_{i}|\lambda(f_{i}))}{d^{3}\\lambda(f)} = \\frac{-2(v+1)((y_{i} - \lambda(f_{i}))^3 - 3(y_{i} - \lambda(f_{i})) \\sigma^{2} v))}{((y_{i} - \lambda(f_{i})) + \\sigma^{2} v)^3} + + :param inv_link_f: latent variables link(f) + :type inv_link_f: Nx1 array + :param y: data + :type y: Nx1 array + :param Y_metadata: Y_metadata which is not used in student t distribution + :returns: third derivative of likelihood evaluated at points f + :rtype: Nx1 array + """ + assert np.atleast_1d(inv_link_f).shape == np.atleast_1d(y).shape + e = y - inv_link_f + d3lik_dlink3 = ( -(2*(self.v + 1)*(-e)*(e**2 - 3*self.v*self.sigma2)) / + ((e**2 + self.sigma2*self.v)**3) + ) + return d3lik_dlink3 + + def dlogpdf_link_dvar(self, inv_link_f, y, Y_metadata=None): + """ + Gradient of the log-likelihood function at y given f, w.r.t variance parameter (t_noise) + + .. math:: + \\frac{d \\ln p(y_{i}|\lambda(f_{i}))}{d\\sigma^{2}} = \\frac{v((y_{i} - \lambda(f_{i}))^{2} - \\sigma^{2})}{2\\sigma^{2}(\\sigma^{2}v + (y_{i} - \lambda(f_{i}))^{2})} + + :param inv_link_f: latent variables link(f) + :type inv_link_f: Nx1 array + :param y: data + :type y: Nx1 array + :param Y_metadata: Y_metadata which is not used in student t distribution + :returns: derivative of likelihood evaluated at points f w.r.t variance parameter + :rtype: float + """ + assert np.atleast_1d(inv_link_f).shape == np.atleast_1d(y).shape + e = y - inv_link_f + dlogpdf_dvar = self.v*(e**2 - self.sigma2)/(2*self.sigma2*(self.sigma2*self.v + e**2)) + return np.sum(dlogpdf_dvar) + + def dlogpdf_dlink_dvar(self, inv_link_f, y, Y_metadata=None): + """ + Derivative of the dlogpdf_dlink w.r.t variance parameter (t_noise) + + .. math:: + \\frac{d}{d\\sigma^{2}}(\\frac{d \\ln p(y_{i}|\lambda(f_{i}))}{df}) = \\frac{-2\\sigma v(v + 1)(y_{i}-\lambda(f_{i}))}{(y_{i}-\lambda(f_{i}))^2 + \\sigma^2 v)^2} + + :param inv_link_f: latent variables inv_link_f + :type inv_link_f: Nx1 array + :param y: data + :type y: Nx1 array + :param Y_metadata: Y_metadata which is not used in student t distribution + :returns: derivative of likelihood evaluated at points f w.r.t variance parameter + :rtype: Nx1 array + """ + assert np.atleast_1d(inv_link_f).shape == np.atleast_1d(y).shape + e = y - inv_link_f + dlogpdf_dlink_dvar = (self.v*(self.v+1)*(-e))/((self.sigma2*self.v + e**2)**2) + return dlogpdf_dlink_dvar + + def d2logpdf_dlink2_dvar(self, inv_link_f, y, Y_metadata=None): + """ + Gradient of the hessian (d2logpdf_dlink2) w.r.t variance parameter (t_noise) + + .. math:: + \\frac{d}{d\\sigma^{2}}(\\frac{d^{2} \\ln p(y_{i}|\lambda(f_{i}))}{d^{2}f}) = \\frac{v(v+1)(\\sigma^{2}v - 3(y_{i} - \lambda(f_{i}))^{2})}{(\\sigma^{2}v + (y_{i} - \lambda(f_{i}))^{2})^{3}} + + :param inv_link_f: latent variables link(f) + :type inv_link_f: Nx1 array + :param y: data + :type y: Nx1 array + :param Y_metadata: Y_metadata which is not used in student t distribution + :returns: derivative of hessian evaluated at points f and f_j w.r.t variance parameter + :rtype: Nx1 array + """ + assert np.atleast_1d(inv_link_f).shape == np.atleast_1d(y).shape + e = y - inv_link_f + d2logpdf_dlink2_dvar = ( (self.v*(self.v+1)*(self.sigma2*self.v - 3*(e**2))) + / ((self.sigma2*self.v + (e**2))**3) + ) + return d2logpdf_dlink2_dvar + + def dlogpdf_link_dtheta(self, f, y, Y_metadata=None): + dlogpdf_dvar = self.dlogpdf_link_dvar(f, y, Y_metadata=Y_metadata) + dlogpdf_dv = np.zeros_like(dlogpdf_dvar) #FIXME: Not done yet + return np.hstack((dlogpdf_dvar, dlogpdf_dv)) + + def dlogpdf_dlink_dtheta(self, f, y, Y_metadata=None): + dlogpdf_dlink_dvar = self.dlogpdf_dlink_dvar(f, y, Y_metadata=Y_metadata) + dlogpdf_dlink_dv = np.zeros_like(dlogpdf_dlink_dvar) #FIXME: Not done yet + return np.hstack((dlogpdf_dlink_dvar, dlogpdf_dlink_dv)) + + def d2logpdf_dlink2_dtheta(self, f, y, Y_metadata=None): + d2logpdf_dlink2_dvar = self.d2logpdf_dlink2_dvar(f, y, Y_metadata=Y_metadata) + d2logpdf_dlink2_dv = np.zeros_like(d2logpdf_dlink2_dvar) #FIXME: Not done yet + return np.hstack((d2logpdf_dlink2_dvar, d2logpdf_dlink2_dv)) + + def predictive_mean(self, mu, sigma, Y_metadata=None): + # The comment here confuses mean and median. + return self.gp_link.transf(mu) # only true if link is monotonic, which it is. + + def predictive_variance(self, mu,variance, predictive_mean=None, Y_metadata=None): + if self.deg_free<=2.: + return np.empty(mu.shape)*np.nan # does not exist for degrees of freedom <= 2. + else: + return super(StudentT, self).predictive_variance(mu, variance, predictive_mean, Y_metadata) + + def conditional_mean(self, gp): + return self.gp_link.transf(gp) + + def conditional_variance(self, gp): + return self.deg_free/(self.deg_free - 2.) + + def samples(self, gp, Y_metadata=None): + """ + Returns a set of samples of observations based on a given value of the latent variable. + + :param gp: latent variable + """ + orig_shape = gp.shape + gp = gp.flatten() + #FIXME: Very slow as we are computing a new random variable per input! + #Can't get it to sample all at the same time + #student_t_samples = np.array([stats.t.rvs(self.v, self.gp_link.transf(gpj),scale=np.sqrt(self.sigma2), size=1) for gpj in gp]) + dfs = np.ones_like(gp)*self.v + scales = np.ones_like(gp)*np.sqrt(self.sigma2) + student_t_samples = stats.t.rvs(dfs, loc=self.gp_link.transf(gp), + scale=scales) + return student_t_samples.reshape(orig_shape) diff --git a/GPy/mappings/__init__.py b/GPy/mappings/__init__.py index 97573aba..d331c678 100644 --- a/GPy/mappings/__init__.py +++ b/GPy/mappings/__init__.py @@ -1,4 +1,4 @@ -# Copyright (c) 2013, GPy authors (see AUTHORS.txt). +# Copyright (c) 2013, 2014 GPy authors (see AUTHORS.txt). # Licensed under the BSD 3-clause license (see LICENSE.txt) from kernel import Kernel diff --git a/GPy/mappings/additive.py b/GPy/mappings/additive.py new file mode 100644 index 00000000..5297982b --- /dev/null +++ b/GPy/mappings/additive.py @@ -0,0 +1,61 @@ +# Copyright (c) 2013, GPy authors (see AUTHORS.txt). +# Licensed under the BSD 3-clause license (see LICENSE.txt) + +import numpy as np +from ..core.mapping import Mapping +import GPy + +class Additive(Mapping): + """ + Mapping based on adding two existing mappings together. + + .. math:: + + f(\mathbf{x}*) = f_1(\mathbf{x}*) + f_2(\mathbf(x)*) + + :param mapping1: first mapping to add together. + :type mapping1: GPy.mappings.Mapping + :param mapping2: second mapping to add together. + :type mapping2: GPy.mappings.Mapping + :param tensor: whether or not to use the tensor product of input spaces + :type tensor: bool + + """ + + def __init__(self, mapping1, mapping2, tensor=False): + if tensor: + input_dim = mapping1.input_dim + mapping2.input_dim + else: + input_dim = mapping1.input_dim + assert(mapping1.input_dim==mapping2.input_dim) + assert(mapping1.output_dim==mapping2.output_dim) + output_dim = mapping1.output_dim + Mapping.__init__(self, input_dim=input_dim, output_dim=output_dim) + self.mapping1 = mapping1 + self.mapping2 = mapping2 + self.num_params = self.mapping1.num_params + self.mapping2.num_params + self.name = self.mapping1.name + '+' + self.mapping2.name + def _get_param_names(self): + return self.mapping1._get_param_names + self.mapping2._get_param_names + + def _get_params(self): + return np.hstack((self.mapping1._get_params(), self.mapping2._get_params())) + + def _set_params(self, x): + self.mapping1._set_params(x[:self.mapping1.num_params]) + self.mapping2._set_params(x[self.mapping1.num_params:]) + + def randomize(self): + self.mapping1._randomize() + self.mapping2._randomize() + + def f(self, X): + return self.mapping1.f(X) + self.mapping2.f(X) + + def df_dtheta(self, dL_df, X): + self._df_dA = (dL_df[:, :, None]*self.kern.K(X, self.X)[:, None, :]).sum(0).T + self._df_dbias = (dL_df.sum(0)) + return np.hstack((self._df_dA.flatten(), self._df_dbias)) + + def df_dX(self, dL_df, X): + return self.kern.dK_dX((dL_df[:, None, :]*self.A[None, :, :]).sum(2), X, self.X) diff --git a/GPy/mappings/kernel.py b/GPy/mappings/kernel.py index 5c802c13..74fa344f 100644 --- a/GPy/mappings/kernel.py +++ b/GPy/mappings/kernel.py @@ -17,7 +17,7 @@ class Kernel(Mapping): :type X: ndarray :param output_dim: dimension of output. :type output_dim: int - :param kernel: a GPy kernel, defaults to GPy.kern.rbf + :param kernel: a GPy kernel, defaults to GPy.kern.RBF :type kernel: GPy.kern.kern """ @@ -25,7 +25,7 @@ class Kernel(Mapping): def __init__(self, X, output_dim=1, kernel=None): Mapping.__init__(self, input_dim=X.shape[1], output_dim=output_dim) if kernel is None: - kernel = GPy.kern.rbf(self.input_dim) + kernel = GPy.kern.RBF(self.input_dim) self.kern = kernel self.X = X self.num_data = X.shape[0] @@ -43,7 +43,7 @@ class Kernel(Mapping): def _set_params(self, x): self.A = x[:self.num_data * self.output_dim].reshape(self.num_data, self.output_dim).copy() self.bias = x[self.num_data*self.output_dim:].copy() - + def randomize(self): self.A = np.random.randn(self.num_data, self.output_dim)/np.sqrt(self.num_data+1) self.bias = np.random.randn(self.output_dim)/np.sqrt(self.num_data+1) @@ -57,4 +57,4 @@ class Kernel(Mapping): return np.hstack((self._df_dA.flatten(), self._df_dbias)) def df_dX(self, dL_df, X): - return self.kern.dK_dX((dL_df[:, None, :]*self.A[None, :, :]).sum(2), X, self.X) + return self.kern.gradients_X((dL_df[:, None, :]*self.A[None, :, :]).sum(2), X, self.X) diff --git a/GPy/mappings/linear.py b/GPy/mappings/linear.py index 5846903d..315dfc0e 100644 --- a/GPy/mappings/linear.py +++ b/GPy/mappings/linear.py @@ -1,10 +1,11 @@ -# Copyright (c) 2013, GPy authors (see AUTHORS.txt). +# Copyright (c) 2013, 2014 GPy authors (see AUTHORS.txt). # Licensed under the BSD 3-clause license (see LICENSE.txt) import numpy as np -from ..core.mapping import Mapping +from ..core.mapping import Bijective_mapping +from ..core.parameterization import Param -class Linear(Mapping): +class Linear(Bijective_mapping): """ Mapping based on a linear model. @@ -16,38 +17,27 @@ class Linear(Mapping): :type X: ndarray :param output_dim: dimension of output. :type output_dim: int - + """ - def __init__(self, input_dim=1, output_dim=1): - self.name = 'linear' - Mapping.__init__(self, input_dim=input_dim, output_dim=output_dim) - self.num_params = self.output_dim*(self.input_dim + 1) - self.W = np.array((self.input_dim, self.output_dim)) - self.bias = np.array(self.output_dim) - self.randomize() - - def _get_param_names(self): - return sum([['W_%i_%i' % (n, d) for d in range(self.output_dim)] for n in range(self.input_dim)], []) + ['bias_%i' % d for d in range(self.output_dim)] - - def _get_params(self): - return np.hstack((self.W.flatten(), self.bias)) - - def _set_params(self, x): - self.W = x[:self.input_dim * self.output_dim].reshape(self.input_dim, self.output_dim).copy() - self.bias = x[self.input_dim*self.output_dim:].copy() - def randomize(self): - self.W = np.random.randn(self.input_dim, self.output_dim)/np.sqrt(self.input_dim + 1) - self.bias = np.random.randn(self.output_dim)/np.sqrt(self.input_dim + 1) + def __init__(self, input_dim=1, output_dim=1, name='linear'): + Bijective_mapping.__init__(self, input_dim=input_dim, output_dim=output_dim, name=name) + self.W = Param('W',np.array((self.input_dim, self.output_dim))) + self.bias = Param('bias',np.array(self.output_dim)) + self.link_parameters(self.W, self.bias) def f(self, X): return np.dot(X,self.W) + self.bias + def g(self, f): + V = np.linalg.solve(np.dot(self.W.T, self.W), W.T) + return np.dot(f-self.bias, V) + def df_dtheta(self, dL_df, X): - self._df_dW = (dL_df[:, :, None]*X[:, None, :]).sum(0).T - self._df_dbias = (dL_df.sum(0)) - return np.hstack((self._df_dW.flatten(), self._df_dbias)) - - def df_dX(self, dL_df, X): - return (dL_df[:, None, :]*self.W[None, :, :]).sum(2) - + df_dW = (dL_df[:, :, None]*X[:, None, :]).sum(0).T + df_dbias = (dL_df.sum(0)) + return np.hstack((df_dW.flatten(), df_dbias)) + + def dL_dX(self, partial, X): + """The gradient of L with respect to the inputs to the mapping, where L is a function that is dependent on the output of the mapping, f.""" + return (partial[:, None, :]*self.W[None, :, :]).sum(2) diff --git a/GPy/models/__init__.py b/GPy/models/__init__.py new file mode 100644 index 00000000..c6abb5de --- /dev/null +++ b/GPy/models/__init__.py @@ -0,0 +1,23 @@ +# Copyright (c) 2012, GPy authors (see AUTHORS.txt). +# Licensed under the BSD 3-clause license (see LICENSE.txt) + +from gp_regression import GPRegression +from gp_classification import GPClassification +from sparse_gp_regression import SparseGPRegression, SparseGPRegressionUncertainInput +from sparse_gp_classification import SparseGPClassification +from gplvm import GPLVM +from bcgplvm import BCGPLVM +from sparse_gplvm import SparseGPLVM +from warped_gp import WarpedGP +from bayesian_gplvm import BayesianGPLVM +from mrd import MRD +from gradient_checker import GradientChecker +from ss_gplvm import SSGPLVM +from gp_coregionalized_regression import GPCoregionalizedRegression +from sparse_gp_coregionalized_regression import SparseGPCoregionalizedRegression +from gp_heteroscedastic_regression import GPHeteroscedasticRegression +from ss_mrd import SSMRD +from gp_kronecker_gaussian_regression import GPKroneckerGaussianRegression +from gp_var_gauss import GPVariationalGaussianApproximation +from one_vs_all_classification import OneVsAllClassification +from one_vs_all_sparse_classification import OneVsAllSparseClassification diff --git a/GPy/models/bayesian_gplvm.py b/GPy/models/bayesian_gplvm.py new file mode 100644 index 00000000..7cbd69eb --- /dev/null +++ b/GPy/models/bayesian_gplvm.py @@ -0,0 +1,234 @@ +# Copyright (c) 2012 - 2014 the GPy Austhors (see AUTHORS.txt) +# Licensed under the BSD 3-clause license (see LICENSE.txt) + +import numpy as np +from .. import kern +from ..core.sparse_gp_mpi import SparseGP_MPI +from ..likelihoods import Gaussian +from ..core.parameterization.variational import NormalPosterior, NormalPrior +from ..inference.latent_function_inference.var_dtc_parallel import VarDTC_minibatch +import logging + +class BayesianGPLVM(SparseGP_MPI): + """ + Bayesian Gaussian Process Latent Variable Model + + :param Y: observed data (np.ndarray) or GPy.likelihood + :type Y: np.ndarray| GPy.likelihood instance + :param input_dim: latent dimensionality + :type input_dim: int + :param init: initialisation method for the latent space + :type init: 'PCA'|'random' + + """ + def __init__(self, Y, input_dim, X=None, X_variance=None, init='PCA', num_inducing=10, + Z=None, kernel=None, inference_method=None, likelihood=None, + name='bayesian gplvm', mpi_comm=None, normalizer=None, + missing_data=False, stochastic=False, batchsize=1): + + self.logger = logging.getLogger(self.__class__.__name__) + if X is None: + from ..util.initialization import initialize_latent + self.logger.info("initializing latent space X with method {}".format(init)) + X, fracs = initialize_latent(init, input_dim, Y) + else: + fracs = np.ones(input_dim) + + self.init = init + + if X_variance is None: + self.logger.info("initializing latent space variance ~ uniform(0,.1)") + X_variance = np.random.uniform(0,.1,X.shape) + + if Z is None: + self.logger.info("initializing inducing inputs") + Z = np.random.permutation(X.copy())[:num_inducing] + assert Z.shape[1] == X.shape[1] + + if kernel is None: + self.logger.info("initializing kernel RBF") + kernel = kern.RBF(input_dim, lengthscale=1./fracs, ARD=True) #+ kern.Bias(input_dim) + kern.White(input_dim) + + if likelihood is None: + likelihood = Gaussian() + + self.variational_prior = NormalPrior() + X = NormalPosterior(X, X_variance) + + if inference_method is None: + if mpi_comm is not None: + inference_method = VarDTC_minibatch(mpi_comm=mpi_comm) + else: + from ..inference.latent_function_inference.var_dtc import VarDTC + self.logger.debug("creating inference_method var_dtc") + inference_method = VarDTC(limit=1 if not missing_data else Y.shape[1]) + if isinstance(inference_method,VarDTC_minibatch): + inference_method.mpi_comm = mpi_comm + + super(BayesianGPLVM,self).__init__(X, Y, Z, kernel, likelihood=likelihood, + name=name, inference_method=inference_method, + normalizer=normalizer, mpi_comm=mpi_comm, + variational_prior=self.variational_prior, + ) + self.link_parameter(self.X, index=0) + + def set_X_gradients(self, X, X_grad): + """Set the gradients of the posterior distribution of X in its specific form.""" + X.mean.gradient, X.variance.gradient = X_grad + + def get_X_gradients(self, X): + """Get the gradients of the posterior distribution of X in its specific form.""" + return X.mean.gradient, X.variance.gradient + + def parameters_changed(self): + super(BayesianGPLVM,self).parameters_changed() + if isinstance(self.inference_method, VarDTC_minibatch): + return + + kl_fctr = 1. + self._log_marginal_likelihood -= kl_fctr*self.variational_prior.KL_divergence(self.X) + + self.X.mean.gradient, self.X.variance.gradient = self.kern.gradients_qX_expectations( + variational_posterior=self.X, + Z=self.Z, + dL_dpsi0=self.grad_dict['dL_dpsi0'], + dL_dpsi1=self.grad_dict['dL_dpsi1'], + dL_dpsi2=self.grad_dict['dL_dpsi2']) + + self.variational_prior.update_gradients_KL(self.X) + + + #super(BayesianGPLVM, self).parameters_changed() + #self._log_marginal_likelihood -= self.variational_prior.KL_divergence(self.X) + + #self.X.mean.gradient, self.X.variance.gradient = self.kern.gradients_qX_expectations(variational_posterior=self.X, Z=self.Z, dL_dpsi0=self.grad_dict['dL_dpsi0'], dL_dpsi1=self.grad_dict['dL_dpsi1'], dL_dpsi2=self.grad_dict['dL_dpsi2']) + + # This is testing code ------------------------- +# i = np.random.randint(self.X.shape[0]) +# X_ = self.X.mean +# which = np.sqrt(((X_ - X_[i:i+1])**2).sum(1)).argsort()>(max(0, self.X.shape[0]-51)) +# _, _, grad_dict = self.inference_method.inference(self.kern, self.X[which], self.Z, self.likelihood, self.Y[which], self.Y_metadata) +# grad = self.kern.gradients_qX_expectations(variational_posterior=self.X[which], Z=self.Z, dL_dpsi0=grad_dict['dL_dpsi0'], dL_dpsi1=grad_dict['dL_dpsi1'], dL_dpsi2=grad_dict['dL_dpsi2']) +# +# self.X.mean.gradient[:] = 0 +# self.X.variance.gradient[:] = 0 +# self.X.mean.gradient[which] = grad[0] +# self.X.variance.gradient[which] = grad[1] + + # update for the KL divergence +# self.variational_prior.update_gradients_KL(self.X, which) + # ----------------------------------------------- + + # update for the KL divergence + #self.variational_prior.update_gradients_KL(self.X) + + def plot_latent(self, labels=None, which_indices=None, + resolution=50, ax=None, marker='o', s=40, + fignum=None, plot_inducing=True, legend=True, + plot_limits=None, + aspect='auto', updates=False, predict_kwargs={}, imshow_kwargs={}): + import sys + assert "matplotlib" in sys.modules, "matplotlib package has not been imported." + from ..plotting.matplot_dep import dim_reduction_plots + + return dim_reduction_plots.plot_latent(self, labels, which_indices, + resolution, ax, marker, s, + fignum, plot_inducing, legend, + plot_limits, aspect, updates, predict_kwargs, imshow_kwargs) + + def do_test_latents(self, Y): + """ + Compute the latent representation for a set of new points Y + + Notes: + This will only work with a univariate Gaussian likelihood (for now) + """ + N_test = Y.shape[0] + input_dim = self.Z.shape[1] + + means = np.zeros((N_test, input_dim)) + covars = np.zeros((N_test, input_dim)) + + dpsi0 = -0.5 * self.input_dim / self.likelihood.variance + dpsi2 = self.grad_dict['dL_dpsi2'][0][None, :, :] # TODO: this may change if we ignore het. likelihoods + V = Y/self.likelihood.variance + + #compute CPsi1V + #if self.Cpsi1V is None: + # psi1V = np.dot(self.psi1.T, self.likelihood.V) + # tmp, _ = linalg.dtrtrs(self._Lm, np.asfortranarray(psi1V), lower=1, trans=0) + # tmp, _ = linalg.dpotrs(self.LB, tmp, lower=1) + # self.Cpsi1V, _ = linalg.dtrtrs(self._Lm, tmp, lower=1, trans=1) + + dpsi1 = np.dot(self.posterior.woodbury_vector, V.T) + + #start = np.zeros(self.input_dim * 2) + + + from scipy.optimize import minimize + + for n, dpsi1_n in enumerate(dpsi1.T[:, :, None]): + args = (input_dim, self.kern.copy(), self.Z, dpsi0, dpsi1_n.T, dpsi2) + res = minimize(latent_cost_and_grad, jac=True, x0=np.hstack((means[n], covars[n])), args=args, method='BFGS') + xopt = res.x + mu, log_S = xopt.reshape(2, 1, -1) + means[n] = mu[0].copy() + covars[n] = np.exp(log_S[0]).copy() + + X = NormalPosterior(means, covars) + + return X + + def dmu_dX(self, Xnew): + """ + Calculate the gradient of the prediction at Xnew w.r.t Xnew. + """ + dmu_dX = np.zeros_like(Xnew) + for i in range(self.Z.shape[0]): + dmu_dX += self.kern.gradients_X(self.grad_dict['dL_dpsi1'][i:i + 1, :], Xnew, self.Z[i:i + 1, :]) + return dmu_dX + + def dmu_dXnew(self, Xnew): + """ + Individual gradient of prediction at Xnew w.r.t. each sample in Xnew + """ + gradients_X = np.zeros((Xnew.shape[0], self.num_inducing)) + ones = np.ones((1, 1)) + for i in range(self.Z.shape[0]): + gradients_X[:, i] = self.kern.gradients_X(ones, Xnew, self.Z[i:i + 1, :]).sum(-1) + return np.dot(gradients_X, self.grad_dict['dL_dpsi1']) + + def plot_steepest_gradient_map(self, *args, ** kwargs): + """ + See GPy.plotting.matplot_dep.dim_reduction_plots.plot_steepest_gradient_map + """ + import sys + assert "matplotlib" in sys.modules, "matplotlib package has not been imported." + from ..plotting.matplot_dep import dim_reduction_plots + + return dim_reduction_plots.plot_steepest_gradient_map(self,*args,**kwargs) + + +def latent_cost_and_grad(mu_S, input_dim, kern, Z, dL_dpsi0, dL_dpsi1, dL_dpsi2): + """ + objective function for fitting the latent variables for test points + (negative log-likelihood: should be minimised!) + """ + mu = mu_S[:input_dim][None] + log_S = mu_S[input_dim:][None] + S = np.exp(log_S) + + X = NormalPosterior(mu, S) + + psi0 = kern.psi0(Z, X) + psi1 = kern.psi1(Z, X) + psi2 = kern.psi2(Z, X) + + lik = dL_dpsi0 * psi0.sum() + np.einsum('ij,kj->...', dL_dpsi1, psi1) + np.einsum('ijk,lkj->...', dL_dpsi2, psi2) - 0.5 * np.sum(np.square(mu) + S) + 0.5 * np.sum(log_S) + + dLdmu, dLdS = kern.gradients_qX_expectations(dL_dpsi0, dL_dpsi1, dL_dpsi2, Z, X) + dmu = dLdmu - mu + # dS = S0 + S1 + S2 -0.5 + .5/S + dlnS = S * (dLdS - 0.5) + .5 + + return -lik, -np.hstack((dmu.flatten(), dlnS.flatten())) diff --git a/GPy/models/bayesian_gplvm_minibatch.py b/GPy/models/bayesian_gplvm_minibatch.py new file mode 100644 index 00000000..f164b466 --- /dev/null +++ b/GPy/models/bayesian_gplvm_minibatch.py @@ -0,0 +1,269 @@ +# Copyright (c) 2012-2014, GPy authors (see AUTHORS.txt). +# Licensed under the BSD 3-clause license (see LICENSE.txt) + +import numpy as np +from .. import kern +from ..likelihoods import Gaussian +from ..core.parameterization.variational import NormalPosterior, NormalPrior +from ..inference.latent_function_inference.var_dtc_parallel import VarDTC_minibatch +import logging +from GPy.models.sparse_gp_minibatch import SparseGPMiniBatch + +class BayesianGPLVMMiniBatch(SparseGPMiniBatch): + """ + Bayesian Gaussian Process Latent Variable Model + + :param Y: observed data (np.ndarray) or GPy.likelihood + :type Y: np.ndarray| GPy.likelihood instance + :param input_dim: latent dimensionality + :type input_dim: int + :param init: initialisation method for the latent space + :type init: 'PCA'|'random' + + """ + def __init__(self, Y, input_dim, X=None, X_variance=None, init='PCA', num_inducing=10, + Z=None, kernel=None, inference_method=None, likelihood=None, + name='bayesian gplvm', normalizer=None, + missing_data=False, stochastic=False, batchsize=1): + self.logger = logging.getLogger(self.__class__.__name__) + if X is None: + from ..util.initialization import initialize_latent + self.logger.info("initializing latent space X with method {}".format(init)) + X, fracs = initialize_latent(init, input_dim, Y) + else: + fracs = np.ones(input_dim) + + self.init = init + + if X_variance is None: + self.logger.info("initializing latent space variance ~ uniform(0,.1)") + X_variance = np.random.uniform(0,.1,X.shape) + + if Z is None: + self.logger.info("initializing inducing inputs") + Z = np.random.permutation(X.copy())[:num_inducing] + assert Z.shape[1] == X.shape[1] + + if kernel is None: + self.logger.info("initializing kernel RBF") + kernel = kern.RBF(input_dim, lengthscale=1./fracs, ARD=True) #+ kern.Bias(input_dim) + kern.White(input_dim) + + if likelihood is None: + likelihood = Gaussian() + + self.variational_prior = NormalPrior() + X = NormalPosterior(X, X_variance) + + self.kl_factr = 1. + + if inference_method is None: + from ..inference.latent_function_inference.var_dtc import VarDTC + self.logger.debug("creating inference_method var_dtc") + inference_method = VarDTC(limit=1 if not missing_data else Y.shape[1]) + + if kernel.useGPU and isinstance(inference_method, VarDTC_GPU): + kernel.psicomp.GPU_direct = True + + super(BayesianGPLVMMiniBatch,self).__init__(X, Y, Z, kernel, likelihood=likelihood, + name=name, inference_method=inference_method, + normalizer=normalizer, + missing_data=missing_data, stochastic=stochastic, + batchsize=batchsize) + self.X = X + self.link_parameter(self.X, 0) + + def set_X_gradients(self, X, X_grad): + """Set the gradients of the posterior distribution of X in its specific form.""" + X.mean.gradient, X.variance.gradient = X_grad + + def get_X_gradients(self, X): + """Get the gradients of the posterior distribution of X in its specific form.""" + return X.mean.gradient, X.variance.gradient + + def _inner_parameters_changed(self, kern, X, Z, likelihood, Y, Y_metadata, Lm=None, dL_dKmm=None, subset_indices=None): + posterior, log_marginal_likelihood, grad_dict, current_values, value_indices = super(BayesianGPLVMMiniBatch, self)._inner_parameters_changed(kern, X, Z, likelihood, Y, Y_metadata, Lm=Lm, dL_dKmm=dL_dKmm, subset_indices=subset_indices) + + current_values['meangrad'], current_values['vargrad'] = self.kern.gradients_qX_expectations( + variational_posterior=X, + Z=Z, dL_dpsi0=grad_dict['dL_dpsi0'], + dL_dpsi1=grad_dict['dL_dpsi1'], + dL_dpsi2=grad_dict['dL_dpsi2']) + + kl_fctr = self.kl_factr + if self.missing_data: + d = self.output_dim + log_marginal_likelihood -= kl_fctr*self.variational_prior.KL_divergence(X)/d + else: + log_marginal_likelihood -= kl_fctr*self.variational_prior.KL_divergence(X) + + + # Subsetting Variational Posterior objects, makes the gradients + # empty. We need them to be 0 though: + X.mean.gradient[:] = 0 + X.variance.gradient[:] = 0 + + self.variational_prior.update_gradients_KL(X) + if self.missing_data: + current_values['meangrad'] += kl_fctr*X.mean.gradient/d + current_values['vargrad'] += kl_fctr*X.variance.gradient/d + else: + current_values['meangrad'] += kl_fctr*X.mean.gradient + current_values['vargrad'] += kl_fctr*X.variance.gradient + + if subset_indices is not None: + value_indices['meangrad'] = subset_indices['samples'] + value_indices['vargrad'] = subset_indices['samples'] + return posterior, log_marginal_likelihood, grad_dict, current_values, value_indices + + def _outer_values_update(self, full_values): + """ + Here you put the values, which were collected before in the right places. + E.g. set the gradients of parameters, etc. + """ + super(BayesianGPLVMMiniBatch, self)._outer_values_update(full_values) + self.X.mean.gradient = full_values['meangrad'] + self.X.variance.gradient = full_values['vargrad'] + + def _outer_init_full_values(self): + return dict(meangrad=np.zeros(self.X.mean.shape), + vargrad=np.zeros(self.X.variance.shape)) + + def parameters_changed(self): + super(BayesianGPLVMMiniBatch,self).parameters_changed() + if isinstance(self.inference_method, VarDTC_minibatch): + return + + #super(BayesianGPLVM, self).parameters_changed() + #self._log_marginal_likelihood -= self.variational_prior.KL_divergence(self.X) + + #self.X.mean.gradient, self.X.variance.gradient = self.kern.gradients_qX_expectations(variational_posterior=self.X, Z=self.Z, dL_dpsi0=self.grad_dict['dL_dpsi0'], dL_dpsi1=self.grad_dict['dL_dpsi1'], dL_dpsi2=self.grad_dict['dL_dpsi2']) + + # This is testing code ------------------------- +# i = np.random.randint(self.X.shape[0]) +# X_ = self.X.mean +# which = np.sqrt(((X_ - X_[i:i+1])**2).sum(1)).argsort()>(max(0, self.X.shape[0]-51)) +# _, _, grad_dict = self.inference_method.inference(self.kern, self.X[which], self.Z, self.likelihood, self.Y[which], self.Y_metadata) +# grad = self.kern.gradients_qX_expectations(variational_posterior=self.X[which], Z=self.Z, dL_dpsi0=grad_dict['dL_dpsi0'], dL_dpsi1=grad_dict['dL_dpsi1'], dL_dpsi2=grad_dict['dL_dpsi2']) +# +# self.X.mean.gradient[:] = 0 +# self.X.variance.gradient[:] = 0 +# self.X.mean.gradient[which] = grad[0] +# self.X.variance.gradient[which] = grad[1] + + # update for the KL divergence +# self.variational_prior.update_gradients_KL(self.X, which) + # ----------------------------------------------- + + # update for the KL divergence + #self.variational_prior.update_gradients_KL(self.X) + + def plot_latent(self, labels=None, which_indices=None, + resolution=50, ax=None, marker='o', s=40, + fignum=None, plot_inducing=True, legend=True, + plot_limits=None, + aspect='auto', updates=False, predict_kwargs={}, imshow_kwargs={}): + import sys + assert "matplotlib" in sys.modules, "matplotlib package has not been imported." + from ..plotting.matplot_dep import dim_reduction_plots + + return dim_reduction_plots.plot_latent(self, labels, which_indices, + resolution, ax, marker, s, + fignum, plot_inducing, legend, + plot_limits, aspect, updates, predict_kwargs, imshow_kwargs) + + def do_test_latents(self, Y): + """ + Compute the latent representation for a set of new points Y + + Notes: + This will only work with a univariate Gaussian likelihood (for now) + """ + N_test = Y.shape[0] + input_dim = self.Z.shape[1] + + means = np.zeros((N_test, input_dim)) + covars = np.zeros((N_test, input_dim)) + + dpsi0 = -0.5 * self.input_dim / self.likelihood.variance + dpsi2 = self.grad_dict['dL_dpsi2'][0][None, :, :] # TODO: this may change if we ignore het. likelihoods + V = Y/self.likelihood.variance + + #compute CPsi1V + #if self.Cpsi1V is None: + # psi1V = np.dot(self.psi1.T, self.likelihood.V) + # tmp, _ = linalg.dtrtrs(self._Lm, np.asfortranarray(psi1V), lower=1, trans=0) + # tmp, _ = linalg.dpotrs(self.LB, tmp, lower=1) + # self.Cpsi1V, _ = linalg.dtrtrs(self._Lm, tmp, lower=1, trans=1) + + dpsi1 = np.dot(self.posterior.woodbury_vector, V.T) + + #start = np.zeros(self.input_dim * 2) + + + from scipy.optimize import minimize + + for n, dpsi1_n in enumerate(dpsi1.T[:, :, None]): + args = (input_dim, self.kern.copy(), self.Z, dpsi0, dpsi1_n.T, dpsi2) + res = minimize(latent_cost_and_grad, jac=True, x0=np.hstack((means[n], covars[n])), args=args, method='BFGS') + xopt = res.x + mu, log_S = xopt.reshape(2, 1, -1) + means[n] = mu[0].copy() + covars[n] = np.exp(log_S[0]).copy() + + X = NormalPosterior(means, covars) + + return X + + def dmu_dX(self, Xnew): + """ + Calculate the gradient of the prediction at Xnew w.r.t Xnew. + """ + dmu_dX = np.zeros_like(Xnew) + for i in range(self.Z.shape[0]): + dmu_dX += self.kern.gradients_X(self.grad_dict['dL_dpsi1'][i:i + 1, :], Xnew, self.Z[i:i + 1, :]) + return dmu_dX + + def dmu_dXnew(self, Xnew): + """ + Individual gradient of prediction at Xnew w.r.t. each sample in Xnew + """ + gradients_X = np.zeros((Xnew.shape[0], self.num_inducing)) + ones = np.ones((1, 1)) + for i in range(self.Z.shape[0]): + gradients_X[:, i] = self.kern.gradients_X(ones, Xnew, self.Z[i:i + 1, :]).sum(-1) + return np.dot(gradients_X, self.grad_dict['dL_dpsi1']) + + def plot_steepest_gradient_map(self, *args, ** kwargs): + """ + See GPy.plotting.matplot_dep.dim_reduction_plots.plot_steepest_gradient_map + """ + import sys + assert "matplotlib" in sys.modules, "matplotlib package has not been imported." + from ..plotting.matplot_dep import dim_reduction_plots + + return dim_reduction_plots.plot_steepest_gradient_map(self,*args,**kwargs) + + +def latent_cost_and_grad(mu_S, input_dim, kern, Z, dL_dpsi0, dL_dpsi1, dL_dpsi2): + """ + objective function for fitting the latent variables for test points + (negative log-likelihood: should be minimised!) + """ + mu = mu_S[:input_dim][None] + log_S = mu_S[input_dim:][None] + S = np.exp(log_S) + + X = NormalPosterior(mu, S) + + psi0 = kern.psi0(Z, X) + psi1 = kern.psi1(Z, X) + psi2 = kern.psi2(Z, X) + + lik = dL_dpsi0 * psi0.sum() + np.einsum('ij,kj->...', dL_dpsi1, psi1) + np.einsum('ijk,lkj->...', dL_dpsi2, psi2) - 0.5 * np.sum(np.square(mu) + S) + 0.5 * np.sum(log_S) + + dLdmu, dLdS = kern.gradients_qX_expectations(dL_dpsi0, dL_dpsi1, dL_dpsi2, Z, X) + dmu = dLdmu - mu + # dS = S0 + S1 + S2 -0.5 + .5/S + dlnS = S * (dLdS - 0.5) + .5 + + return -lik, -np.hstack((dmu.flatten(), dlnS.flatten())) diff --git a/GPy/models/bcgplvm.py b/GPy/models/bcgplvm.py new file mode 100644 index 00000000..899bb2f8 --- /dev/null +++ b/GPy/models/bcgplvm.py @@ -0,0 +1,48 @@ +# Copyright (c) 2012-2014, GPy authors (see AUTHORS.txt). +# Licensed under the BSD 3-clause license (see LICENSE.txt) + + +import numpy as np +from ..core import GP +from ..models import GPLVM +from ..mappings import * + + +class BCGPLVM(GPLVM): + """ + Back constrained Gaussian Process Latent Variable Model + + :param Y: observed data + :type Y: np.ndarray + :param input_dim: latent dimensionality + :type input_dim: int + :param init: initialisation method for the latent space + :type init: 'PCA'|'random' + :param mapping: mapping for back constraint + :type mapping: GPy.core.Mapping object + + """ + def __init__(self, Y, input_dim, init='PCA', X=None, kernel=None, normalize_Y=False, mapping=None): + + if mapping is None: + mapping = Kernel(X=Y, output_dim=input_dim) + self.mapping = mapping + GPLVM.__init__(self, Y, input_dim, init, X, kernel, normalize_Y) + self.X = self.mapping.f(self.likelihood.Y) + + def _get_param_names(self): + return self.mapping._get_param_names() + GP._get_param_names(self) + + def _get_params(self): + return np.hstack((self.mapping._get_params(), GP._get_params(self))) + + def _set_params(self, x): + self.mapping._set_params(x[:self.mapping.num_params]) + self.X = self.mapping.f(self.likelihood.Y) + GP._set_params(self, x[self.mapping.num_params:]) + + def _log_likelihood_gradients(self): + dL_df = self.kern.gradients_X(self.dL_dK, self.X) + dL_dtheta = self.mapping.df_dtheta(dL_df, self.likelihood.Y) + return np.hstack((dL_dtheta.flatten(), GP._log_likelihood_gradients(self))) + diff --git a/GPy/models/gp_classification.py b/GPy/models/gp_classification.py new file mode 100644 index 00000000..bbf4f316 --- /dev/null +++ b/GPy/models/gp_classification.py @@ -0,0 +1,29 @@ +# Copyright (c) 2013, the GPy Authors (see AUTHORS.txt) +# Licensed under the BSD 3-clause license (see LICENSE.txt) + +from ..core import GP +from .. import likelihoods +from .. import kern +from ..inference.latent_function_inference.expectation_propagation import EP + +class GPClassification(GP): + """ + Gaussian Process classification + + This is a thin wrapper around the models.GP class, with a set of sensible defaults + + :param X: input observations + :param Y: observed values, can be None if likelihood is not None + :param kernel: a GPy kernel, defaults to rbf + + .. Note:: Multiple independent outputs are allowed using columns of Y + + """ + + def __init__(self, X, Y, kernel=None,Y_metadata=None): + if kernel is None: + kernel = kern.RBF(X.shape[1]) + + likelihood = likelihoods.Bernoulli() + + GP.__init__(self, X=X, Y=Y, kernel=kernel, likelihood=likelihood, inference_method=EP(), name='gp_classification') diff --git a/GPy/models/gp_coregionalized_regression.py b/GPy/models/gp_coregionalized_regression.py new file mode 100644 index 00000000..be5b9ac3 --- /dev/null +++ b/GPy/models/gp_coregionalized_regression.py @@ -0,0 +1,44 @@ +# Copyright (c) 2012 - 2014 the GPy Austhors (see AUTHORS.txt) +# Licensed under the BSD 3-clause license (see LICENSE.txt) + +import numpy as np +from ..core import GP +from .. import likelihoods +from .. import kern +from .. import util + +class GPCoregionalizedRegression(GP): + """ + Gaussian Process model for heteroscedastic multioutput regression + + This is a thin wrapper around the models.GP class, with a set of sensible defaults + + :param X_list: list of input observations corresponding to each output + :type X_list: list of numpy arrays + :param Y_list: list of observed values related to the different noise models + :type Y_list: list of numpy arrays + :param kernel: a GPy kernel, defaults to RBF ** Coregionalized + :type kernel: None | GPy.kernel defaults + :likelihoods_list: a list of likelihoods, defaults to list of Gaussian likelihoods + :type likelihoods_list: None | a list GPy.likelihoods + :param name: model name + :type name: string + :param W_rank: number tuples of the corregionalization parameters 'W' (see coregionalize kernel documentation) + :type W_rank: integer + :param kernel_name: name of the kernel + :type kernel_name: string + """ + def __init__(self, X_list, Y_list, kernel=None, likelihoods_list=None, name='GPCR',W_rank=1,kernel_name='coreg'): + + #Input and Output + X,Y,self.output_index = util.multioutput.build_XY(X_list,Y_list) + Ny = len(Y_list) + + #Kernel + if kernel is None: + kernel = util.multioutput.ICM(input_dim=X.shape[1]-1, num_outputs=Ny, kernel=kern.RBF(X.shape[1]-1), W_rank=1,name=kernel_name) + + #Likelihood + likelihood = util.multioutput.build_likelihood(Y_list,self.output_index,likelihoods_list) + + super(GPCoregionalizedRegression, self).__init__(X,Y,kernel,likelihood, Y_metadata={'output_index':self.output_index}) diff --git a/GPy/models/gp_heteroscedastic_regression.py b/GPy/models/gp_heteroscedastic_regression.py new file mode 100644 index 00000000..19cb18d8 --- /dev/null +++ b/GPy/models/gp_heteroscedastic_regression.py @@ -0,0 +1,41 @@ +# Copyright (c) 2012 - 2014 the GPy Austhors (see AUTHORS.txt) +# Licensed under the BSD 3-clause license (see LICENSE.txt) + +import numpy as np +from ..core import GP +from .. import likelihoods +from .. import kern +from .. import util + +class GPHeteroscedasticRegression(GP): + """ + Gaussian Process model for heteroscedastic regression + + This is a thin wrapper around the models.GP class, with a set of sensible defaults + + :param X: input observations + :param Y: observed values + :param kernel: a GPy kernel, defaults to rbf + """ + def __init__(self, X, Y, kernel=None, Y_metadata=None): + + Ny = Y.shape[0] + + if Y_metadata is None: + Y_metadata = {'output_index':np.arange(Ny)[:,None]} + else: + assert Y_metadata['output_index'].shape[0] == Ny + + if kernel is None: + kernel = kern.RBF(X.shape[1]) + + #Likelihood + #likelihoods_list = [likelihoods.Gaussian(name="Gaussian_noise_%s" %j) for j in range(Ny)] + noise_terms = np.unique(Y_metadata['output_index'].flatten()) + likelihoods_list = [likelihoods.Gaussian(name="Gaussian_noise_%s" %j) for j in noise_terms] + likelihood = likelihoods.MixedNoise(likelihoods_list=likelihoods_list) + + super(GPHeteroscedasticRegression, self).__init__(X,Y,kernel,likelihood, Y_metadata=Y_metadata) + + def plot(self,*args): + return NotImplementedError diff --git a/GPy/models/gp_kronecker_gaussian_regression.py b/GPy/models/gp_kronecker_gaussian_regression.py new file mode 100644 index 00000000..434661d2 --- /dev/null +++ b/GPy/models/gp_kronecker_gaussian_regression.py @@ -0,0 +1,119 @@ +# Copyright (c) 2014, James Hensman, Alan Saul +# Distributed under the terms of the GNU General public License, see LICENSE.txt + +import numpy as np +from ..core.model import Model +from ..core.parameterization import ObsAr +from .. import likelihoods + +class GPKroneckerGaussianRegression(Model): + """ + Kronecker GP regression + + Take two kernels computed on separate spaces K1(X1), K2(X2), and a data + matrix Y which is f size (N1, N2). + + The effective covaraince is np.kron(K2, K1) + The effective data is vec(Y) = Y.flatten(order='F') + + The noise must be iid Gaussian. + + See Stegle et al. + @inproceedings{stegle2011efficient, + title={Efficient inference in matrix-variate gaussian models with $\\backslash$ iid observation noise}, + author={Stegle, Oliver and Lippert, Christoph and Mooij, Joris M and Lawrence, Neil D and Borgwardt, Karsten M}, + booktitle={Advances in Neural Information Processing Systems}, + pages={630--638}, + year={2011} + } + + """ + def __init__(self, X1, X2, Y, kern1, kern2, noise_var=1., name='KGPR'): + Model.__init__(self, name=name) + # accept the construction arguments + self.X1 = ObsAr(X1) + self.X2 = ObsAr(X2) + self.Y = Y + self.kern1, self.kern2 = kern1, kern2 + self.link_parameter(self.kern1) + self.link_parameter(self.kern2) + + self.likelihood = likelihoods.Gaussian() + self.likelihood.variance = noise_var + self.link_parameter(self.likelihood) + + self.num_data1, self.input_dim1 = self.X1.shape + self.num_data2, self.input_dim2 = self.X2.shape + + assert kern1.input_dim == self.input_dim1 + assert kern2.input_dim == self.input_dim2 + assert Y.shape == (self.num_data1, self.num_data2) + + def log_likelihood(self): + return self._log_marginal_likelihood + + def parameters_changed(self): + (N1, D1), (N2, D2) = self.X1.shape, self.X2.shape + K1, K2 = self.kern1.K(self.X1), self.kern2.K(self.X2) + + # eigendecompositon + S1, U1 = np.linalg.eigh(K1) + S2, U2 = np.linalg.eigh(K2) + W = np.kron(S2, S1) + self.likelihood.variance + + Y_ = U1.T.dot(self.Y).dot(U2) + + # store these quantities: needed for prediction + Wi = 1./W + Ytilde = Y_.flatten(order='F')*Wi + + self._log_marginal_likelihood = -0.5*self.num_data1*self.num_data2*np.log(2*np.pi)\ + -0.5*np.sum(np.log(W))\ + -0.5*np.dot(Y_.flatten(order='F'), Ytilde) + + # gradients for data fit part + Yt_reshaped = Ytilde.reshape(N1, N2, order='F') + tmp = U1.dot(Yt_reshaped) + dL_dK1 = .5*(tmp*S2).dot(tmp.T) + tmp = U2.dot(Yt_reshaped.T) + dL_dK2 = .5*(tmp*S1).dot(tmp.T) + + # gradients for logdet + Wi_reshaped = Wi.reshape(N1, N2, order='F') + tmp = np.dot(Wi_reshaped, S2) + dL_dK1 += -0.5*(U1*tmp).dot(U1.T) + tmp = np.dot(Wi_reshaped.T, S1) + dL_dK2 += -0.5*(U2*tmp).dot(U2.T) + + self.kern1.update_gradients_full(dL_dK1, self.X1) + self.kern2.update_gradients_full(dL_dK2, self.X2) + + # gradients for noise variance + dL_dsigma2 = -0.5*Wi.sum() + 0.5*np.sum(np.square(Ytilde)) + self.likelihood.variance.gradient = dL_dsigma2 + + # store these quantities for prediction: + self.Wi, self.Ytilde, self.U1, self.U2 = Wi, Ytilde, U1, U2 + + def predict(self, X1new, X2new): + """ + Return the predictive mean and variance at a series of new points X1new, X2new + Only returns the diagonal of the predictive variance, for now. + + :param X1new: The points at which to make a prediction + :type X1new: np.ndarray, Nnew x self.input_dim1 + :param X2new: The points at which to make a prediction + :type X2new: np.ndarray, Nnew x self.input_dim2 + + """ + k1xf = self.kern1.K(X1new, self.X1) + k2xf = self.kern2.K(X2new, self.X2) + A = k1xf.dot(self.U1) + B = k2xf.dot(self.U2) + mu = A.dot(self.Ytilde.reshape(self.num_data1, self.num_data2, order='F')).dot(B.T).flatten(order='F') + k1xx = self.kern1.Kdiag(X1new) + k2xx = self.kern2.Kdiag(X2new) + BA = np.kron(B, A) + var = np.kron(k2xx, k1xx) - np.sum(BA**2*self.Wi, 1) + self.likelihood.variance + + return mu[:, None], var[:, None] diff --git a/GPy/models/gp_regression.py b/GPy/models/gp_regression.py new file mode 100644 index 00000000..7b8fb63f --- /dev/null +++ b/GPy/models/gp_regression.py @@ -0,0 +1,36 @@ +# Copyright (c) 2012 - 2014 the GPy Austhors (see AUTHORS.txt) +# Licensed under the BSD 3-clause license (see LICENSE.txt) + +import numpy as np +from ..core import GP +from .. import likelihoods +from .. import kern + +class GPRegression(GP): + """ + Gaussian Process model for regression + + This is a thin wrapper around the models.GP class, with a set of sensible defaults + + :param X: input observations + :param Y: observed values + :param kernel: a GPy kernel, defaults to rbf + :param Norm normalizer: [False] + + Normalize Y with the norm given. + If normalizer is False, no normalization will be done + If it is None, we use GaussianNorm(alization) + + .. Note:: Multiple independent outputs are allowed using columns of Y + + """ + + def __init__(self, X, Y, kernel=None, Y_metadata=None, normalizer=None): + + if kernel is None: + kernel = kern.RBF(X.shape[1]) + + likelihood = likelihoods.Gaussian() + + super(GPRegression, self).__init__(X, Y, kernel, likelihood, name='GP regression', Y_metadata=Y_metadata, normalizer=normalizer) + diff --git a/GPy/models/gp_var_gauss.py b/GPy/models/gp_var_gauss.py new file mode 100644 index 00000000..cd688360 --- /dev/null +++ b/GPy/models/gp_var_gauss.py @@ -0,0 +1,108 @@ +# Copyright (c) 2014, James Hensman, Alan Saul +# Distributed under the terms of the GNU General public License, see LICENSE.txt + +import numpy as np +from scipy import stats +from scipy.special import erf +from ..core.model import Model +from ..core.parameterization import ObsAr +from .. import kern +from ..core.parameterization.param import Param +from ..util.linalg import pdinv + +log_2_pi = np.log(2*np.pi) + + +class GPVariationalGaussianApproximation(Model): + """ + The Variational Gaussian Approximation revisited implementation for regression + + @article{Opper:2009, + title = {The Variational Gaussian Approximation Revisited}, + author = {Opper, Manfred and Archambeau, C{\'e}dric}, + journal = {Neural Comput.}, + year = {2009}, + pages = {786--792}, + } + """ + def __init__(self, X, Y, kernel=None): + Model.__init__(self,'Variational GP classification') + # accept the construction arguments + self.X = ObsAr(X) + if kernel is None: + kernel = kern.RBF(X.shape[1]) + kern.White(X.shape[1], 0.01) + self.kern = kernel + self.link_parameter(self.kern) + self.num_data, self.input_dim = self.X.shape + + self.alpha = Param('alpha', np.zeros(self.num_data)) + self.beta = Param('beta', np.ones(self.num_data)) + self.link_parameter(self.alpha) + self.link_parameter(self.beta) + + self.gh_x, self.gh_w = np.polynomial.hermite.hermgauss(20) + self.Ysign = np.where(Y==1, 1, -1).flatten() + + def log_likelihood(self): + """ + Marginal log likelihood evaluation + """ + return self._log_lik + + def likelihood_quadrature(self, m, v): + """ + Perform Gauss-Hermite quadrature over the log of the likelihood, with a fixed weight + """ + # assume probit for now. + X = self.gh_x[None, :]*np.sqrt(2.*v[:, None]) + (m*self.Ysign)[:, None] + p = stats.norm.cdf(X) + N = stats.norm.pdf(X) + F = np.log(p).dot(self.gh_w) + NoverP = N/p + dF_dm = (NoverP*self.Ysign[:,None]).dot(self.gh_w) + dF_dv = -0.5*(NoverP**2 + NoverP*X).dot(self.gh_w) + return F, dF_dm, dF_dv + + def parameters_changed(self): + K = self.kern.K(self.X) + m = K.dot(self.alpha) + KB = K*self.beta[:, None] + BKB = KB*self.beta[None, :] + A = np.eye(self.num_data) + BKB + Ai, LA, _, Alogdet = pdinv(A) + Sigma = np.diag(self.beta**-2) - Ai/self.beta[:, None]/self.beta[None, :] # posterior coavairance: need full matrix for gradients + var = np.diag(Sigma) + + F, dF_dm, dF_dv = self.likelihood_quadrature(m, var) + dF_da = np.dot(K, dF_dm) + SigmaB = Sigma*self.beta + dF_db = -np.diag(Sigma.dot(np.diag(dF_dv)).dot(SigmaB))*2 + KL = 0.5*(Alogdet + np.trace(Ai) - self.num_data + m.dot(self.alpha)) + dKL_da = m + A_A2 = Ai - Ai.dot(Ai) + dKL_db = np.diag(np.dot(KB.T, A_A2)) + self._log_lik = F.sum() - KL + self.alpha.gradient = dF_da - dKL_da + self.beta.gradient = dF_db - dKL_db + + # K-gradients + dKL_dK = 0.5*(self.alpha[None, :]*self.alpha[:, None] + self.beta[:, None]*self.beta[None, :]*A_A2) + tmp = Ai*self.beta[:, None]/self.beta[None, :] + dF_dK = self.alpha[:, None]*dF_dm[None, :] + np.dot(tmp*dF_dv, tmp.T) + self.kern.update_gradients_full(dF_dK - dKL_dK, self.X) + + def predict(self, Xnew): + """ + Predict the function(s) at the new point(s) Xnew. + + :param Xnew: The points at which to make a prediction + :type Xnew: np.ndarray, Nnew x self.input_dim + """ + Wi, _, _, _ = pdinv(self.kern.K(self.X) + np.diag(self.beta**-2)) + Kux = self.kern.K(self.X, Xnew) + mu = np.dot(Kux.T, self.alpha) + WiKux = np.dot(Wi, Kux) + Kxx = self.kern.Kdiag(Xnew) + var = Kxx - np.sum(WiKux*Kux, 0) + + return 0.5*(1+erf(mu/np.sqrt(2.*(var+1)))) diff --git a/GPy/models/gplvm.py b/GPy/models/gplvm.py new file mode 100644 index 00000000..6318829d --- /dev/null +++ b/GPy/models/gplvm.py @@ -0,0 +1,83 @@ +# Copyright (c) 2012-2014, GPy authors (see AUTHORS.txt). +# Licensed under the BSD 3-clause license (see LICENSE.txt) + + +import numpy as np +from .. import kern +from ..core import GP, Param +from ..likelihoods import Gaussian +from .. import util + + +class GPLVM(GP): + """ + Gaussian Process Latent Variable Model + + + """ + def __init__(self, Y, input_dim, init='PCA', X=None, kernel=None, name="gplvm"): + + """ + :param Y: observed data + :type Y: np.ndarray + :param input_dim: latent dimensionality + :type input_dim: int + :param init: initialisation method for the latent space + :type init: 'PCA'|'random' + """ + if X is None: + from ..util.initialization import initialize_latent + X, fracs = initialize_latent(init, input_dim, Y) + else: + fracs = np.ones(input_dim) + if kernel is None: + kernel = kern.RBF(input_dim, lengthscale=fracs, ARD=input_dim > 1) + kern.Bias(input_dim, np.exp(-2)) + + likelihood = Gaussian() + + super(GPLVM, self).__init__(X, Y, kernel, likelihood, name='GPLVM') + self.X = Param('latent_mean', X) + self.link_parameter(self.X, index=0) + + def parameters_changed(self): + super(GPLVM, self).parameters_changed() + self.X.gradient = self.kern.gradients_X(self.grad_dict['dL_dK'], self.X, None) + + def jacobian(self,X): + J = np.zeros((X.shape[0],X.shape[1],self.output_dim)) + for i in range(self.output_dim): + J[:,:,i] = self.kern.gradients_X(self.posterior.woodbury_vector[:,i:i+1], X, self.X) + return J + + def magnification(self,X): + target=np.zeros(X.shape[0]) + #J = np.zeros((X.shape[0],X.shape[1],self.output_dim)) + J = self.jacobian(X) + for i in range(X.shape[0]): + target[i]=np.sqrt(np.linalg.det(np.dot(J[i,:,:],np.transpose(J[i,:,:])))) + return target + + def plot(self): + assert self.likelihood.Y.shape[1] == 2 + pb.scatter(self.likelihood.Y[:, 0], self.likelihood.Y[:, 1], 40, self.X[:, 0].copy(), linewidth=0, cmap=pb.cm.jet) # @UndefinedVariable + Xnew = np.linspace(self.X.min(), self.X.max(), 200)[:, None] + mu, _ = self.predict(Xnew) + import pylab as pb + pb.plot(mu[:, 0], mu[:, 1], 'k', linewidth=1.5) + + def plot_latent(self, labels=None, which_indices=None, + resolution=50, ax=None, marker='o', s=40, + fignum=None, legend=True, + plot_limits=None, + aspect='auto', updates=False, **kwargs): + import sys + assert "matplotlib" in sys.modules, "matplotlib package has not been imported." + from ..plotting.matplot_dep import dim_reduction_plots + + return dim_reduction_plots.plot_latent(self, labels, which_indices, + resolution, ax, marker, s, + fignum, False, legend, + plot_limits, aspect, updates, **kwargs) + + def plot_magnification(self, *args, **kwargs): + return util.plot_latent.plot_magnification(self, *args, **kwargs) diff --git a/GPy/models/gradient_checker.py b/GPy/models/gradient_checker.py new file mode 100644 index 00000000..74026f8e --- /dev/null +++ b/GPy/models/gradient_checker.py @@ -0,0 +1,113 @@ +# ## Copyright (c) 2012, GPy authors (see AUTHORS.txt). +# Licensed under the BSD 3-clause license (see LICENSE.txt) + +from ..core.model import Model +import itertools +import numpy +from ..core.parameterization import Param + +def get_shape(x): + if isinstance(x, numpy.ndarray): + return x.shape + return () + +def at_least_one_element(x): + if isinstance(x, (list, tuple)): + return x + return [x] + +def flatten_if_needed(x): + return numpy.atleast_1d(x).flatten() + +class GradientChecker(Model): + + def __init__(self, f, df, x0, names=None, *args, **kwargs): + """ + :param f: Function to check gradient for + :param df: Gradient of function to check + :param x0: + Initial guess for inputs x (if it has a shape (a,b) this will be reflected in the parameter names). + Can be a list of arrays, if takes a list of arrays. This list will be passed + to f and df in the same order as given here. + If only one argument, make sure not to pass a list!!! + + :type x0: [array-like] | array-like | float | int + :param names: + Names to print, when performing gradcheck. If a list was passed to x0 + a list of names with the same length is expected. + :param args: Arguments passed as f(x, *args, **kwargs) and df(x, *args, **kwargs) + + Examples: + --------- + from GPy.models import GradientChecker + N, M, Q = 10, 5, 3 + + Sinusoid: + + X = numpy.random.rand(N, Q) + grad = GradientChecker(numpy.sin,numpy.cos,X,'x') + grad.checkgrad(verbose=1) + + Using GPy: + + X, Z = numpy.random.randn(N,Q), numpy.random.randn(M,Q) + kern = GPy.kern.linear(Q, ARD=True) + GPy.kern.rbf(Q, ARD=True) + grad = GradientChecker(kern.K, + lambda x: 2*kern.dK_dX(numpy.ones((1,1)), x), + x0 = X.copy(), + names='X') + grad.checkgrad(verbose=1) + grad.randomize() + grad.checkgrad(verbose=1) + """ + Model.__init__(self, 'GradientChecker') + if isinstance(x0, (list, tuple)) and names is None: + self.shapes = [get_shape(xi) for xi in x0] + self.names = ['X{i}'.format(i=i) for i in range(len(x0))] + elif isinstance(x0, (list, tuple)) and names is not None: + self.shapes = [get_shape(xi) for xi in x0] + self.names = names + elif names is None: + self.names = ['X'] + self.shapes = [get_shape(x0)] + else: + self.names = names + self.shapes = [get_shape(x0)] + + for name, xi in zip(self.names, at_least_one_element(x0)): + self.__setattr__(name, Param(name, xi)) + self.link_parameter(self.__getattribute__(name)) +# self._param_names = [] +# for name, shape in zip(self.names, self.shapes): +# self._param_names.extend(map(lambda nameshape: ('_'.join(nameshape)).strip('_'), itertools.izip(itertools.repeat(name), itertools.imap(lambda t: '_'.join(map(str, t)), itertools.product(*map(lambda xi: range(xi), shape)))))) + self.args = args + self.kwargs = kwargs + self.f = f + self.df = df + + def _get_x(self): + if len(self.names) > 1: + return [self.__getattribute__(name) for name in self.names] + list(self.args) + return [self.__getattribute__(self.names[0])] + list(self.args) + + def log_likelihood(self): + return float(numpy.sum(self.f(*self._get_x(), **self.kwargs))) + + def _log_likelihood_gradients(self): + return numpy.atleast_1d(self.df(*self._get_x(), **self.kwargs)).flatten() + + #def _get_params(self): + #return numpy.atleast_1d(numpy.hstack(map(lambda name: flatten_if_needed(self.__getattribute__(name)), self.names))) + + #def _set_params(self, x): + #current_index = 0 + #for name, shape in zip(self.names, self.shapes): + #current_size = numpy.prod(shape) + #self.__setattr__(name, x[current_index:current_index + current_size].reshape(shape)) + #current_index += current_size + + #def _get_param_names(self): + #_param_names = [] + #for name, shape in zip(self.names, self.shapes): + #_param_names.extend(map(lambda nameshape: ('_'.join(nameshape)).strip('_'), itertools.izip(itertools.repeat(name), itertools.imap(lambda t: '_'.join(map(str, t)), itertools.product(*map(lambda xi: range(xi), shape)))))) + #return _param_names diff --git a/GPy/models/mrd.py b/GPy/models/mrd.py new file mode 100644 index 00000000..645cdf88 --- /dev/null +++ b/GPy/models/mrd.py @@ -0,0 +1,341 @@ +# ## Copyright (c) 2013, GPy authors (see AUTHORS.txt). +# Licensed under the BSD 3-clause license (see LICENSE.txt) + +import numpy as np +import itertools, logging + +from ..kern import Kern +from ..core.parameterization.variational import NormalPosterior, NormalPrior +from ..core.parameterization import Param, Parameterized +from ..core.parameterization.observable_array import ObsAr +from ..inference.latent_function_inference.var_dtc import VarDTC +from ..inference.latent_function_inference import InferenceMethodList +from ..likelihoods import Gaussian +from ..util.initialization import initialize_latent +from ..core.sparse_gp import SparseGP, GP +from GPy.core.parameterization.variational import VariationalPosterior +from GPy.models.bayesian_gplvm_minibatch import BayesianGPLVMMiniBatch +from GPy.models.sparse_gp_minibatch import SparseGPMiniBatch + +class MRD(BayesianGPLVMMiniBatch): + """ + !WARNING: This is bleeding edge code and still in development. + Functionality may change fundamentally during development! + + Apply MRD to all given datasets Y in Ylist. + + Y_i in [n x p_i] + + If Ylist is a dictionary, the keys of the dictionary are the names, and the + values are the different datasets to compare. + + The samples n in the datasets need + to match up, whereas the dimensionality p_d can differ. + + :param [array-like] Ylist: List of datasets to apply MRD on + :param input_dim: latent dimensionality + :type input_dim: int + :param array-like X: mean of starting latent space q in [n x q] + :param array-like X_variance: variance of starting latent space q in [n x q] + :param initx: initialisation method for the latent space : + + * 'concat' - PCA on concatenation of all datasets + * 'single' - Concatenation of PCA on datasets, respectively + * 'random' - Random draw from a Normal(0,1) + + :type initx: ['concat'|'single'|'random'] + :param initz: initialisation method for inducing inputs + :type initz: 'permute'|'random' + :param num_inducing: number of inducing inputs to use + :param Z: initial inducing inputs + :param kernel: list of kernels or kernel to copy for each output + :type kernel: [GPy.kernels.kernels] | GPy.kernels.kernels | None (default) + :param :class:`~GPy.inference.latent_function_inference inference_method: + InferenceMethodList of inferences, or one inference method for all + :param :class:`~GPy.likelihoodss.likelihoods.likelihoods` likelihoods: the likelihoods to use + :param str name: the name of this model + :param [str] Ynames: the names for the datasets given, must be of equal length as Ylist or None + :param bool|Norm normalizer: How to normalize the data? + :param bool stochastic: Should this model be using stochastic gradient descent over the dimensions? + :param bool|[bool] batchsize: either one batchsize for all, or one batchsize per dataset. + """ + def __init__(self, Ylist, input_dim, X=None, X_variance=None, + initx = 'PCA', initz = 'permute', + num_inducing=10, Z=None, kernel=None, + inference_method=None, likelihoods=None, name='mrd', + Ynames=None, normalizer=False, stochastic=False, batchsize=10): + + self.logger = logging.getLogger(self.__class__.__name__) + self.input_dim = input_dim + self.num_inducing = num_inducing + + if isinstance(Ylist, dict): + Ynames, Ylist = zip(*Ylist.items()) + + self.logger.debug("creating observable arrays") + self.Ylist = [ObsAr(Y) for Y in Ylist] + + if Ynames is None: + self.logger.debug("creating Ynames") + Ynames = ['Y{}'.format(i) for i in range(len(Ylist))] + self.names = Ynames + assert len(self.names) == len(self.Ylist), "one name per dataset, or None if Ylist is a dict" + + if inference_method is None: + self.inference_method = InferenceMethodList([VarDTC() for _ in xrange(len(self.Ylist))]) + else: + assert isinstance(inference_method, InferenceMethodList), "please provide one inference method per Y in the list and provide it as InferenceMethodList, inference_method given: {}".format(inference_method) + self.inference_method = inference_method + + if X is None: + X, fracs = self._init_X(initx, Ylist) + else: + fracs = [X.var(0)]*len(Ylist) + + Z = self._init_Z(initz, X) + self.Z = Param('inducing inputs', Z) + self.num_inducing = self.Z.shape[0] # ensure M==N if M>N + + # sort out the kernels + self.logger.info("building kernels") + if kernel is None: + from ..kern import RBF + kernels = [RBF(input_dim, ARD=1, lengthscale=1./fracs[i]) for i in range(len(Ylist))] + elif isinstance(kernel, Kern): + kernels = [] + for i in range(len(Ylist)): + k = kernel.copy() + kernels.append(k) + else: + assert len(kernel) == len(Ylist), "need one kernel per output" + assert all([isinstance(k, Kern) for k in kernel]), "invalid kernel object detected!" + kernels = kernel + + if X_variance is None: + X_variance = np.random.uniform(0.1, 0.2, X.shape) + + self.variational_prior = NormalPrior() + #self.X = NormalPosterior(X, X_variance) + + if likelihoods is None: + likelihoods = [Gaussian(name='Gaussian_noise'.format(i)) for i in range(len(Ylist))] + else: likelihoods = likelihoods + + self.logger.info("adding X and Z") + super(MRD, self).__init__(Y, input_dim, X=X, X_variance=X_variance, num_inducing=num_inducing, + Z=self.Z, kernel=None, inference_method=self.inference_method, likelihood=Gaussian(), + name='manifold relevance determination', normalizer=None, + missing_data=False, stochastic=False, batchsize=1) + + self._log_marginal_likelihood = 0 + + self.unlink_parameter(self.likelihood) + self.unlink_parameter(self.kern) + del self.kern + del self.likelihood + + self.num_data = Ylist[0].shape[0] + if isinstance(batchsize, int): + batchsize = itertools.repeat(batchsize) + + self.bgplvms = [] + + for i, n, k, l, Y, im, bs in itertools.izip(itertools.count(), Ynames, kernels, likelihoods, Ylist, self.inference_method, batchsize): + assert Y.shape[0] == self.num_data, "All datasets need to share the number of datapoints, and those have to correspond to one another" + md = np.isnan(Y).any() + spgp = BayesianGPLVMMiniBatch(Y, input_dim, X, X_variance, + Z=Z, kernel=k, likelihood=l, + inference_method=im, name=n, + normalizer=normalizer, + missing_data=md, + stochastic=stochastic, + batchsize=bs) + spgp.kl_factr = 1./len(Ynames) + spgp.unlink_parameter(spgp.Z) + spgp.unlink_parameter(spgp.X) + del spgp.Z + del spgp.X + spgp.Z = self.Z + spgp.X = self.X + self.link_parameter(spgp, i+2) + self.bgplvms.append(spgp) + + self.posterior = None + self.logger.info("init done") + + def parameters_changed(self): + self._log_marginal_likelihood = 0 + self.Z.gradient[:] = 0. + self.X.gradient[:] = 0. + for b, i in itertools.izip(self.bgplvms, self.inference_method): + self._log_marginal_likelihood += b._log_marginal_likelihood + + self.logger.info('working on im <{}>'.format(hex(id(i)))) + self.Z.gradient[:] += b.full_values['Zgrad'] + grad_dict = b.full_values + + self.X.mean.gradient += grad_dict['meangrad'] + self.X.variance.gradient += grad_dict['vargrad'] + + if isinstance(self.X, VariationalPosterior): + # update for the KL divergence + self.variational_prior.update_gradients_KL(self.X) + self._log_marginal_likelihood -= self.variational_prior.KL_divergence(self.X) + pass + + def log_likelihood(self): + return self._log_marginal_likelihood + + def _init_X(self, init='PCA', Ylist=None): + if Ylist is None: + Ylist = self.Ylist + if init in "PCA_concat": + X, fracs = initialize_latent('PCA', self.input_dim, np.hstack(Ylist)) + fracs = [fracs]*len(Ylist) + elif init in "PCA_single": + X = np.zeros((Ylist[0].shape[0], self.input_dim)) + fracs = [] + for qs, Y in itertools.izip(np.array_split(np.arange(self.input_dim), len(Ylist)), Ylist): + x,frcs = initialize_latent('PCA', len(qs), Y) + X[:, qs] = x + fracs.append(frcs) + else: # init == 'random': + X = np.random.randn(Ylist[0].shape[0], self.input_dim) + fracs = X.var(0) + fracs = [fracs]*len(Ylist) + X -= X.mean() + X /= X.std() + return X, fracs + + def _init_Z(self, init="permute", X=None): + if X is None: + X = self.X + if init in "permute": + Z = np.random.permutation(X.copy())[:self.num_inducing] + elif init in "random": + Z = np.random.randn(self.num_inducing, self.input_dim) * X.var() + return Z + + def _handle_plotting(self, fignum, axes, plotf, sharex=False, sharey=False): + import matplotlib.pyplot as plt + if axes is None: + fig = plt.figure(num=fignum) + sharex_ax = None + sharey_ax = None + plots = [] + for i, g in enumerate(self.bgplvms): + try: + if sharex: + sharex_ax = ax # @UndefinedVariable + sharex = False # dont set twice + if sharey: + sharey_ax = ax # @UndefinedVariable + sharey = False # dont set twice + except: + pass + if axes is None: + ax = fig.add_subplot(1, len(self.bgplvms), i + 1, sharex=sharex_ax, sharey=sharey_ax) + elif isinstance(axes, (tuple, list, np.ndarray)): + ax = axes[i] + else: + raise ValueError("Need one axes per latent dimension input_dim") + plots.append(plotf(i, g, ax)) + if sharey_ax is not None: + plt.setp(ax.get_yticklabels(), visible=False) + plt.draw() + if axes is None: + try: + fig.tight_layout() + except: + pass + return plots + + def predict(self, Xnew, full_cov=False, Y_metadata=None, kern=None, Yindex=0): + """ + Prediction for data set Yindex[default=0]. + This predicts the output mean and variance for the dataset given in Ylist[Yindex] + """ + b = self.bgplvms[Yindex] + self.posterior = b.posterior + self.kern = b.kern + self.likelihood = b.likelihood + return super(MRD, self).predict(Xnew, full_cov, Y_metadata, kern) + + #=============================================================================== + # TODO: Predict! Maybe even change to several bgplvms, which share an X? + #=============================================================================== + # def plot_predict(self, fignum=None, ax=None, sharex=False, sharey=False, **kwargs): + # fig = self._handle_plotting(fignum, + # ax, + # lambda i, g, ax: ax.imshow(g.predict(g.X)[0], **kwargs), + # sharex=sharex, sharey=sharey) + # return fig + + def plot_scales(self, fignum=None, ax=None, titles=None, sharex=False, sharey=True, *args, **kwargs): + """ + + TODO: Explain other parameters + + :param titles: titles for axes of datasets + + """ + if titles is None: + titles = [r'${}$'.format(name) for name in self.names] + ymax = reduce(max, [np.ceil(max(g.kern.input_sensitivity())) for g in self.bgplvms]) + def plotf(i, g, ax): + #ax.set_ylim([0,ymax]) + return g.kern.plot_ARD(ax=ax, title=titles[i], *args, **kwargs) + fig = self._handle_plotting(fignum, ax, plotf, sharex=sharex, sharey=sharey) + return fig + + def plot_latent(self, labels=None, which_indices=None, + resolution=50, ax=None, marker='o', s=40, + fignum=None, plot_inducing=True, legend=True, + plot_limits=None, + aspect='auto', updates=False, predict_kwargs={}, imshow_kwargs={}): + """ + see plotting.matplot_dep.dim_reduction_plots.plot_latent + if predict_kwargs is None, will plot latent spaces for 0th dataset (and kernel), otherwise give + predict_kwargs=dict(Yindex='index') for plotting only the latent space of dataset with 'index'. + """ + import sys + assert "matplotlib" in sys.modules, "matplotlib package has not been imported." + from matplotlib import pyplot as plt + from ..plotting.matplot_dep import dim_reduction_plots + if "Yindex" not in predict_kwargs: + predict_kwargs['Yindex'] = 0 + + Yindex = predict_kwargs['Yindex'] + if ax is None: + fig = plt.figure(num=fignum) + ax = fig.add_subplot(111) + else: + fig = ax.figure + self.kern = self.bgplvms[Yindex].kern + self.likelihood = self.bgplvms[Yindex].likelihood + plot = dim_reduction_plots.plot_latent(self, labels, which_indices, + resolution, ax, marker, s, + fignum, plot_inducing, legend, + plot_limits, aspect, updates, predict_kwargs, imshow_kwargs) + ax.set_title(self.bgplvms[Yindex].name) + try: + fig.tight_layout() + except: + pass + + return plot + + def __getstate__(self): + state = super(MRD, self).__getstate__() + if state.has_key('kern'): + del state['kern'] + if state.has_key('likelihood'): + del state['likelihood'] + return state + + def __setstate__(self, state): + # TODO: + super(MRD, self).__setstate__(state) + self.kern = self.bgplvms[0].kern + self.likelihood = self.bgplvms[0].likelihood + self.parameters_changed() \ No newline at end of file diff --git a/GPy/models/one_vs_all_classification.py b/GPy/models/one_vs_all_classification.py new file mode 100644 index 00000000..10457d75 --- /dev/null +++ b/GPy/models/one_vs_all_classification.py @@ -0,0 +1,44 @@ +# Copyright (c) 2013, the GPy Authors (see AUTHORS.txt) +# Licensed under the BSD 3-clause license (see LICENSE.txt) + +from ..core import GP +from . import SparseGPClassification +from .. import likelihoods +from .. import kern +from ..inference.latent_function_inference.expectation_propagation import EP +import numpy as np + +class OneVsAllClassification(object): + """ + Gaussian Process classification: One vs all + + This is a thin wrapper around the models.GPClassification class, with a set of sensible defaults + + :param X: input observations + :param Y: observed values, can be None if likelihood is not None + :param kernel: a GPy kernel, defaults to rbf + + .. Note:: Multiple independent outputs are not allowed + + """ + + def __init__(self, X, Y, kernel=None,Y_metadata=None,messages=True): + if kernel is None: + kernel = kern.RBF(X.shape[1]) + + likelihood = likelihoods.Bernoulli() + + assert Y.shape[1] == 1, 'Y should be 1 column vector' + + labels = np.unique(Y.flatten()) + + self.results = {} + for yj in labels: + Ynew = Y.copy() + Ynew[Y.flatten()!=yj] = 0 + Ynew[Y.flatten()==yj] = 1 + + m = SparseGPClassification(X,Ynew,kernel=kernel,Y_metadata=Y_metadata) + m.optimize(messages=messages) + stop + self.results[yj] = m.predict(X) diff --git a/GPy/models/one_vs_all_sparse_classification.py b/GPy/models/one_vs_all_sparse_classification.py new file mode 100644 index 00000000..3bdd2647 --- /dev/null +++ b/GPy/models/one_vs_all_sparse_classification.py @@ -0,0 +1,42 @@ +# Copyright (c) 2013, the GPy Authors (see AUTHORS.txt) +# Licensed under the BSD 3-clause license (see LICENSE.txt) + +import numpy as np +import GPy + +class OneVsAllSparseClassification(object): + """ + Gaussian Process classification: One vs all + + This is a thin wrapper around the models.GPClassification class, with a set of sensible defaults + + :param X: input observations + :param Y: observed values, can be None if likelihood is not None + :param kernel: a GPy kernel, defaults to rbf + + .. Note:: Multiple independent outputs are not allowed + + """ + + def __init__(self, X, Y, kernel=None,Y_metadata=None,messages=True,num_inducing=10): + if kernel is None: + kernel = GPy.kern.RBF(X.shape[1]) + GPy.kern.White(X.shape[1]) + GPy.kern.Bias(X.shape[1]) + + likelihood = GPy.likelihoods.Bernoulli() + + assert Y.shape[1] == 1, 'Y should be 1 column vector' + + labels = np.unique(Y.flatten()) + + self.results = {} + for yj in labels: + print 'Class %s vs all' %yj + Ynew = Y.copy() + Ynew[Y.flatten()!=yj] = 0 + Ynew[Y.flatten()==yj] = 1 + + m = GPy.models.SparseGPClassification(X,Ynew,kernel=kernel.copy(),Y_metadata=Y_metadata,num_inducing=num_inducing) + m.optimize(messages=messages) + self.results[yj] = m.predict(X)[0] + del m + del Ynew diff --git a/GPy/models/sparse_gp_classification.py b/GPy/models/sparse_gp_classification.py new file mode 100644 index 00000000..e281a4b9 --- /dev/null +++ b/GPy/models/sparse_gp_classification.py @@ -0,0 +1,46 @@ +# Copyright (c) 2013, Ricardo Andrade +# Licensed under the BSD 3-clause license (see LICENSE.txt) + + +import numpy as np +from ..core import SparseGP +from .. import likelihoods +from .. import kern +from ..likelihoods import likelihood +from ..inference.latent_function_inference import expectation_propagation_dtc + +class SparseGPClassification(SparseGP): + """ + sparse Gaussian Process model for classification + + This is a thin wrapper around the sparse_GP class, with a set of sensible defaults + + :param X: input observations + :param Y: observed values + :param likelihood: a GPy likelihood, defaults to Binomial with probit link_function + :param kernel: a GPy kernel, defaults to rbf+white + :param normalize_X: whether to normalize the input data before computing (predictions will be in original scales) + :type normalize_X: False|True + :param normalize_Y: whether to normalize the input data before computing (predictions will be in original scales) + :type normalize_Y: False|True + :rtype: model object + + """ + + #def __init__(self, X, Y=None, likelihood=None, kernel=None, normalize_X=False, normalize_Y=False, Z=None, num_inducing=10): + def __init__(self, X, Y=None, likelihood=None, kernel=None, Z=None, num_inducing=10, Y_metadata=None): + + + if kernel is None: + kernel = kern.RBF(X.shape[1]) + + likelihood = likelihoods.Bernoulli() + + if Z is None: + i = np.random.permutation(X.shape[0])[:num_inducing] + Z = X[i].copy() + else: + assert Z.shape[1] == X.shape[1] + + SparseGP.__init__(self, X, Y, Z, kernel, likelihood, inference_method=expectation_propagation_dtc.EPDTC(), name='SparseGPClassification',Y_metadata=Y_metadata) + #def __init__(self, X, Y, Z, kernel, likelihood, inference_method=None, name='sparse gp', Y_metadata=None): diff --git a/GPy/models/sparse_gp_coregionalized_regression.py b/GPy/models/sparse_gp_coregionalized_regression.py new file mode 100644 index 00000000..797d8b30 --- /dev/null +++ b/GPy/models/sparse_gp_coregionalized_regression.py @@ -0,0 +1,66 @@ +# Copyright (c) 2012 - 2014 the GPy Austhors (see AUTHORS.txt) +# Licensed under the BSD 3-clause license (see LICENSE.txt) + +import numpy as np +from ..core import SparseGP +from ..inference.latent_function_inference import VarDTC +from .. import likelihoods +from .. import kern +from .. import util + +class SparseGPCoregionalizedRegression(SparseGP): + """ + Sparse Gaussian Process model for heteroscedastic multioutput regression + + This is a thin wrapper around the SparseGP class, with a set of sensible defaults + + :param X_list: list of input observations corresponding to each output + :type X_list: list of numpy arrays + :param Y_list: list of observed values related to the different noise models + :type Y_list: list of numpy arrays + :param Z_list: list of inducing inputs (optional) + :type Z_list: empty list | list of numpy arrays + :param kernel: a GPy kernel, defaults to RBF ** Coregionalized + :type kernel: None | GPy.kernel defaults + :likelihoods_list: a list of likelihoods, defaults to list of Gaussian likelihoods + :type likelihoods_list: None | a list GPy.likelihoods + :param num_inducing: number of inducing inputs, defaults to 10 per output (ignored if Z_list is not empty) + :type num_inducing: integer | list of integers + + :param name: model name + :type name: string + :param W_rank: number tuples of the corregionalization parameters 'W' (see coregionalize kernel documentation) + :type W_rank: integer + :param kernel_name: name of the kernel + :type kernel_name: string + """ + + def __init__(self, X_list, Y_list, Z_list=[], kernel=None, likelihoods_list=None, num_inducing=10, X_variance=None, name='SGPCR',W_rank=1,kernel_name='coreg'): + + #Input and Output + X,Y,self.output_index = util.multioutput.build_XY(X_list,Y_list) + Ny = len(Y_list) + + #Kernel + if kernel is None: + kernel = util.multioutput.ICM(input_dim=X.shape[1]-1, num_outputs=Ny, kernel=kern.RBF(X.shape[1]-1), W_rank=1,name=kernel_name) + + #Likelihood + likelihood = util.multioutput.build_likelihood(Y_list,self.output_index,likelihoods_list) + + #Inducing inputs list + if len(Z_list): + assert len(Z_list) == Ny, 'Number of outputs do not match length of inducing inputs list.' + else: + if isinstance(num_inducing,np.int): + num_inducing = [num_inducing] * Ny + num_inducing = np.asarray(num_inducing) + assert num_inducing.size == Ny, 'Number of outputs do not match length of inducing inputs list.' + for ni,Xi in zip(num_inducing,X_list): + i = np.random.permutation(Xi.shape[0])[:ni] + Z_list.append(Xi[i].copy()) + + Z, _, Iz = util.multioutput.build_XY(Z_list) + + super(SparseGPCoregionalizedRegression, self).__init__(X, Y, Z, kernel, likelihood, inference_method=VarDTC(), Y_metadata={'output_index':self.output_index}) + self['.*inducing'][:,-1].fix() diff --git a/GPy/models/sparse_gp_minibatch.py b/GPy/models/sparse_gp_minibatch.py new file mode 100644 index 00000000..ec2e28f5 --- /dev/null +++ b/GPy/models/sparse_gp_minibatch.py @@ -0,0 +1,348 @@ +# Copyright (c) 2012, GPy authors (see AUTHORS.txt). +# Licensed under the BSD 3-clause license (see LICENSE.txt) + +import numpy as np +from ..core.parameterization.param import Param +from ..core.gp import GP +from ..inference.latent_function_inference import var_dtc +from .. import likelihoods +from ..core.parameterization.variational import VariationalPosterior + +import logging +from GPy.inference.latent_function_inference.posterior import Posterior +from GPy.inference.optimization.stochastics import SparseGPStochastics,\ + SparseGPMissing +#no stochastics.py file added! from GPy.inference.optimization.stochastics import SparseGPStochastics,\ + #SparseGPMissing +logger = logging.getLogger("sparse gp") + +class SparseGPMiniBatch(GP): + """ + A general purpose Sparse GP model +''' +Created on 3 Nov 2014 + +@author: maxz +''' + + This model allows (approximate) inference using variational DTC or FITC + (Gaussian likelihoods) as well as non-conjugate sparse methods based on + these. + + :param X: inputs + :type X: np.ndarray (num_data x input_dim) + :param likelihood: a likelihood instance, containing the observed data + :type likelihood: GPy.likelihood.(Gaussian | EP | Laplace) + :param kernel: the kernel (covariance function). See link kernels + :type kernel: a GPy.kern.kern instance + :param X_variance: The uncertainty in the measurements of X (Gaussian variance) + :type X_variance: np.ndarray (num_data x input_dim) | None + :param Z: inducing inputs + :type Z: np.ndarray (num_inducing x input_dim) + :param num_inducing: Number of inducing points (optional, default 10. Ignored if Z is not None) + :type num_inducing: int + + """ + + def __init__(self, X, Y, Z, kernel, likelihood, inference_method=None, + name='sparse gp', Y_metadata=None, normalizer=False, + missing_data=False, stochastic=False, batchsize=1): + #pick a sensible inference method + if inference_method is None: + if isinstance(likelihood, likelihoods.Gaussian): + inference_method = var_dtc.VarDTC(limit=1 if not self.missing_data else Y.shape[1]) + else: + #inference_method = ?? + raise NotImplementedError, "what to do what to do?" + print "defaulting to ", inference_method, "for latent function inference" + + self.kl_factr = 1. + self.Z = Param('inducing inputs', Z) + self.num_inducing = Z.shape[0] + + GP.__init__(self, X, Y, kernel, likelihood, inference_method=inference_method, name=name, Y_metadata=Y_metadata, normalizer=normalizer) + self.missing_data = missing_data + + if stochastic and missing_data: + self.missing_data = True + self.ninan = ~np.isnan(Y) + self.stochastics = SparseGPStochastics(self, batchsize) + elif stochastic and not missing_data: + self.missing_data = False + self.stochastics = SparseGPStochastics(self, batchsize) + elif missing_data: + self.missing_data = True + self.ninan = ~np.isnan(Y) + self.stochastics = SparseGPMissing(self) + else: + self.stochastics = False + + logger.info("Adding Z as parameter") + self.link_parameter(self.Z, index=0) + if self.missing_data: + self.Ylist = [] + overall = self.Y_normalized.shape[1] + m_f = lambda i: "Precomputing Y for missing data: {: >7.2%}".format(float(i+1)/overall) + message = m_f(-1) + print message, + for d in xrange(overall): + self.Ylist.append(self.Y_normalized[self.ninan[:, d], d][:, None]) + print ' '*(len(message)+1) + '\r', + message = m_f(d) + print message, + print '' + + self.posterior = None + + def has_uncertain_inputs(self): + return isinstance(self.X, VariationalPosterior) + + def _inner_parameters_changed(self, kern, X, Z, likelihood, Y, Y_metadata, Lm=None, dL_dKmm=None, subset_indices=None): + """ + This is the standard part, which usually belongs in parameters_changed. + + For automatic handling of subsampling (such as missing_data, stochastics etc.), we need to put this into an inner + loop, in order to ensure a different handling of gradients etc of different + subsets of data. + + The dict in current_values will be passed aroung as current_values for + the rest of the algorithm, so this is the place to store current values, + such as subsets etc, if necessary. + + If Lm and dL_dKmm can be precomputed (or only need to be computed once) + pass them in here, so they will be passed to the inference_method. + + subset_indices is a dictionary of indices. you can put the indices however you + like them into this dictionary for inner use of the indices inside the + algorithm. + """ + try: + posterior, log_marginal_likelihood, grad_dict = self.inference_method.inference(kern, X, Z, likelihood, Y, Y_metadata, Lm=Lm, dL_dKmm=None) + except: + posterior, log_marginal_likelihood, grad_dict = self.inference_method.inference(kern, X, Z, likelihood, Y, Y_metadata) + current_values = {} + likelihood.update_gradients(grad_dict['dL_dthetaL']) + current_values['likgrad'] = likelihood.gradient.copy() + if subset_indices is None: + subset_indices = {} + if isinstance(X, VariationalPosterior): + #gradients wrt kernel + dL_dKmm = grad_dict['dL_dKmm'] + kern.update_gradients_full(dL_dKmm, Z, None) + current_values['kerngrad'] = kern.gradient.copy() + kern.update_gradients_expectations(variational_posterior=X, + Z=Z, + dL_dpsi0=grad_dict['dL_dpsi0'], + dL_dpsi1=grad_dict['dL_dpsi1'], + dL_dpsi2=grad_dict['dL_dpsi2']) + current_values['kerngrad'] += kern.gradient + + #gradients wrt Z + current_values['Zgrad'] = kern.gradients_X(dL_dKmm, Z) + current_values['Zgrad'] += kern.gradients_Z_expectations( + grad_dict['dL_dpsi0'], + grad_dict['dL_dpsi1'], + grad_dict['dL_dpsi2'], + Z=Z, + variational_posterior=X) + else: + #gradients wrt kernel + kern.update_gradients_diag(grad_dict['dL_dKdiag'], X) + current_values['kerngrad'] = kern.gradient.copy() + kern.update_gradients_full(grad_dict['dL_dKnm'], X, Z) + current_values['kerngrad'] += kern.gradient + kern.update_gradients_full(grad_dict['dL_dKmm'], Z, None) + current_values['kerngrad'] += kern.gradient + #gradients wrt Z + current_values['Zgrad'] = kern.gradients_X(grad_dict['dL_dKmm'], Z) + current_values['Zgrad'] += kern.gradients_X(grad_dict['dL_dKnm'].T, Z, X) + return posterior, log_marginal_likelihood, grad_dict, current_values, subset_indices + + def _inner_take_over_or_update(self, full_values=None, current_values=None, value_indices=None): + """ + This is for automatic updates of values in the inner loop of missing + data handling. Both arguments are dictionaries and the values in + full_values will be updated by the current_gradients. + + If a key from current_values does not exist in full_values, it will be + initialized to the value in current_values. + + If there is indices needed for the update, value_indices can be used for + that. If value_indices has the same key, as current_values, the update + in full_values will be indexed by the indices in value_indices. + + grads: + dictionary of standing gradients (you will have to carefully make sure, that + the ordering is right!). The values in here will be updated such that + full_values[key] += current_values[key] forall key in full_gradients.keys() + + gradients: + dictionary of gradients in the current set of parameters. + + value_indices: + dictionary holding indices for the update in full_values. + if the key exists the update rule is:def df(x): + full_values[key][value_indices[key]] += current_values[key] + """ + for key in current_values.keys(): + if value_indices is not None and value_indices.has_key(key): + index = value_indices[key] + else: + index = slice(None) + if full_values.has_key(key): + full_values[key][index] += current_values[key] + else: + full_values[key] = current_values[key] + + def _inner_values_update(self, current_values): + """ + This exists if there is more to do with the current values. + It will be called allways in the inner loop, so that + you can do additional inner updates for the inside of the missing data + loop etc. This can also be used for stochastic updates, when only working on + one dimension of the output. + """ + pass + + def _outer_values_update(self, full_values): + """ + Here you put the values, which were collected before in the right places. + E.g. set the gradients of parameters, etc. + """ + self.likelihood.gradient = full_values['likgrad'] + self.kern.gradient = full_values['kerngrad'] + self.Z.gradient = full_values['Zgrad'] + + def _outer_init_full_values(self): + """ + If full_values has indices in values_indices, we might want to initialize + the full_values differently, so that subsetting is possible. + + Here you can initialize the full_values for the values needed. + + Keep in mind, that if a key does not exist in full_values when updating + values, it will be set (so e.g. for Z there is no need to initialize Zgrad, + as there is no subsetting needed. For X in BGPLVM on the other hand we probably need + to initialize the gradients for the mean and the variance in order to + have the full gradient for indexing) + """ + return {} + + def _outer_loop_for_missing_data(self): + Lm = None + dL_dKmm = None + + self._log_marginal_likelihood = 0 + self.full_values = self._outer_init_full_values() + + if self.posterior is None: + woodbury_inv = np.zeros((self.num_inducing, self.num_inducing, self.output_dim)) + woodbury_vector = np.zeros((self.num_inducing, self.output_dim)) + else: + woodbury_inv = self.posterior._woodbury_inv + woodbury_vector = self.posterior._woodbury_vector + + if not self.stochastics: + m_f = lambda i: "Inference with missing_data: {: >7.2%}".format(float(i+1)/self.output_dim) + message = m_f(-1) + print message, + + for d in self.stochastics.d: + ninan = self.ninan[:, d] + + if not self.stochastics: + print ' '*(len(message)) + '\r', + message = m_f(d) + print message, + + posterior, log_marginal_likelihood, \ + grad_dict, current_values, value_indices = self._inner_parameters_changed( + self.kern, self.X[ninan], + self.Z, self.likelihood, + self.Ylist[d], self.Y_metadata, + Lm, dL_dKmm, + subset_indices=dict(outputs=d, samples=ninan)) + + self._inner_take_over_or_update(self.full_values, current_values, value_indices) + self._inner_values_update(current_values) + + Lm = posterior.K_chol + dL_dKmm = grad_dict['dL_dKmm'] + woodbury_inv[:, :, d] = posterior.woodbury_inv + woodbury_vector[:, d:d+1] = posterior.woodbury_vector + self._log_marginal_likelihood += log_marginal_likelihood + if not self.stochastics: + print '' + + if self.posterior is None: + self.posterior = Posterior(woodbury_inv=woodbury_inv, woodbury_vector=woodbury_vector, + K=posterior._K, mean=None, cov=None, K_chol=posterior.K_chol) + self._outer_values_update(self.full_values) + + def _outer_loop_without_missing_data(self): + self._log_marginal_likelihood = 0 + + if self.posterior is None: + woodbury_inv = np.zeros((self.num_inducing, self.num_inducing, self.output_dim)) + woodbury_vector = np.zeros((self.num_inducing, self.output_dim)) + else: + woodbury_inv = self.posterior._woodbury_inv + woodbury_vector = self.posterior._woodbury_vector + + d = self.stochastics.d + posterior, log_marginal_likelihood, \ + grad_dict, self.full_values, _ = self._inner_parameters_changed( + self.kern, self.X, + self.Z, self.likelihood, + self.Y_normalized[:, d], self.Y_metadata) + self.grad_dict = grad_dict + + self._log_marginal_likelihood += log_marginal_likelihood + + self._outer_values_update(self.full_values) + + woodbury_inv[:, :, d] = posterior.woodbury_inv[:, :, None] + woodbury_vector[:, d] = posterior.woodbury_vector + if self.posterior is None: + self.posterior = Posterior(woodbury_inv=woodbury_inv, woodbury_vector=woodbury_vector, + K=posterior._K, mean=None, cov=None, K_chol=posterior.K_chol) + + def parameters_changed(self): + if self.missing_data: + self._outer_loop_for_missing_data() + elif self.stochastics: + self._outer_loop_without_missing_data() + else: + self.posterior, self._log_marginal_likelihood, self.grad_dict, self.full_values, _ = self._inner_parameters_changed(self.kern, self.X, self.Z, self.likelihood, self.Y_normalized, self.Y_metadata) + self._outer_values_update(self.full_values) + + def _raw_predict(self, Xnew, full_cov=False, kern=None): + """ + Make a prediction for the latent function values + """ + + if kern is None: kern = self.kern + + if not isinstance(Xnew, VariationalPosterior): + Kx = kern.K(self.Z, Xnew) + mu = np.dot(Kx.T, self.posterior.woodbury_vector) + if full_cov: + Kxx = kern.K(Xnew) + if self.posterior.woodbury_inv.ndim == 2: + var = Kxx - np.dot(Kx.T, np.dot(self.posterior.woodbury_inv, Kx)) + elif self.posterior.woodbury_inv.ndim == 3: + var = Kxx[:,:,None] - np.tensordot(np.dot(np.atleast_3d(self.posterior.woodbury_inv).T, Kx).T, Kx, [1,0]).swapaxes(1,2) + var = var + else: + Kxx = kern.Kdiag(Xnew) + var = (Kxx - np.sum(np.dot(np.atleast_3d(self.posterior.woodbury_inv).T, Kx) * Kx[None,:,:], 1)).T + else: + Kx = kern.psi1(self.Z, Xnew) + mu = np.dot(Kx, self.posterior.woodbury_vector) + if full_cov: + raise NotImplementedError, "TODO" + else: + Kxx = kern.psi0(self.Z, Xnew) + psi2 = kern.psi2(self.Z, Xnew) + var = Kxx - np.sum(np.sum(psi2 * Kmmi_LmiBLmi[None, :, :], 1), 1) + return mu, var diff --git a/GPy/models/sparse_gp_regression.py b/GPy/models/sparse_gp_regression.py new file mode 100644 index 00000000..49c3914c --- /dev/null +++ b/GPy/models/sparse_gp_regression.py @@ -0,0 +1,109 @@ +# Copyright (c) 2012, James Hensman +# Licensed under the BSD 3-clause license (see LICENSE.txt) + + +import numpy as np +from ..core import SparseGP +from ..core.sparse_gp_mpi import SparseGP_MPI +from .. import likelihoods +from .. import kern +from ..inference.latent_function_inference import VarDTC +from ..core.parameterization.variational import NormalPosterior +from GPy.inference.latent_function_inference.var_dtc_parallel import VarDTC_minibatch + +class SparseGPRegression(SparseGP_MPI): + """ + Gaussian Process model for regression + + This is a thin wrapper around the SparseGP class, with a set of sensible defalts + + :param X: input observations + :param Y: observed values + :param kernel: a GPy kernel, defaults to rbf+white + :param Z: inducing inputs (optional, see note) + :type Z: np.ndarray (num_inducing x input_dim) | None + :param num_inducing: number of inducing points (ignored if Z is passed, see note) + :type num_inducing: int + :rtype: model object + + .. Note:: If no Z array is passed, num_inducing (default 10) points are selected from the data. Other wise num_inducing is ignored + .. Note:: Multiple independent outputs are allowed using columns of Y + + """ + + def __init__(self, X, Y, kernel=None, Z=None, num_inducing=10, X_variance=None, normalizer=None, mpi_comm=None): + num_data, input_dim = X.shape + + # kern defaults to rbf (plus white for stability) + if kernel is None: + kernel = kern.RBF(input_dim)# + kern.white(input_dim, variance=1e-3) + + # Z defaults to a subset of the data + if Z is None: + i = np.random.permutation(num_data)[:min(num_inducing, num_data)] + Z = X.view(np.ndarray)[i].copy() + else: + assert Z.shape[1] == input_dim + + likelihood = likelihoods.Gaussian() + + if not (X_variance is None): + X = NormalPosterior(X,X_variance) + + if mpi_comm is not None: + from ..inference.latent_function_inference.var_dtc_parallel import VarDTC_minibatch + infr = VarDTC_minibatch(mpi_comm=mpi_comm) + else: + infr = VarDTC() + + SparseGP_MPI.__init__(self, X, Y, Z, kernel, likelihood, inference_method=infr, normalizer=normalizer, mpi_comm=mpi_comm) + + def parameters_changed(self): + from ..inference.latent_function_inference.var_dtc_parallel import update_gradients_sparsegp,VarDTC_minibatch + if isinstance(self.inference_method,VarDTC_minibatch): + update_gradients_sparsegp(self, mpi_comm=self.mpi_comm) + else: + super(SparseGPRegression, self).parameters_changed() + +class SparseGPRegressionUncertainInput(SparseGP): + """ + Gaussian Process model for regression with Gaussian variance on the inputs (X_variance) + + This is a thin wrapper around the SparseGP class, with a set of sensible defalts + + """ + + def __init__(self, X, X_variance, Y, kernel=None, Z=None, num_inducing=10, normalizer=None): + """ + :param X: input observations + :type X: np.ndarray (num_data x input_dim) + :param X_variance: The uncertainty in the measurements of X (Gaussian variance, optional) + :type X_variance: np.ndarray (num_data x input_dim) + :param Y: observed values + :param kernel: a GPy kernel, defaults to rbf+white + :param Z: inducing inputs (optional, see note) + :type Z: np.ndarray (num_inducing x input_dim) | None + :param num_inducing: number of inducing points (ignored if Z is passed, see note) + :type num_inducing: int + :rtype: model object + + .. Note:: If no Z array is passed, num_inducing (default 10) points are selected from the data. Other wise num_inducing is ignored + .. Note:: Multiple independent outputs are allowed using columns of Y + """ + num_data, input_dim = X.shape + + # kern defaults to rbf (plus white for stability) + if kernel is None: + kernel = kern.RBF(input_dim) + kern.White(input_dim, variance=1e-3) + + # Z defaults to a subset of the data + if Z is None: + i = np.random.permutation(num_data)[:min(num_inducing, num_data)] + Z = X[i].copy() + else: + assert Z.shape[1] == input_dim + + likelihood = likelihoods.Gaussian() + + SparseGP.__init__(self, X, Y, Z, kernel, likelihood, X_variance=X_variance, inference_method=VarDTC(), normalizer=normalizer) + self.ensure_default_constraints() diff --git a/GPy/models/sparse_gplvm.py b/GPy/models/sparse_gplvm.py new file mode 100644 index 00000000..d1ad5884 --- /dev/null +++ b/GPy/models/sparse_gplvm.py @@ -0,0 +1,43 @@ +# Copyright (c) 2012, GPy authors (see AUTHORS.txt). +# Licensed under the BSD 3-clause license (see LICENSE.txt) + + +import numpy as np +import sys +from GPy.models.sparse_gp_regression import SparseGPRegression + +class SparseGPLVM(SparseGPRegression): + """ + Sparse Gaussian Process Latent Variable Model + + :param Y: observed data + :type Y: np.ndarray + :param input_dim: latent dimensionality + :type input_dim: int + :param init: initialisation method for the latent space + :type init: 'PCA'|'random' + + """ + def __init__(self, Y, input_dim, X=None, kernel=None, init='PCA', num_inducing=10): + if X is None: + from ..util.initialization import initialize_latent + X, fracs = initialize_latent(init, input_dim, Y) + SparseGPRegression.__init__(self, X, Y, kernel=kernel, num_inducing=num_inducing) + + def parameters_changed(self): + super(SparseGPLVM, self).parameters_changed() + self.X.gradient = self.kern.gradients_X_diag(self.grad_dict['dL_dKdiag'], self.X) + self.X.gradient += self.kern.gradients_X(self.grad_dict['dL_dKnm'], self.X, self.Z) + + def plot_latent(self, labels=None, which_indices=None, + resolution=50, ax=None, marker='o', s=40, + fignum=None, plot_inducing=True, legend=True, + plot_limits=None, + aspect='auto', updates=False, predict_kwargs={}, imshow_kwargs={}): + assert "matplotlib" in sys.modules, "matplotlib package has not been imported." + from ..plotting.matplot_dep import dim_reduction_plots + + return dim_reduction_plots.plot_latent(self, labels, which_indices, + resolution, ax, marker, s, + fignum, plot_inducing, legend, + plot_limits, aspect, updates, predict_kwargs, imshow_kwargs) diff --git a/GPy/models/ss_gplvm.py b/GPy/models/ss_gplvm.py new file mode 100644 index 00000000..a61ad2a0 --- /dev/null +++ b/GPy/models/ss_gplvm.py @@ -0,0 +1,108 @@ +# Copyright (c) 2012, GPy authors (see AUTHORS.txt). +# Licensed under the BSD 3-clause license (see LICENSE.txt) + +import numpy as np + +from ..core.sparse_gp_mpi import SparseGP_MPI +from .. import kern +from ..likelihoods import Gaussian +from ..core.parameterization.variational import SpikeAndSlabPrior, SpikeAndSlabPosterior +from ..inference.latent_function_inference.var_dtc_parallel import update_gradients, VarDTC_minibatch +from ..kern._src.psi_comp.ssrbf_psi_gpucomp import PSICOMP_SSRBF_GPU + +class SSGPLVM(SparseGP_MPI): + """ + Spike-and-Slab Gaussian Process Latent Variable Model + + :param Y: observed data (np.ndarray) or GPy.likelihood + :type Y: np.ndarray| GPy.likelihood instance + :param input_dim: latent dimensionality + :type input_dim: int + :param init: initialisation method for the latent space + :type init: 'PCA'|'random' + + """ + def __init__(self, Y, input_dim, X=None, X_variance=None, Gamma=None, init='PCA', num_inducing=10, + Z=None, kernel=None, inference_method=None, likelihood=None, name='Spike_and_Slab GPLVM', group_spike=False, mpi_comm=None, pi=None, learnPi=True,normalizer=False, **kwargs): + + self.group_spike = group_spike + + if X == None: + from ..util.initialization import initialize_latent + X, fracs = initialize_latent(init, input_dim, Y) + else: + fracs = np.ones(input_dim) + + self.init = init + + if X_variance is None: # The variance of the variational approximation (S) + X_variance = np.random.uniform(0,.1,X.shape) + + if Gamma is None: + gamma = np.random.randn(X.shape[0], input_dim) + else: + gamma = Gamma.copy() + + if Z is None: + Z = np.random.permutation(X.copy())[:num_inducing] + assert Z.shape[1] == X.shape[1] + + if likelihood is None: + likelihood = Gaussian() + + if kernel is None: + kernel = kern.RBF(input_dim, lengthscale=fracs, ARD=True) # + kern.white(input_dim) + if kernel.useGPU: + kernel.psicomp = PSICOMP_SSRBF_GPU() + + if inference_method is None: + inference_method = VarDTC_minibatch(mpi_comm=mpi_comm) + + if pi is None: + pi = np.empty((input_dim)) + pi[:] = 0.5 + self.variational_prior = SpikeAndSlabPrior(pi=pi,learnPi=learnPi) # the prior probability of the latent binary variable b + + X = SpikeAndSlabPosterior(X, X_variance, gamma) + + super(SSGPLVM,self).__init__(X, Y, Z, kernel, likelihood, variational_prior=self.variational_prior, inference_method=inference_method, name=name, mpi_comm=mpi_comm, normalizer=normalizer, **kwargs) +# self.X.unfix() +# self.X.variance.constrain_positive() + self.link_parameter(self.X, index=0) + + if self.group_spike: + [self.X.gamma[:,i].tie('tieGamma'+str(i)) for i in xrange(self.X.gamma.shape[1])] # Tie columns together + + def set_X_gradients(self, X, X_grad): + """Set the gradients of the posterior distribution of X in its specific form.""" + X.mean.gradient, X.variance.gradient, X.binary_prob.gradient = X_grad + + def get_X_gradients(self, X): + """Get the gradients of the posterior distribution of X in its specific form.""" + return X.mean.gradient, X.variance.gradient, X.binary_prob.gradient + + def parameters_changed(self): + super(SSGPLVM,self).parameters_changed() + if isinstance(self.inference_method, VarDTC_minibatch): + return + + self._log_marginal_likelihood -= self.variational_prior.KL_divergence(self.X) + + self.X.mean.gradient, self.X.variance.gradient, self.X.binary_prob.gradient = self.kern.gradients_qX_expectations(variational_posterior=self.X, Z=self.Z, dL_dpsi0=self.grad_dict['dL_dpsi0'], dL_dpsi1=self.grad_dict['dL_dpsi1'], dL_dpsi2=self.grad_dict['dL_dpsi2']) + + # update for the KL divergence + self.variational_prior.update_gradients_KL(self.X) + + def input_sensitivity(self): + if self.kern.ARD: + return self.kern.input_sensitivity() + else: + return self.variational_prior.pi + + def plot_latent(self, plot_inducing=True, *args, **kwargs): + import sys + assert "matplotlib" in sys.modules, "matplotlib package has not been imported." + from ..plotting.matplot_dep import dim_reduction_plots + + return dim_reduction_plots.plot_latent(self, plot_inducing=plot_inducing, *args, **kwargs) + diff --git a/GPy/models/ss_mrd.py b/GPy/models/ss_mrd.py new file mode 100644 index 00000000..036ac095 --- /dev/null +++ b/GPy/models/ss_mrd.py @@ -0,0 +1,34 @@ +""" +The Maniforld Relevance Determination model with the spike-and-slab prior +""" + +from ..core import Model +from .ss_gplvm import SSGPLVM + +class SSMRD(Model): + + def __init__(self, Ylist, input_dim, X=None, X_variance=None, + initx = 'PCA', initz = 'permute', + num_inducing=10, Z=None, kernel=None, + inference_method=None, likelihoods=None, name='ss_mrd', Ynames=None): + super(SSMRD, self).__init__(name) + + self.updates = False + self.models = [SSGPLVM(y, input_dim, X=X, X_variance=X_variance, num_inducing=num_inducing,Z=Z,init=initx, + kernel=kernel.copy() if kernel else None,inference_method=inference_method,likelihood=likelihoods, + name='model_'+str(i)) for i,y in enumerate(Ylist)] + self.add_parameters(*(self.models)) + + [[[self.models[m].X.mean[i,j:j+1].tie('mean_'+str(i)+'_'+str(j)) for m in xrange(len(self.models))] for j in xrange(self.models[0].X.mean.shape[1])] + for i in xrange(self.models[0].X.mean.shape[0])] + [[[self.models[m].X.variance[i,j:j+1].tie('var_'+str(i)+'_'+str(j)) for m in xrange(len(self.models))] for j in xrange(self.models[0].X.variance.shape[1])] + for i in xrange(self.models[0].X.variance.shape[0])] + + self.updates = True + + def parameters_changed(self): + super(SSMRD, self).parameters_changed() + self._log_marginal_likelihood = sum([m._log_marginal_likelihood for m in self.models]) + + def log_likelihood(self): + return self._log_marginal_likelihood \ No newline at end of file diff --git a/GPy/models/warped_gp.py b/GPy/models/warped_gp.py new file mode 100644 index 00000000..4b982ed2 --- /dev/null +++ b/GPy/models/warped_gp.py @@ -0,0 +1,99 @@ +# Copyright (c) 2012, GPy authors (see AUTHORS.txt). +# Licensed under the BSD 3-clause license (see LICENSE.txt) + + +import numpy as np +from ..util.warping_functions import * +from ..core import GP +from .. import likelihoods +from GPy.util.warping_functions import TanhWarpingFunction_d +from GPy import kern + +class WarpedGP(GP): + def __init__(self, X, Y, kernel=None, warping_function=None, warping_terms=3, normalize_X=False, normalize_Y=False): + + if kernel is None: + kernel = kern.rbf(X.shape[1]) + + if warping_function == None: + self.warping_function = TanhWarpingFunction_d(warping_terms) + self.warping_params = (np.random.randn(self.warping_function.n_terms * 3 + 1,) * 1) + + self.scale_data = False + if self.scale_data: + Y = self._scale_data(Y) + self.has_uncertain_inputs = False + self.Y_untransformed = Y.copy() + self.predict_in_warped_space = False + likelihood = likelihoods.Gaussian(self.transform_data(), normalize=normalize_Y) + + GP.__init__(self, X, likelihood, kernel, normalize_X=normalize_X) + self._set_params(self._get_params()) + + def _scale_data(self, Y): + self._Ymax = Y.max() + self._Ymin = Y.min() + return (Y - self._Ymin) / (self._Ymax - self._Ymin) - 0.5 + + def _unscale_data(self, Y): + return (Y + 0.5) * (self._Ymax - self._Ymin) + self._Ymin + + def _set_params(self, x): + self.warping_params = x[:self.warping_function.num_parameters] + Y = self.transform_data() + self.likelihood.set_data(Y) + GP._set_params(self, x[self.warping_function.num_parameters:].copy()) + + def _get_params(self): + return np.hstack((self.warping_params.flatten().copy(), GP._get_params(self).copy())) + + def _get_param_names(self): + warping_names = self.warping_function._get_param_names() + param_names = GP._get_param_names(self) + return warping_names + param_names + + def transform_data(self): + Y = self.warping_function.f(self.Y_untransformed.copy(), self.warping_params).copy() + return Y + + def log_likelihood(self): + ll = GP.log_likelihood(self) + jacobian = self.warping_function.fgrad_y(self.Y_untransformed, self.warping_params) + return ll + np.log(jacobian).sum() + + def _log_likelihood_gradients(self): + ll_grads = GP._log_likelihood_gradients(self) + alpha = np.dot(self.Ki, self.likelihood.Y.flatten()) + warping_grads = self.warping_function_gradients(alpha) + + warping_grads = np.append(warping_grads[:, :-1].flatten(), warping_grads[0, -1]) + return np.hstack((warping_grads.flatten(), ll_grads.flatten())) + + def warping_function_gradients(self, Kiy): + grad_y = self.warping_function.fgrad_y(self.Y_untransformed, self.warping_params) + grad_y_psi, grad_psi = self.warping_function.fgrad_y_psi(self.Y_untransformed, self.warping_params, + return_covar_chain=True) + djac_dpsi = ((1.0 / grad_y[:, :, None, None]) * grad_y_psi).sum(axis=0).sum(axis=0) + dquad_dpsi = (Kiy[:, None, None, None] * grad_psi).sum(axis=0).sum(axis=0) + + return -dquad_dpsi + djac_dpsi + + def plot_warping(self): + self.warping_function.plot(self.warping_params, self.Y_untransformed.min(), self.Y_untransformed.max()) + + def predict(self, Xnew, which_parts='all', full_cov=False, pred_init=None): + # normalize X values + Xnew = (Xnew.copy() - self._Xoffset) / self._Xscale + mu, var = GP._raw_predict(self, Xnew, full_cov=full_cov, which_parts=which_parts) + + # now push through likelihood + mean, var, _025pm, _975pm = self.likelihood.predictive_values(mu, var, full_cov) + + if self.predict_in_warped_space: + mean = self.warping_function.f_inv(mean, self.warping_params, y=pred_init) + var = self.warping_function.f_inv(var, self.warping_params) + + if self.scale_data: + mean = self._unscale_data(mean) + + return mean, var, _025pm, _975pm diff --git a/GPy/models_modules/bayesian_gplvm.py b/GPy/models_modules/bayesian_gplvm.py index efee5c05..7cbd69eb 100644 --- a/GPy/models_modules/bayesian_gplvm.py +++ b/GPy/models_modules/bayesian_gplvm.py @@ -1,21 +1,15 @@ -# Copyright (c) 2012, GPy authors (see AUTHORS.txt). +# Copyright (c) 2012 - 2014 the GPy Austhors (see AUTHORS.txt) # Licensed under the BSD 3-clause license (see LICENSE.txt) import numpy as np -import itertools -from matplotlib import pyplot - -from ..core.sparse_gp import SparseGP -from ..likelihoods import Gaussian from .. import kern -from ..inference.optimization import SCG -from ..util import plot_latent, linalg -from .gplvm import GPLVM, initialise_latent -from ..util.plot_latent import most_significant_input_dimensions -from ..core.model import Model -from ..util.subarray_and_sorting import common_subarrays +from ..core.sparse_gp_mpi import SparseGP_MPI +from ..likelihoods import Gaussian +from ..core.parameterization.variational import NormalPosterior, NormalPrior +from ..inference.latent_function_inference.var_dtc_parallel import VarDTC_minibatch +import logging -class BayesianGPLVM(SparseGP, GPLVM): +class BayesianGPLVM(SparseGP_MPI): """ Bayesian Gaussian Process Latent Variable Model @@ -27,92 +21,120 @@ class BayesianGPLVM(SparseGP, GPLVM): :type init: 'PCA'|'random' """ - def __init__(self, likelihood_or_Y, input_dim, X=None, X_variance=None, init='PCA', num_inducing=10, - Z=None, kernel=None, **kwargs): - if type(likelihood_or_Y) is np.ndarray: - likelihood = Gaussian(likelihood_or_Y) - else: - likelihood = likelihood_or_Y + def __init__(self, Y, input_dim, X=None, X_variance=None, init='PCA', num_inducing=10, + Z=None, kernel=None, inference_method=None, likelihood=None, + name='bayesian gplvm', mpi_comm=None, normalizer=None, + missing_data=False, stochastic=False, batchsize=1): + + self.logger = logging.getLogger(self.__class__.__name__) + if X is None: + from ..util.initialization import initialize_latent + self.logger.info("initializing latent space X with method {}".format(init)) + X, fracs = initialize_latent(init, input_dim, Y) + else: + fracs = np.ones(input_dim) - if X == None: - X = initialise_latent(init, input_dim, likelihood.Y) self.init = init if X_variance is None: - X_variance = np.clip((np.ones_like(X) * 0.5) + .01 * np.random.randn(*X.shape), 0.001, 1) + self.logger.info("initializing latent space variance ~ uniform(0,.1)") + X_variance = np.random.uniform(0,.1,X.shape) if Z is None: + self.logger.info("initializing inducing inputs") Z = np.random.permutation(X.copy())[:num_inducing] assert Z.shape[1] == X.shape[1] if kernel is None: - kernel = kern.rbf(input_dim) # + kern.white(input_dim) + self.logger.info("initializing kernel RBF") + kernel = kern.RBF(input_dim, lengthscale=1./fracs, ARD=True) #+ kern.Bias(input_dim) + kern.White(input_dim) - SparseGP.__init__(self, X, likelihood, kernel, Z=Z, X_variance=X_variance, **kwargs) - self.ensure_default_constraints() + if likelihood is None: + likelihood = Gaussian() - def _get_param_names(self): - X_names = sum([['X_%i_%i' % (n, q) for q in range(self.input_dim)] for n in range(self.num_data)], []) - S_names = sum([['X_variance_%i_%i' % (n, q) for q in range(self.input_dim)] for n in range(self.num_data)], []) - return (X_names + S_names + SparseGP._get_param_names(self)) + self.variational_prior = NormalPrior() + X = NormalPosterior(X, X_variance) - #def _get_print_names(self): - # return SparseGP._get_print_names(self) + if inference_method is None: + if mpi_comm is not None: + inference_method = VarDTC_minibatch(mpi_comm=mpi_comm) + else: + from ..inference.latent_function_inference.var_dtc import VarDTC + self.logger.debug("creating inference_method var_dtc") + inference_method = VarDTC(limit=1 if not missing_data else Y.shape[1]) + if isinstance(inference_method,VarDTC_minibatch): + inference_method.mpi_comm = mpi_comm - def _get_params(self): - """ - Horizontally stacks the parameters in order to present them to the optimizer. - The resulting 1-input_dim array has this structure: + super(BayesianGPLVM,self).__init__(X, Y, Z, kernel, likelihood=likelihood, + name=name, inference_method=inference_method, + normalizer=normalizer, mpi_comm=mpi_comm, + variational_prior=self.variational_prior, + ) + self.link_parameter(self.X, index=0) - =============================================================== - | mu | S | Z | theta | beta | - =============================================================== + def set_X_gradients(self, X, X_grad): + """Set the gradients of the posterior distribution of X in its specific form.""" + X.mean.gradient, X.variance.gradient = X_grad - """ - x = np.hstack((self.X.flatten(), self.X_variance.flatten(), SparseGP._get_params(self))) - return x + def get_X_gradients(self, X): + """Get the gradients of the posterior distribution of X in its specific form.""" + return X.mean.gradient, X.variance.gradient - def _set_params(self, x, save_old=True, save_count=0): - N, input_dim = self.num_data, self.input_dim - self.X = x[:self.X.size].reshape(N, input_dim).copy() - self.X_variance = x[(N * input_dim):(2 * N * input_dim)].reshape(N, input_dim).copy() - SparseGP._set_params(self, x[(2 * N * input_dim):]) + def parameters_changed(self): + super(BayesianGPLVM,self).parameters_changed() + if isinstance(self.inference_method, VarDTC_minibatch): + return - def dKL_dmuS(self): - dKL_dS = (1. - (1. / (self.X_variance))) * 0.5 - dKL_dmu = self.X - return dKL_dmu, dKL_dS + kl_fctr = 1. + self._log_marginal_likelihood -= kl_fctr*self.variational_prior.KL_divergence(self.X) - def dL_dmuS(self): - dL_dmu_psi0, dL_dS_psi0 = self.kern.dpsi0_dmuS(self.dL_dpsi0, self.Z, self.X, self.X_variance) - dL_dmu_psi1, dL_dS_psi1 = self.kern.dpsi1_dmuS(self.dL_dpsi1, self.Z, self.X, self.X_variance) - dL_dmu_psi2, dL_dS_psi2 = self.kern.dpsi2_dmuS(self.dL_dpsi2, self.Z, self.X, self.X_variance) - dL_dmu = dL_dmu_psi0 + dL_dmu_psi1 + dL_dmu_psi2 - dL_dS = dL_dS_psi0 + dL_dS_psi1 + dL_dS_psi2 + self.X.mean.gradient, self.X.variance.gradient = self.kern.gradients_qX_expectations( + variational_posterior=self.X, + Z=self.Z, + dL_dpsi0=self.grad_dict['dL_dpsi0'], + dL_dpsi1=self.grad_dict['dL_dpsi1'], + dL_dpsi2=self.grad_dict['dL_dpsi2']) - return dL_dmu, dL_dS + self.variational_prior.update_gradients_KL(self.X) - def KL_divergence(self): - var_mean = np.square(self.X).sum() - var_S = np.sum(self.X_variance - np.log(self.X_variance)) - return 0.5 * (var_mean + var_S) - 0.5 * self.input_dim * self.num_data - def log_likelihood(self): - ll = SparseGP.log_likelihood(self) - kl = self.KL_divergence() - return ll - kl + #super(BayesianGPLVM, self).parameters_changed() + #self._log_marginal_likelihood -= self.variational_prior.KL_divergence(self.X) - def _log_likelihood_gradients(self): - dKL_dmu, dKL_dS = self.dKL_dmuS() - dL_dmu, dL_dS = self.dL_dmuS() - d_dmu = (dL_dmu - dKL_dmu).flatten() - d_dS = (dL_dS - dKL_dS).flatten() - self.dbound_dmuS = np.hstack((d_dmu, d_dS)) - self.dbound_dZtheta = SparseGP._log_likelihood_gradients(self) - return np.hstack((self.dbound_dmuS.flatten(), self.dbound_dZtheta)) + #self.X.mean.gradient, self.X.variance.gradient = self.kern.gradients_qX_expectations(variational_posterior=self.X, Z=self.Z, dL_dpsi0=self.grad_dict['dL_dpsi0'], dL_dpsi1=self.grad_dict['dL_dpsi1'], dL_dpsi2=self.grad_dict['dL_dpsi2']) - def plot_latent(self, plot_inducing=True, *args, **kwargs): - return plot_latent.plot_latent(self, plot_inducing=plot_inducing, *args, **kwargs) + # This is testing code ------------------------- +# i = np.random.randint(self.X.shape[0]) +# X_ = self.X.mean +# which = np.sqrt(((X_ - X_[i:i+1])**2).sum(1)).argsort()>(max(0, self.X.shape[0]-51)) +# _, _, grad_dict = self.inference_method.inference(self.kern, self.X[which], self.Z, self.likelihood, self.Y[which], self.Y_metadata) +# grad = self.kern.gradients_qX_expectations(variational_posterior=self.X[which], Z=self.Z, dL_dpsi0=grad_dict['dL_dpsi0'], dL_dpsi1=grad_dict['dL_dpsi1'], dL_dpsi2=grad_dict['dL_dpsi2']) +# +# self.X.mean.gradient[:] = 0 +# self.X.variance.gradient[:] = 0 +# self.X.mean.gradient[which] = grad[0] +# self.X.variance.gradient[which] = grad[1] + + # update for the KL divergence +# self.variational_prior.update_gradients_KL(self.X, which) + # ----------------------------------------------- + + # update for the KL divergence + #self.variational_prior.update_gradients_KL(self.X) + + def plot_latent(self, labels=None, which_indices=None, + resolution=50, ax=None, marker='o', s=40, + fignum=None, plot_inducing=True, legend=True, + plot_limits=None, + aspect='auto', updates=False, predict_kwargs={}, imshow_kwargs={}): + import sys + assert "matplotlib" in sys.modules, "matplotlib package has not been imported." + from ..plotting.matplot_dep import dim_reduction_plots + + return dim_reduction_plots.plot_latent(self, labels, which_indices, + resolution, ax, marker, s, + fignum, plot_inducing, legend, + plot_limits, aspect, updates, predict_kwargs, imshow_kwargs) def do_test_latents(self, Y): """ @@ -121,36 +143,41 @@ class BayesianGPLVM(SparseGP, GPLVM): Notes: This will only work with a univariate Gaussian likelihood (for now) """ - assert not self.likelihood.is_heteroscedastic N_test = Y.shape[0] input_dim = self.Z.shape[1] + means = np.zeros((N_test, input_dim)) covars = np.zeros((N_test, input_dim)) - dpsi0 = -0.5 * self.input_dim * self.likelihood.precision - dpsi2 = self.dL_dpsi2[0][None, :, :] # TODO: this may change if we ignore het. likelihoods - V = self.likelihood.precision * Y + dpsi0 = -0.5 * self.input_dim / self.likelihood.variance + dpsi2 = self.grad_dict['dL_dpsi2'][0][None, :, :] # TODO: this may change if we ignore het. likelihoods + V = Y/self.likelihood.variance #compute CPsi1V - if self.Cpsi1V is None: - psi1V = np.dot(self.psi1.T, self.likelihood.V) - tmp, _ = linalg.dtrtrs(self._Lm, np.asfortranarray(psi1V), lower=1, trans=0) - tmp, _ = linalg.dpotrs(self.LB, tmp, lower=1) - self.Cpsi1V, _ = linalg.dtrtrs(self._Lm, tmp, lower=1, trans=1) + #if self.Cpsi1V is None: + # psi1V = np.dot(self.psi1.T, self.likelihood.V) + # tmp, _ = linalg.dtrtrs(self._Lm, np.asfortranarray(psi1V), lower=1, trans=0) + # tmp, _ = linalg.dpotrs(self.LB, tmp, lower=1) + # self.Cpsi1V, _ = linalg.dtrtrs(self._Lm, tmp, lower=1, trans=1) - dpsi1 = np.dot(self.Cpsi1V, V.T) + dpsi1 = np.dot(self.posterior.woodbury_vector, V.T) - start = np.zeros(self.input_dim * 2) + #start = np.zeros(self.input_dim * 2) + + + from scipy.optimize import minimize for n, dpsi1_n in enumerate(dpsi1.T[:, :, None]): - args = (self.kern, self.Z, dpsi0, dpsi1_n.T, dpsi2) - xopt, fopt, neval, status = SCG(f=latent_cost, gradf=latent_grad, x=start, optargs=args, display=False) - + args = (input_dim, self.kern.copy(), self.Z, dpsi0, dpsi1_n.T, dpsi2) + res = minimize(latent_cost_and_grad, jac=True, x0=np.hstack((means[n], covars[n])), args=args, method='BFGS') + xopt = res.x mu, log_S = xopt.reshape(2, 1, -1) means[n] = mu[0].copy() covars[n] = np.exp(log_S[0]).copy() - return means, covars + X = NormalPosterior(means, covars) + + return X def dmu_dX(self, Xnew): """ @@ -158,303 +185,50 @@ class BayesianGPLVM(SparseGP, GPLVM): """ dmu_dX = np.zeros_like(Xnew) for i in range(self.Z.shape[0]): - dmu_dX += self.kern.dK_dX(self.Cpsi1Vf[i:i + 1, :], Xnew, self.Z[i:i + 1, :]) + dmu_dX += self.kern.gradients_X(self.grad_dict['dL_dpsi1'][i:i + 1, :], Xnew, self.Z[i:i + 1, :]) return dmu_dX def dmu_dXnew(self, Xnew): """ Individual gradient of prediction at Xnew w.r.t. each sample in Xnew """ - dK_dX = np.zeros((Xnew.shape[0], self.num_inducing)) + gradients_X = np.zeros((Xnew.shape[0], self.num_inducing)) ones = np.ones((1, 1)) for i in range(self.Z.shape[0]): - dK_dX[:, i] = self.kern.dK_dX(ones, Xnew, self.Z[i:i + 1, :]).sum(-1) - return np.dot(dK_dX, self.Cpsi1Vf) + gradients_X[:, i] = self.kern.gradients_X(ones, Xnew, self.Z[i:i + 1, :]).sum(-1) + return np.dot(gradients_X, self.grad_dict['dL_dpsi1']) - def plot_steepest_gradient_map(self, fignum=None, ax=None, which_indices=None, labels=None, data_labels=None, data_marker='o', data_s=40, resolution=20, aspect='auto', updates=False, ** kwargs): - input_1, input_2 = significant_dims = most_significant_input_dimensions(self, which_indices) - - X = np.zeros((resolution ** 2, self.input_dim)) - indices = np.r_[:X.shape[0]] - if labels is None: - labels = range(self.output_dim) - - def plot_function(x): - X[:, significant_dims] = x - dmu_dX = self.dmu_dXnew(X) - argmax = np.argmax(dmu_dX, 1) - return dmu_dX[indices, argmax], np.array(labels)[argmax] - - if ax is None: - fig = pyplot.figure(num=fignum) - ax = fig.add_subplot(111) - - if data_labels is None: - data_labels = np.ones(self.num_data) - ulabels = [] - for lab in data_labels: - if not lab in ulabels: - ulabels.append(lab) - marker = itertools.cycle(list(data_marker)) - from GPy.util import Tango - for i, ul in enumerate(ulabels): - if type(ul) is np.string_: - this_label = ul - elif type(ul) is np.int64: - this_label = 'class %i' % ul - else: - this_label = 'class %i' % i - m = marker.next() - index = np.nonzero(data_labels == ul)[0] - x = self.X[index, input_1] - y = self.X[index, input_2] - ax.scatter(x, y, marker=m, s=data_s, color=Tango.nextMedium(), label=this_label) - - ax.set_xlabel('latent dimension %i' % input_1) - ax.set_ylabel('latent dimension %i' % input_2) - - from matplotlib.cm import get_cmap - from GPy.util.latent_space_visualizations.controllers.imshow_controller import ImAnnotateController - if not 'cmap' in kwargs.keys(): - kwargs.update(cmap=get_cmap('jet')) - controller = ImAnnotateController(ax, - plot_function, - tuple(self.X.min(0)[:, significant_dims]) + tuple(self.X.max(0)[:, significant_dims]), - resolution=resolution, - aspect=aspect, - **kwargs) - ax.legend() - ax.figure.tight_layout() - if updates: - pyplot.show() - clear = raw_input('Enter to continue') - if clear.lower() in 'yes' or clear == '': - controller.deactivate() - return controller.view - - def plot_X_1d(self, fignum=None, ax=None, colors=None): + def plot_steepest_gradient_map(self, *args, ** kwargs): """ - Plot latent space X in 1D: - - - if fig is given, create input_dim subplots in fig and plot in these - - if ax is given plot input_dim 1D latent space plots of X into each `axis` - - if neither fig nor ax is given create a figure with fignum and plot in there - - colors: - colors of different latent space dimensions input_dim - + See GPy.plotting.matplot_dep.dim_reduction_plots.plot_steepest_gradient_map """ - import pylab - if ax is None: - fig = pylab.figure(num=fignum, figsize=(8, min(12, (2 * self.X.shape[1])))) - if colors is None: - colors = pylab.gca()._get_lines.color_cycle - pylab.clf() - else: - colors = iter(colors) - plots = [] - x = np.arange(self.X.shape[0]) - for i in range(self.X.shape[1]): - if ax is None: - a = fig.add_subplot(self.X.shape[1], 1, i + 1) - elif isinstance(ax, (tuple, list)): - a = ax[i] - else: - raise ValueError("Need one ax per latent dimnesion input_dim") - a.plot(self.X, c='k', alpha=.3) - plots.extend(a.plot(x, self.X.T[i], c=colors.next(), label=r"$\mathbf{{X_{{{}}}}}$".format(i))) - a.fill_between(x, - self.X.T[i] - 2 * np.sqrt(self.X_variance.T[i]), - self.X.T[i] + 2 * np.sqrt(self.X_variance.T[i]), - facecolor=plots[-1].get_color(), - alpha=.3) - a.legend(borderaxespad=0.) - a.set_xlim(x.min(), x.max()) - if i < self.X.shape[1] - 1: - a.set_xticklabels('') - pylab.draw() - if ax is None: - fig.tight_layout(h_pad=.01) # , rect=(0, 0, 1, .95)) - return fig + import sys + assert "matplotlib" in sys.modules, "matplotlib package has not been imported." + from ..plotting.matplot_dep import dim_reduction_plots - def getstate(self): - """ - Get the current state of the class, - here just all the indices, rest can get recomputed - """ - return SparseGP.getstate(self) + [self.init] + return dim_reduction_plots.plot_steepest_gradient_map(self,*args,**kwargs) - def setstate(self, state): - self._const_jitter = None - self.init = state.pop() - SparseGP.setstate(self, state) -class BayesianGPLVMWithMissingData(Model): - """ - Bayesian Gaussian Process Latent Variable Model with missing data support. - NOTE: Missing data is assumed to be missing at random! - - This extension comes with a large memory and computing time deficiency. - Use only if fraction of missing data at random is higher than 60%. - Otherwise, try filtering data before using this extension. - - Y can hold missing data as given by `missing`, standard is :class:`~numpy.nan`. - - If likelihood is given for Y, this likelihood will be discarded, but the parameters - of the likelihood will be taken. Also every effort of creating the same likelihood - will be done. - - :param likelihood_or_Y: observed data (np.ndarray) or GPy.likelihood - :type likelihood_or_Y: :class:`~numpy.ndarray` | :class:`~GPy.likelihoods.likelihood.likelihood` instance - :param int input_dim: latent dimensionality - :param init: initialisation method for the latent space - :type init: 'PCA' | 'random' - """ - def __init__(self, likelihood_or_Y, input_dim, X=None, X_variance=None, init='PCA', num_inducing=10, - Z=None, kernel=None, **kwargs): - #======================================================================= - # Filter Y, such that same missing data is at same positions. - # If full rows are missing, delete them entirely! - if type(likelihood_or_Y) is np.ndarray: - Y = likelihood_or_Y - likelihood = Gaussian - params = 1. - normalize=None - else: - Y = likelihood_or_Y.Y - likelihood = likelihood_or_Y.__class__ - params = likelihood_or_Y._get_params() - if isinstance(likelihood_or_Y, Gaussian): - normalize = True - scale = likelihood_or_Y._scale - offset = likelihood_or_Y._offset - # Get common subrows - filter_ = np.isnan(Y) - self.subarray_indices = common_subarrays(filter_,axis=1) - likelihoods = [likelihood(Y[~np.array(v,dtype=bool),:][:,ind]) for v,ind in self.subarray_indices.iteritems()] - for l in likelihoods: - l._set_params(params) - if normalize: # get normalization in common - l._scale = scale - l._offset = offset - #======================================================================= - - if X == None: - X = initialise_latent(init, input_dim, Y[:,np.any(np.isnan(Y),1)]) - self.init = init - - if X_variance is None: - X_variance = np.clip((np.ones_like(X) * 0.5) + .01 * np.random.randn(*X.shape), 0.001, 1) - - if Z is None: - Z = np.random.permutation(X.copy())[:num_inducing] - assert Z.shape[1] == X.shape[1] - - if kernel is None: - kernel = kern.rbf(input_dim) # + kern.white(input_dim) - - self.submodels = [BayesianGPLVM(l, input_dim, X, X_variance, init, num_inducing, Z, kernel) for l in likelihoods] - self.gref = self.submodels[0] - #:type self.gref: BayesianGPLVM - self.ensure_default_constraints() - - def log_likelihood(self): - ll = -self.gref.KL_divergence() - for g in self.submodels: - ll += SparseGP.log_likelihood(g) - return ll - - def _log_likelihood_gradients(self): - dLdmu, dLdS = reduce(lambda a, b: [a[0] + b[0], a[1] + b[1]], (g.dL_dmuS() for g in self.bgplvms)) - dKLmu, dKLdS = self.gref.dKL_dmuS() - dLdmu -= dKLmu - dLdS -= dKLdS - dLdmuS = np.hstack((dLdmu.flatten(), dLdS.flatten())).flatten() - dldzt1 = reduce(lambda a, b: a + b, (SparseGP._log_likelihood_gradients(g)[:self.gref.num_inducing*self.gref.input_dim] for g in self.submodels)) - - return np.hstack((dLdmuS, - dldzt1, - np.hstack([np.hstack([g.dL_dtheta(), - g.likelihood._gradients(\ - partial=g.partial_for_likelihood)]) \ - for g in self.submodels]))) - - def getstate(self): - return Model.getstate(self)+[self.submodels,self.subarray_indices] - - def setstate(self, state): - self.subarray_indices = state.pop() - self.submodels = state.pop() - self.gref = self.submodels[0] - Model.setstate(self, state) - self._set_params(self._get_params()) - - def _get_param_names(self): - X_names = sum([['X_%i_%i' % (n, q) for q in range(self.input_dim)] for n in range(self.num_data)], []) - S_names = sum([['X_variance_%i_%i' % (n, q) for q in range(self.input_dim)] for n in range(self.num_data)], []) - return (X_names + S_names + SparseGP._get_param_names(self.gref)) - - def _get_params(self): - return self.gref._get_params() - def _set_params(self, x): - [g._set_params(x) for g in self.submodels] - - - pass - -def latent_cost_and_grad(mu_S, kern, Z, dL_dpsi0, dL_dpsi1, dL_dpsi2): +def latent_cost_and_grad(mu_S, input_dim, kern, Z, dL_dpsi0, dL_dpsi1, dL_dpsi2): """ objective function for fitting the latent variables for test points (negative log-likelihood: should be minimised!) """ - mu, log_S = mu_S.reshape(2, 1, -1) + mu = mu_S[:input_dim][None] + log_S = mu_S[input_dim:][None] S = np.exp(log_S) - psi0 = kern.psi0(Z, mu, S) - psi1 = kern.psi1(Z, mu, S) - psi2 = kern.psi2(Z, mu, S) + X = NormalPosterior(mu, S) - lik = dL_dpsi0 * psi0 + np.dot(dL_dpsi1.flatten(), psi1.flatten()) + np.dot(dL_dpsi2.flatten(), psi2.flatten()) - 0.5 * np.sum(np.square(mu) + S) + 0.5 * np.sum(log_S) + psi0 = kern.psi0(Z, X) + psi1 = kern.psi1(Z, X) + psi2 = kern.psi2(Z, X) - mu0, S0 = kern.dpsi0_dmuS(dL_dpsi0, Z, mu, S) - mu1, S1 = kern.dpsi1_dmuS(dL_dpsi1, Z, mu, S) - mu2, S2 = kern.dpsi2_dmuS(dL_dpsi2, Z, mu, S) + lik = dL_dpsi0 * psi0.sum() + np.einsum('ij,kj->...', dL_dpsi1, psi1) + np.einsum('ijk,lkj->...', dL_dpsi2, psi2) - 0.5 * np.sum(np.square(mu) + S) + 0.5 * np.sum(log_S) - dmu = mu0 + mu1 + mu2 - mu + dLdmu, dLdS = kern.gradients_qX_expectations(dL_dpsi0, dL_dpsi1, dL_dpsi2, Z, X) + dmu = dLdmu - mu # dS = S0 + S1 + S2 -0.5 + .5/S - dlnS = S * (S0 + S1 + S2 - 0.5) + .5 + dlnS = S * (dLdS - 0.5) + .5 + return -lik, -np.hstack((dmu.flatten(), dlnS.flatten())) - -def latent_cost(mu_S, kern, Z, dL_dpsi0, dL_dpsi1, dL_dpsi2): - """ - objective function for fitting the latent variables (negative log-likelihood: should be minimised!) - This is the same as latent_cost_and_grad but only for the objective - """ - mu, log_S = mu_S.reshape(2, 1, -1) - S = np.exp(log_S) - - psi0 = kern.psi0(Z, mu, S) - psi1 = kern.psi1(Z, mu, S) - psi2 = kern.psi2(Z, mu, S) - - lik = dL_dpsi0 * psi0 + np.dot(dL_dpsi1.flatten(), psi1.flatten()) + np.dot(dL_dpsi2.flatten(), psi2.flatten()) - 0.5 * np.sum(np.square(mu) + S) + 0.5 * np.sum(log_S) - return -float(lik) - -def latent_grad(mu_S, kern, Z, dL_dpsi0, dL_dpsi1, dL_dpsi2): - """ - This is the same as latent_cost_and_grad but only for the grad - """ - mu, log_S = mu_S.reshape(2, 1, -1) - S = np.exp(log_S) - - mu0, S0 = kern.dpsi0_dmuS(dL_dpsi0, Z, mu, S) - mu1, S1 = kern.dpsi1_dmuS(dL_dpsi1, Z, mu, S) - mu2, S2 = kern.dpsi2_dmuS(dL_dpsi2, Z, mu, S) - - dmu = mu0 + mu1 + mu2 - mu - # dS = S0 + S1 + S2 -0.5 + .5/S - dlnS = S * (S0 + S1 + S2 - 0.5) + .5 - - return -np.hstack((dmu.flatten(), dlnS.flatten())) - - diff --git a/GPy/models_modules/bcgplvm.py b/GPy/models_modules/bcgplvm.py index 92db6953..af8dc643 100644 --- a/GPy/models_modules/bcgplvm.py +++ b/GPy/models_modules/bcgplvm.py @@ -1,10 +1,8 @@ -# ## Copyright (c) 2012, GPy authors (see AUTHORS.txt). +# Copyright (c) 2012-2014, GPy authors (see AUTHORS.txt). # Licensed under the BSD 3-clause license (see LICENSE.txt) import numpy as np -import pylab as pb -import sys, pdb from ..core import GP from ..models import GPLVM from ..mappings import Kernel @@ -44,7 +42,7 @@ class BCGPLVM(GPLVM): GP._set_params(self, x[self.mapping.num_params:]) def _log_likelihood_gradients(self): - dL_df = self.kern.dK_dX(self.dL_dK, self.X) + dL_df = self.kern.gradients_X(self.dL_dK, self.X) dL_dtheta = self.mapping.df_dtheta(dL_df, self.likelihood.Y) return np.hstack((dL_dtheta.flatten(), GP._log_likelihood_gradients(self))) diff --git a/GPy/models_modules/fitc_classification.py b/GPy/models_modules/fitc_classification.py deleted file mode 100644 index 0aa21db9..00000000 --- a/GPy/models_modules/fitc_classification.py +++ /dev/null @@ -1,47 +0,0 @@ -# Copyright (c) 2013, Ricardo Andrade -# Licensed under the BSD 3-clause license (see LICENSE.txt) - - -import numpy as np -from ..core import FITC -from .. import likelihoods -from .. import kern -from ..likelihoods import likelihood - -class FITCClassification(FITC): - """ - FITC approximation for classification - - This is a thin wrapper around the FITC class, with a set of sensible defaults - - :param X: input observations - :param Y: observed values - :param likelihood: a GPy likelihood, defaults to Bernoulli with probit link function - :param kernel: a GPy kernel, defaults to rbf+white - :param normalize_X: whether to normalize the input data before computing (predictions will be in original scales) - :type normalize_X: False|True - :param normalize_Y: whether to normalize the input data before computing (predictions will be in original scales) - :type normalize_Y: False|True - :rtype: model object - - """ - - def __init__(self, X, Y=None, likelihood=None, kernel=None, normalize_X=False, normalize_Y=False, Z=None, num_inducing=10): - if kernel is None: - kernel = kern.rbf(X.shape[1]) + kern.white(X.shape[1],1e-3) - - if likelihood is None: - noise_model = likelihoods.bernoulli() - likelihood = likelihoods.EP(Y, noise_model) - elif Y is not None: - if not all(Y.flatten() == likelihood.data.flatten()): - raise Warning, 'likelihood.data and Y are different.' - - if Z is None: - i = np.random.permutation(X.shape[0])[:num_inducing] - Z = X[i].copy() - else: - assert Z.shape[1]==X.shape[1] - - FITC.__init__(self, X, likelihood, kernel, Z=Z, normalize_X=normalize_X) - self.ensure_default_constraints() diff --git a/GPy/models_modules/gp_classification.py b/GPy/models_modules/gp_classification.py index 7fc61bb7..bbf4f316 100644 --- a/GPy/models_modules/gp_classification.py +++ b/GPy/models_modules/gp_classification.py @@ -1,11 +1,10 @@ -# Copyright (c) 2013, Ricardo Andrade +# Copyright (c) 2013, the GPy Authors (see AUTHORS.txt) # Licensed under the BSD 3-clause license (see LICENSE.txt) - -import numpy as np from ..core import GP from .. import likelihoods from .. import kern +from ..inference.latent_function_inference.expectation_propagation import EP class GPClassification(GP): """ @@ -15,27 +14,16 @@ class GPClassification(GP): :param X: input observations :param Y: observed values, can be None if likelihood is not None - :param likelihood: a GPy likelihood, defaults to Bernoulli with Probit link_function :param kernel: a GPy kernel, defaults to rbf - :param normalize_X: whether to normalize the input data before computing (predictions will be in original scales) - :type normalize_X: False|True - :param normalize_Y: whether to normalize the input data before computing (predictions will be in original scales) - :type normalize_Y: False|True .. Note:: Multiple independent outputs are allowed using columns of Y """ - def __init__(self,X,Y=None,likelihood=None,kernel=None,normalize_X=False,normalize_Y=False): + def __init__(self, X, Y, kernel=None,Y_metadata=None): if kernel is None: - kernel = kern.rbf(X.shape[1]) + kernel = kern.RBF(X.shape[1]) - if likelihood is None: - noise_model = likelihoods.bernoulli() - likelihood = likelihoods.EP(Y, noise_model) - elif Y is not None: - if not all(Y.flatten() == likelihood.data.flatten()): - raise Warning, 'likelihood.data and Y are different.' + likelihood = likelihoods.Bernoulli() - GP.__init__(self, X, likelihood, kernel, normalize_X=normalize_X) - self.ensure_default_constraints() + GP.__init__(self, X=X, Y=Y, kernel=kernel, likelihood=likelihood, inference_method=EP(), name='gp_classification') diff --git a/GPy/models_modules/gp_multioutput_regression.py b/GPy/models_modules/gp_multioutput_regression.py deleted file mode 100644 index 4ce3dfbc..00000000 --- a/GPy/models_modules/gp_multioutput_regression.py +++ /dev/null @@ -1,58 +0,0 @@ -# Copyright (c) 2013, Ricardo Andrade -# Licensed under the BSD 3-clause license (see LICENSE.txt) - - -import numpy as np -from ..core import GP -from .. import likelihoods -from .. import kern - -class GPMultioutputRegression(GP): - """ - Multiple output Gaussian process with Gaussian noise - - This is a wrapper around the models.GP class, with a set of sensible defaults - - :param X_list: input observations - :type X_list: list of numpy arrays (num_data_output_i x input_dim), one array per output - :param Y_list: observed values - :type Y_list: list of numpy arrays (num_data_output_i x 1), one array per output - :param kernel_list: GPy kernels, defaults to rbf - :type kernel_list: list of GPy kernels - :param noise_variance_list: noise parameters per output, defaults to 1.0 for every output - :type noise_variance_list: list of floats - :param normalize_X: whether to normalize the input data before computing (predictions will be in original scales) - :type normalize_X: False|True - :param normalize_Y: whether to normalize the input data before computing (predictions will be in original scales) - :type normalize_Y: False|True - :param rank: number tuples of the corregionalization parameters 'coregion_W' (see coregionalize kernel documentation) - :type rank: integer - """ - - def __init__(self,X_list,Y_list,kernel_list=None,noise_variance_list=None,normalize_X=False,normalize_Y=False,rank=1): - - self.output_dim = len(Y_list) - assert len(X_list) == self.output_dim, 'Number of outputs do not match length of inputs list.' - - #Inputs indexing - i = 0 - index = [] - for x,y in zip(X_list,Y_list): - assert x.shape[0] == y.shape[0] - index.append(np.repeat(i,x.size)[:,None]) - i += 1 - index = np.vstack(index) - X = np.hstack([np.vstack(X_list),index]) - original_dim = X.shape[1] - 1 - - #Mixed noise likelihood definition - likelihood = likelihoods.Gaussian_Mixed_Noise(Y_list,noise_params=noise_variance_list,normalize=normalize_Y) - - #Coregionalization kernel definition - if kernel_list is None: - kernel_list = [kern.rbf(original_dim)] - mkernel = kern.build_lcm(input_dim=original_dim, output_dim=self.output_dim, kernel_list = kernel_list, rank=rank) - - self.multioutput = True - GP.__init__(self, X, likelihood, mkernel, normalize_X=normalize_X) - self.ensure_default_constraints() diff --git a/GPy/models_modules/gp_regression.py b/GPy/models_modules/gp_regression.py index 8b44c1ba..7b8fb63f 100644 --- a/GPy/models_modules/gp_regression.py +++ b/GPy/models_modules/gp_regression.py @@ -1,7 +1,7 @@ -# Copyright (c) 2012, James Hensman +# Copyright (c) 2012 - 2014 the GPy Austhors (see AUTHORS.txt) # Licensed under the BSD 3-clause license (see LICENSE.txt) - +import numpy as np from ..core import GP from .. import likelihoods from .. import kern @@ -15,27 +15,22 @@ class GPRegression(GP): :param X: input observations :param Y: observed values :param kernel: a GPy kernel, defaults to rbf - :param normalize_X: whether to normalize the input data before computing (predictions will be in original scales) - :type normalize_X: False|True - :param normalize_Y: whether to normalize the input data before computing (predictions will be in original scales) - :type normalize_Y: False|True + :param Norm normalizer: [False] + + Normalize Y with the norm given. + If normalizer is False, no normalization will be done + If it is None, we use GaussianNorm(alization) .. Note:: Multiple independent outputs are allowed using columns of Y """ - def __init__(self, X, Y, kernel=None, normalize_X=False, normalize_Y=False, likelihood=None): + def __init__(self, X, Y, kernel=None, Y_metadata=None, normalizer=None): + if kernel is None: - kernel = kern.rbf(X.shape[1]) + kernel = kern.RBF(X.shape[1]) - if likelihood is None: - likelihood = likelihoods.Gaussian(Y, normalize=normalize_Y) + likelihood = likelihoods.Gaussian() - GP.__init__(self, X, likelihood, kernel, normalize_X=normalize_X) - self.ensure_default_constraints() + super(GPRegression, self).__init__(X, Y, kernel, likelihood, name='GP regression', Y_metadata=Y_metadata, normalizer=normalizer) - def getstate(self): - return GP.getstate(self) - - def setstate(self, state): - return GP.setstate(self, state) diff --git a/GPy/models_modules/gplvm.py b/GPy/models_modules/gplvm.py index a5fe4284..6318829d 100644 --- a/GPy/models_modules/gplvm.py +++ b/GPy/models_modules/gplvm.py @@ -1,91 +1,83 @@ -# ## Copyright (c) 2012, GPy authors (see AUTHORS.txt). +# Copyright (c) 2012-2014, GPy authors (see AUTHORS.txt). # Licensed under the BSD 3-clause license (see LICENSE.txt) import numpy as np -import pylab as pb from .. import kern -from ..core import priors -from ..core import GP +from ..core import GP, Param from ..likelihoods import Gaussian from .. import util -from ..util.linalg import pca -def initialise_latent(init, input_dim, Y): - Xr = np.random.randn(Y.shape[0], input_dim) - if init.lower() == 'pca': - PC = pca(Y, input_dim)[0] - Xr[:PC.shape[0], :PC.shape[1]] = PC - return Xr class GPLVM(GP): """ Gaussian Process Latent Variable Model - :param Y: observed data - :type Y: np.ndarray - :param input_dim: latent dimensionality - :type input_dim: int - :param init: initialisation method for the latent space - :type init: 'pca'|'random' """ - def __init__(self, Y, input_dim, init='PCA', X=None, kernel=None, normalize_Y=False): + def __init__(self, Y, input_dim, init='PCA', X=None, kernel=None, name="gplvm"): + + """ + :param Y: observed data + :type Y: np.ndarray + :param input_dim: latent dimensionality + :type input_dim: int + :param init: initialisation method for the latent space + :type init: 'PCA'|'random' + """ if X is None: - X = initialise_latent(init, input_dim, Y) + from ..util.initialization import initialize_latent + X, fracs = initialize_latent(init, input_dim, Y) + else: + fracs = np.ones(input_dim) if kernel is None: - kernel = kern.rbf(input_dim, ARD=input_dim > 1) + kern.bias(input_dim, np.exp(-2)) - likelihood = Gaussian(Y, normalize=normalize_Y, variance=np.exp(-2.)) - GP.__init__(self, X, likelihood, kernel, normalize_X=False) - self.set_prior('.*X', priors.Gaussian(0, 1)) - self.ensure_default_constraints() + kernel = kern.RBF(input_dim, lengthscale=fracs, ARD=input_dim > 1) + kern.Bias(input_dim, np.exp(-2)) - def _get_param_names(self): - return sum([['X_%i_%i' % (n, q) for q in range(self.input_dim)] for n in range(self.num_data)], []) + GP._get_param_names(self) + likelihood = Gaussian() - def _get_params(self): - return np.hstack((self.X.flatten(), GP._get_params(self))) + super(GPLVM, self).__init__(X, Y, kernel, likelihood, name='GPLVM') + self.X = Param('latent_mean', X) + self.link_parameter(self.X, index=0) - def _set_params(self, x): - self.X = x[:self.num_data * self.input_dim].reshape(self.num_data, self.input_dim).copy() - GP._set_params(self, x[self.X.size:]) - - def _log_likelihood_gradients(self): - dL_dX = self.kern.dK_dX(self.dL_dK, self.X) - - return np.hstack((dL_dX.flatten(), GP._log_likelihood_gradients(self))) + def parameters_changed(self): + super(GPLVM, self).parameters_changed() + self.X.gradient = self.kern.gradients_X(self.grad_dict['dL_dK'], self.X, None) def jacobian(self,X): - target = np.zeros((X.shape[0],X.shape[1],self.output_dim)) + J = np.zeros((X.shape[0],X.shape[1],self.output_dim)) for i in range(self.output_dim): - target[:,:,i] = self.kern.dK_dX(np.dot(self.Ki,self.likelihood.Y[:,i])[None, :],X,self.X) - return target + J[:,:,i] = self.kern.gradients_X(self.posterior.woodbury_vector[:,i:i+1], X, self.X) + return J def magnification(self,X): target=np.zeros(X.shape[0]) - J = np.zeros((X.shape[0],X.shape[1],self.output_dim)) - J=self.jacobian(X) + #J = np.zeros((X.shape[0],X.shape[1],self.output_dim)) + J = self.jacobian(X) for i in range(X.shape[0]): - target[i]=np.sqrt(pb.det(np.dot(J[i,:,:],np.transpose(J[i,:,:])))) + target[i]=np.sqrt(np.linalg.det(np.dot(J[i,:,:],np.transpose(J[i,:,:])))) return target def plot(self): assert self.likelihood.Y.shape[1] == 2 - pb.scatter(self.likelihood.Y[:, 0], self.likelihood.Y[:, 1], 40, self.X[:, 0].copy(), linewidth=0, cmap=pb.cm.jet) + pb.scatter(self.likelihood.Y[:, 0], self.likelihood.Y[:, 1], 40, self.X[:, 0].copy(), linewidth=0, cmap=pb.cm.jet) # @UndefinedVariable Xnew = np.linspace(self.X.min(), self.X.max(), 200)[:, None] - mu, var, upper, lower = self.predict(Xnew) + mu, _ = self.predict(Xnew) + import pylab as pb pb.plot(mu[:, 0], mu[:, 1], 'k', linewidth=1.5) - def plot_latent(self, *args, **kwargs): - return util.plot_latent.plot_latent(self, *args, **kwargs) + def plot_latent(self, labels=None, which_indices=None, + resolution=50, ax=None, marker='o', s=40, + fignum=None, legend=True, + plot_limits=None, + aspect='auto', updates=False, **kwargs): + import sys + assert "matplotlib" in sys.modules, "matplotlib package has not been imported." + from ..plotting.matplot_dep import dim_reduction_plots + + return dim_reduction_plots.plot_latent(self, labels, which_indices, + resolution, ax, marker, s, + fignum, False, legend, + plot_limits, aspect, updates, **kwargs) def plot_magnification(self, *args, **kwargs): return util.plot_latent.plot_magnification(self, *args, **kwargs) - - def getstate(self): - return GP.getstate(self) - - def setstate(self, state): - GP.setstate(self, state) - - diff --git a/GPy/models_modules/gradient_checker.py b/GPy/models_modules/gradient_checker.py index dfd0640f..74026f8e 100644 --- a/GPy/models_modules/gradient_checker.py +++ b/GPy/models_modules/gradient_checker.py @@ -1,11 +1,10 @@ -''' -Created on 17 Jul 2013 +# ## Copyright (c) 2012, GPy authors (see AUTHORS.txt). +# Licensed under the BSD 3-clause license (see LICENSE.txt) -@author: maxz -''' -from GPy.core.model import Model +from ..core.model import Model import itertools import numpy +from ..core.parameterization import Param def get_shape(x): if isinstance(x, numpy.ndarray): @@ -28,39 +27,40 @@ class GradientChecker(Model): :param df: Gradient of function to check :param x0: Initial guess for inputs x (if it has a shape (a,b) this will be reflected in the parameter names). - Can be a list of arrays, if f takes a list of arrays. This list will be passed + Can be a list of arrays, if takes a list of arrays. This list will be passed to f and df in the same order as given here. - If f takes only one argument, make sure not to pass a list for x0!!! + If only one argument, make sure not to pass a list!!! + :type x0: [array-like] | array-like | float | int - :param list names: + :param names: Names to print, when performing gradcheck. If a list was passed to x0 a list of names with the same length is expected. - :param args kwargs: Arguments passed as f(x, *args, **kwargs) and df(x, *args, **kwargs) + :param args: Arguments passed as f(x, *args, **kwargs) and df(x, *args, **kwargs) Examples: --------- - from GPy.models import GradientChecker - N, M, Q = 10, 5, 3 + from GPy.models import GradientChecker + N, M, Q = 10, 5, 3 - Sinusoid: + Sinusoid: - X = numpy.random.rand(N, Q) - grad = GradientChecker(numpy.sin,numpy.cos,X,'sin_in') - grad.checkgrad(verbose=1) + X = numpy.random.rand(N, Q) + grad = GradientChecker(numpy.sin,numpy.cos,X,'x') + grad.checkgrad(verbose=1) - Using GPy: + Using GPy: - X, Z = numpy.random.randn(N,Q), numpy.random.randn(M,Q) - kern = GPy.kern.linear(Q, ARD=True) + GPy.kern.rbf(Q, ARD=True) - grad = GradientChecker(kern.K, - lambda x: kern.dK_dX(numpy.ones((1,1)), x), - x0 = X.copy(), - names=['X_input']) - grad.checkgrad(verbose=1) - grad.randomize() - grad.checkgrad(verbose=1) + X, Z = numpy.random.randn(N,Q), numpy.random.randn(M,Q) + kern = GPy.kern.linear(Q, ARD=True) + GPy.kern.rbf(Q, ARD=True) + grad = GradientChecker(kern.K, + lambda x: 2*kern.dK_dX(numpy.ones((1,1)), x), + x0 = X.copy(), + names='X') + grad.checkgrad(verbose=1) + grad.randomize() + grad.checkgrad(verbose=1) """ - Model.__init__(self) + Model.__init__(self, 'GradientChecker') if isinstance(x0, (list, tuple)) and names is None: self.shapes = [get_shape(xi) for xi in x0] self.names = ['X{i}'.format(i=i) for i in range(len(x0))] @@ -73,15 +73,17 @@ class GradientChecker(Model): else: self.names = names self.shapes = [get_shape(x0)] + for name, xi in zip(self.names, at_least_one_element(x0)): - self.__setattr__(name, numpy.float_(xi)) + self.__setattr__(name, Param(name, xi)) + self.link_parameter(self.__getattribute__(name)) # self._param_names = [] # for name, shape in zip(self.names, self.shapes): # self._param_names.extend(map(lambda nameshape: ('_'.join(nameshape)).strip('_'), itertools.izip(itertools.repeat(name), itertools.imap(lambda t: '_'.join(map(str, t)), itertools.product(*map(lambda xi: range(xi), shape)))))) self.args = args self.kwargs = kwargs - self._f = f - self._df = df + self.f = f + self.df = df def _get_x(self): if len(self.names) > 1: @@ -89,25 +91,23 @@ class GradientChecker(Model): return [self.__getattribute__(self.names[0])] + list(self.args) def log_likelihood(self): - return float(numpy.sum(self._f(*self._get_x(), **self.kwargs))) + return float(numpy.sum(self.f(*self._get_x(), **self.kwargs))) def _log_likelihood_gradients(self): - return numpy.atleast_1d(self._df(*self._get_x(), **self.kwargs)).flatten() + return numpy.atleast_1d(self.df(*self._get_x(), **self.kwargs)).flatten() + #def _get_params(self): + #return numpy.atleast_1d(numpy.hstack(map(lambda name: flatten_if_needed(self.__getattribute__(name)), self.names))) - def _get_params(self): - return numpy.atleast_1d(numpy.hstack(map(lambda name: flatten_if_needed(self.__getattribute__(name)), self.names))) + #def _set_params(self, x): + #current_index = 0 + #for name, shape in zip(self.names, self.shapes): + #current_size = numpy.prod(shape) + #self.__setattr__(name, x[current_index:current_index + current_size].reshape(shape)) + #current_index += current_size - - def _set_params(self, x): - current_index = 0 - for name, shape in zip(self.names, self.shapes): - current_size = numpy.prod(shape) - self.__setattr__(name, x[current_index:current_index + current_size].reshape(shape)) - current_index += current_size - - def _get_param_names(self): - _param_names = [] - for name, shape in zip(self.names, self.shapes): - _param_names.extend(map(lambda nameshape: ('_'.join(nameshape)).strip('_'), itertools.izip(itertools.repeat(name), itertools.imap(lambda t: '_'.join(map(str, t)), itertools.product(*map(lambda xi: range(xi), shape)))))) - return _param_names + #def _get_param_names(self): + #_param_names = [] + #for name, shape in zip(self.names, self.shapes): + #_param_names.extend(map(lambda nameshape: ('_'.join(nameshape)).strip('_'), itertools.izip(itertools.repeat(name), itertools.imap(lambda t: '_'.join(map(str, t)), itertools.product(*map(lambda xi: range(xi), shape)))))) + #return _param_names diff --git a/GPy/models_modules/mrd.py b/GPy/models_modules/mrd.py index 7a6bd386..645cdf88 100644 --- a/GPy/models_modules/mrd.py +++ b/GPy/models_modules/mrd.py @@ -1,281 +1,228 @@ -''' -Created on 10 Apr 2013 +# ## Copyright (c) 2013, GPy authors (see AUTHORS.txt). +# Licensed under the BSD 3-clause license (see LICENSE.txt) -@author: Max Zwiessele -''' -from GPy.core import Model -from GPy.core import SparseGP -from GPy.util.linalg import pca -import numpy -import itertools -import pylab -from ..kern import kern -from bayesian_gplvm import BayesianGPLVM +import numpy as np +import itertools, logging -class MRD(Model): +from ..kern import Kern +from ..core.parameterization.variational import NormalPosterior, NormalPrior +from ..core.parameterization import Param, Parameterized +from ..core.parameterization.observable_array import ObsAr +from ..inference.latent_function_inference.var_dtc import VarDTC +from ..inference.latent_function_inference import InferenceMethodList +from ..likelihoods import Gaussian +from ..util.initialization import initialize_latent +from ..core.sparse_gp import SparseGP, GP +from GPy.core.parameterization.variational import VariationalPosterior +from GPy.models.bayesian_gplvm_minibatch import BayesianGPLVMMiniBatch +from GPy.models.sparse_gp_minibatch import SparseGPMiniBatch + +class MRD(BayesianGPLVMMiniBatch): """ - Do MRD on given Datasets in Ylist. - All Ys in likelihood_list are in [N x Dn], where Dn can be different per Yn, - N must be shared across datasets though. + !WARNING: This is bleeding edge code and still in development. + Functionality may change fundamentally during development! - :param likelihood_list: list of observed datasets (:py:class:`~GPy.likelihoods.gaussian.Gaussian` if not supplied directly) - :type likelihood_list: [:py:class:`~GPy.likelihoods.likelihood.likelihood` | :py:class:`ndarray`] - :param names: names for different gplvm models - :type names: [str] + Apply MRD to all given datasets Y in Ylist. + + Y_i in [n x p_i] + + If Ylist is a dictionary, the keys of the dictionary are the names, and the + values are the different datasets to compare. + + The samples n in the datasets need + to match up, whereas the dimensionality p_d can differ. + + :param [array-like] Ylist: List of datasets to apply MRD on :param input_dim: latent dimensionality :type input_dim: int + :param array-like X: mean of starting latent space q in [n x q] + :param array-like X_variance: variance of starting latent space q in [n x q] :param initx: initialisation method for the latent space : - * 'concat' - pca on concatenation of all datasets - * 'single' - Concatenation of pca on datasets, respectively - * 'random' - Random draw from a normal + * 'concat' - PCA on concatenation of all datasets + * 'single' - Concatenation of PCA on datasets, respectively + * 'random' - Random draw from a Normal(0,1) :type initx: ['concat'|'single'|'random'] :param initz: initialisation method for inducing inputs :type initz: 'permute'|'random' - :param X: Initial latent space - :param X_variance: Initial latent space variance - :param Z: initial inducing inputs :param num_inducing: number of inducing inputs to use - :param kernels: list of kernels or kernel shared for all BGPLVMS - :type kernels: [GPy.kern.kern] | GPy.kern.kern | None (default) - + :param Z: initial inducing inputs + :param kernel: list of kernels or kernel to copy for each output + :type kernel: [GPy.kernels.kernels] | GPy.kernels.kernels | None (default) + :param :class:`~GPy.inference.latent_function_inference inference_method: + InferenceMethodList of inferences, or one inference method for all + :param :class:`~GPy.likelihoodss.likelihoods.likelihoods` likelihoods: the likelihoods to use + :param str name: the name of this model + :param [str] Ynames: the names for the datasets given, must be of equal length as Ylist or None + :param bool|Norm normalizer: How to normalize the data? + :param bool stochastic: Should this model be using stochastic gradient descent over the dimensions? + :param bool|[bool] batchsize: either one batchsize for all, or one batchsize per dataset. """ - def __init__(self, likelihood_or_Y_list, input_dim, num_inducing=10, names=None, - kernels=None, initx='PCA', - initz='permute', _debug=False, **kw): - if names is None: - self.names = ["{}".format(i) for i in range(len(likelihood_or_Y_list))] - else: - self.names = names - assert len(names) == len(likelihood_or_Y_list), "one name per data set required" - # sort out the kernels - if kernels is None: - kernels = [None] * len(likelihood_or_Y_list) - elif isinstance(kernels, kern): - kernels = [kernels.copy() for i in range(len(likelihood_or_Y_list))] - else: - assert len(kernels) == len(likelihood_or_Y_list), "need one kernel per output" - assert all([isinstance(k, kern) for k in kernels]), "invalid kernel object detected!" - assert not ('kernel' in kw), "pass kernels through `kernels` argument" + def __init__(self, Ylist, input_dim, X=None, X_variance=None, + initx = 'PCA', initz = 'permute', + num_inducing=10, Z=None, kernel=None, + inference_method=None, likelihoods=None, name='mrd', + Ynames=None, normalizer=False, stochastic=False, batchsize=10): + self.logger = logging.getLogger(self.__class__.__name__) self.input_dim = input_dim - self._debug = _debug self.num_inducing = num_inducing - self._init = True - X = self._init_X(initx, likelihood_or_Y_list) + if isinstance(Ylist, dict): + Ynames, Ylist = zip(*Ylist.items()) + + self.logger.debug("creating observable arrays") + self.Ylist = [ObsAr(Y) for Y in Ylist] + + if Ynames is None: + self.logger.debug("creating Ynames") + Ynames = ['Y{}'.format(i) for i in range(len(Ylist))] + self.names = Ynames + assert len(self.names) == len(self.Ylist), "one name per dataset, or None if Ylist is a dict" + + if inference_method is None: + self.inference_method = InferenceMethodList([VarDTC() for _ in xrange(len(self.Ylist))]) + else: + assert isinstance(inference_method, InferenceMethodList), "please provide one inference method per Y in the list and provide it as InferenceMethodList, inference_method given: {}".format(inference_method) + self.inference_method = inference_method + + if X is None: + X, fracs = self._init_X(initx, Ylist) + else: + fracs = [X.var(0)]*len(Ylist) + Z = self._init_Z(initz, X) - self.num_inducing = Z.shape[0] # ensure M==N if M>N + self.Z = Param('inducing inputs', Z) + self.num_inducing = self.Z.shape[0] # ensure M==N if M>N - self.bgplvms = [BayesianGPLVM(l, input_dim=input_dim, kernel=k, X=X, Z=Z, num_inducing=self.num_inducing, **kw) for l, k in zip(likelihood_or_Y_list, kernels)] - del self._init + # sort out the kernels + self.logger.info("building kernels") + if kernel is None: + from ..kern import RBF + kernels = [RBF(input_dim, ARD=1, lengthscale=1./fracs[i]) for i in range(len(Ylist))] + elif isinstance(kernel, Kern): + kernels = [] + for i in range(len(Ylist)): + k = kernel.copy() + kernels.append(k) + else: + assert len(kernel) == len(Ylist), "need one kernel per output" + assert all([isinstance(k, Kern) for k in kernel]), "invalid kernel object detected!" + kernels = kernel - self.gref = self.bgplvms[0] - nparams = numpy.array([0] + [SparseGP._get_params(g).size - g.Z.size for g in self.bgplvms]) - self.nparams = nparams.cumsum() + if X_variance is None: + X_variance = np.random.uniform(0.1, 0.2, X.shape) - self.num_data = self.gref.num_data + self.variational_prior = NormalPrior() + #self.X = NormalPosterior(X, X_variance) - self.NQ = self.num_data * self.input_dim - self.MQ = self.num_inducing * self.input_dim + if likelihoods is None: + likelihoods = [Gaussian(name='Gaussian_noise'.format(i)) for i in range(len(Ylist))] + else: likelihoods = likelihoods - Model.__init__(self) - self.ensure_default_constraints() + self.logger.info("adding X and Z") + super(MRD, self).__init__(Y, input_dim, X=X, X_variance=X_variance, num_inducing=num_inducing, + Z=self.Z, kernel=None, inference_method=self.inference_method, likelihood=Gaussian(), + name='manifold relevance determination', normalizer=None, + missing_data=False, stochastic=False, batchsize=1) - @property - def X(self): - return self.gref.X - @X.setter - def X(self, X): - try: - self.propagate_param(X=X) - except AttributeError: - if not self._init: - raise AttributeError("bgplvm list not initialized") - @property - def Z(self): - return self.gref.Z - @Z.setter - def Z(self, Z): - try: - self.propagate_param(Z=Z) - except AttributeError: - if not self._init: - raise AttributeError("bgplvm list not initialized") - @property - def X_variance(self): - return self.gref.X_variance - @X_variance.setter - def X_variance(self, X_var): - try: - self.propagate_param(X_variance=X_var) - except AttributeError: - if not self._init: - raise AttributeError("bgplvm list not initialized") - @property - def likelihood_list(self): - return [g.likelihood.Y for g in self.bgplvms] - @likelihood_list.setter - def likelihood_list(self, likelihood_list): - for g, Y in itertools.izip(self.bgplvms, likelihood_list): - g.likelihood.Y = Y + self._log_marginal_likelihood = 0 - @property - def auto_scale_factor(self): - """ - set auto_scale_factor for all gplvms - :param b: auto_scale_factor - :type b: - """ - return self.gref.auto_scale_factor - @auto_scale_factor.setter - def auto_scale_factor(self, b): - self.propagate_param(auto_scale_factor=b) + self.unlink_parameter(self.likelihood) + self.unlink_parameter(self.kern) + del self.kern + del self.likelihood - def propagate_param(self, **kwargs): - for key, val in kwargs.iteritems(): - for g in self.bgplvms: - g.__setattr__(key, val) + self.num_data = Ylist[0].shape[0] + if isinstance(batchsize, int): + batchsize = itertools.repeat(batchsize) - def randomize(self, initx='concat', initz='permute', *args, **kw): - super(MRD, self).randomize(*args, **kw) - self._init_X(initx, self.likelihood_list) - self._init_Z(initz, self.X) + self.bgplvms = [] - #def _get_latent_param_names(self): - def _get_param_names(self): - n1 = self.gref._get_param_names() - n1var = n1[:self.NQ * 2 + self.MQ] - # return n1var - # - #def _get_kernel_names(self): - map_names = lambda ns, name: map(lambda x: "{1}_{0}".format(*x), - itertools.izip(ns, - itertools.repeat(name))) - return list(itertools.chain(n1var, *(map_names(\ - SparseGP._get_param_names(g)[self.MQ:], n) \ - for g, n in zip(self.bgplvms, self.names)))) - # kernel_names = (map_names(SparseGP._get_param_names(g)[self.MQ:], n) for g, n in zip(self.bgplvms, self.names)) - # return kernel_names + for i, n, k, l, Y, im, bs in itertools.izip(itertools.count(), Ynames, kernels, likelihoods, Ylist, self.inference_method, batchsize): + assert Y.shape[0] == self.num_data, "All datasets need to share the number of datapoints, and those have to correspond to one another" + md = np.isnan(Y).any() + spgp = BayesianGPLVMMiniBatch(Y, input_dim, X, X_variance, + Z=Z, kernel=k, likelihood=l, + inference_method=im, name=n, + normalizer=normalizer, + missing_data=md, + stochastic=stochastic, + batchsize=bs) + spgp.kl_factr = 1./len(Ynames) + spgp.unlink_parameter(spgp.Z) + spgp.unlink_parameter(spgp.X) + del spgp.Z + del spgp.X + spgp.Z = self.Z + spgp.X = self.X + self.link_parameter(spgp, i+2) + self.bgplvms.append(spgp) - #def _get_param_names(self): - # X_names = sum([['X_%i_%i' % (n, q) for q in range(self.input_dim)] for n in range(self.num_data)], []) - # S_names = sum([['X_variance_%i_%i' % (n, q) for q in range(self.input_dim)] for n in range(self.num_data)], []) - # n1var = self._get_latent_param_names() - # kernel_names = self._get_kernel_names() - # return list(itertools.chain(n1var, *kernel_names)) + self.posterior = None + self.logger.info("init done") - #def _get_print_names(self): - # return list(itertools.chain(*self._get_kernel_names())) + def parameters_changed(self): + self._log_marginal_likelihood = 0 + self.Z.gradient[:] = 0. + self.X.gradient[:] = 0. + for b, i in itertools.izip(self.bgplvms, self.inference_method): + self._log_marginal_likelihood += b._log_marginal_likelihood - def _get_params(self): - """ - return parameter list containing private and shared parameters as follows: + self.logger.info('working on im <{}>'.format(hex(id(i)))) + self.Z.gradient[:] += b.full_values['Zgrad'] + grad_dict = b.full_values - ================================================================= - | mu | S | Z || theta1 | theta2 | .. | thetaN | - ================================================================= - """ - X = self.gref.X.ravel() - X_var = self.gref.X_variance.ravel() - Z = self.gref.Z.ravel() - thetas = [SparseGP._get_params(g)[g.Z.size:] for g in self.bgplvms] - params = numpy.hstack([X, X_var, Z, numpy.hstack(thetas)]) - return params + self.X.mean.gradient += grad_dict['meangrad'] + self.X.variance.gradient += grad_dict['vargrad'] -# def _set_var_params(self, g, X, X_var, Z): -# g.X = X.reshape(self.num_data, self.input_dim) -# g.X_variance = X_var.reshape(self.num_data, self.input_dim) -# g.Z = Z.reshape(self.num_inducing, self.input_dim) -# -# def _set_kern_params(self, g, p): -# g.kern._set_params(p[:g.kern.num_params]) -# g.likelihood._set_params(p[g.kern.num_params:]) - - def _set_params(self, x): - start = 0; end = self.NQ - X = x[start:end] - start = end; end += start - X_var = x[start:end] - start = end; end += self.MQ - Z = x[start:end] - thetas = x[end:] - - # set params for all: - for g, s, e in itertools.izip(self.bgplvms, self.nparams, self.nparams[1:]): - g._set_params(numpy.hstack([X, X_var, Z, thetas[s:e]])) -# self._set_var_params(g, X, X_var, Z) -# self._set_kern_params(g, thetas[s:e].copy()) -# g._compute_kernel_matrices() -# if self.auto_scale_factor: -# g.scale_factor = numpy.sqrt(g.psi2.sum(0).mean() * g.likelihood.precision) -# # self.scale_factor = numpy.sqrt(self.psi2.sum(0).mean() * self.likelihood.precision) -# g._computations() - - - def update_likelihood_approximation(self): # TODO: object oriented vs script base - for bgplvm in self.bgplvms: - bgplvm.update_likelihood_approximation() + if isinstance(self.X, VariationalPosterior): + # update for the KL divergence + self.variational_prior.update_gradients_KL(self.X) + self._log_marginal_likelihood -= self.variational_prior.KL_divergence(self.X) + pass def log_likelihood(self): - ll = -self.gref.KL_divergence() - for g in self.bgplvms: - ll += SparseGP.log_likelihood(g) - return ll + return self._log_marginal_likelihood - def _log_likelihood_gradients(self): - dLdmu, dLdS = reduce(lambda a, b: [a[0] + b[0], a[1] + b[1]], (g.dL_dmuS() for g in self.bgplvms)) - dKLmu, dKLdS = self.gref.dKL_dmuS() - dLdmu -= dKLmu - dLdS -= dKLdS - dLdmuS = numpy.hstack((dLdmu.flatten(), dLdS.flatten())).flatten() - dldzt1 = reduce(lambda a, b: a + b, (SparseGP._log_likelihood_gradients(g)[:self.MQ] for g in self.bgplvms)) - - return numpy.hstack((dLdmuS, - dldzt1, - numpy.hstack([numpy.hstack([g.dL_dtheta(), - g.likelihood._gradients(\ - partial=g.partial_for_likelihood)]) \ - for g in self.bgplvms]))) - - def _init_X(self, init='PCA', likelihood_list=None): - if likelihood_list is None: - likelihood_list = self.likelihood_list - Ylist = [] - for likelihood_or_Y in likelihood_list: - if type(likelihood_or_Y) is numpy.ndarray: - Ylist.append(likelihood_or_Y) - else: - Ylist.append(likelihood_or_Y.Y) - del likelihood_list + def _init_X(self, init='PCA', Ylist=None): + if Ylist is None: + Ylist = self.Ylist if init in "PCA_concat": - X = pca(numpy.hstack(Ylist), self.input_dim)[0] + X, fracs = initialize_latent('PCA', self.input_dim, np.hstack(Ylist)) + fracs = [fracs]*len(Ylist) elif init in "PCA_single": - X = numpy.zeros((Ylist[0].shape[0], self.input_dim)) - for qs, Y in itertools.izip(numpy.array_split(numpy.arange(self.input_dim), len(Ylist)), Ylist): - X[:, qs] = pca(Y, len(qs))[0] + X = np.zeros((Ylist[0].shape[0], self.input_dim)) + fracs = [] + for qs, Y in itertools.izip(np.array_split(np.arange(self.input_dim), len(Ylist)), Ylist): + x,frcs = initialize_latent('PCA', len(qs), Y) + X[:, qs] = x + fracs.append(frcs) else: # init == 'random': - X = numpy.random.randn(Ylist[0].shape[0], self.input_dim) - self.X = X - return X - + X = np.random.randn(Ylist[0].shape[0], self.input_dim) + fracs = X.var(0) + fracs = [fracs]*len(Ylist) + X -= X.mean() + X /= X.std() + return X, fracs def _init_Z(self, init="permute", X=None): if X is None: X = self.X if init in "permute": - Z = numpy.random.permutation(X.copy())[:self.num_inducing] + Z = np.random.permutation(X.copy())[:self.num_inducing] elif init in "random": - Z = numpy.random.randn(self.num_inducing, self.input_dim) * X.var() - self.Z = Z + Z = np.random.randn(self.num_inducing, self.input_dim) * X.var() return Z def _handle_plotting(self, fignum, axes, plotf, sharex=False, sharey=False): + import matplotlib.pyplot as plt if axes is None: - fig = pylab.figure(num=fignum) + fig = plt.figure(num=fignum) sharex_ax = None sharey_ax = None + plots = [] for i, g in enumerate(self.bgplvms): try: if sharex: @@ -288,33 +235,41 @@ class MRD(Model): pass if axes is None: ax = fig.add_subplot(1, len(self.bgplvms), i + 1, sharex=sharex_ax, sharey=sharey_ax) - elif isinstance(axes, (tuple, list)): + elif isinstance(axes, (tuple, list, np.ndarray)): ax = axes[i] else: raise ValueError("Need one axes per latent dimension input_dim") - plotf(i, g, ax) + plots.append(plotf(i, g, ax)) if sharey_ax is not None: - pylab.setp(ax.get_yticklabels(), visible=False) - pylab.draw() + plt.setp(ax.get_yticklabels(), visible=False) + plt.draw() if axes is None: - fig.tight_layout() - return fig - else: - return pylab.gcf() + try: + fig.tight_layout() + except: + pass + return plots - def plot_X_1d(self, *a, **kw): - return self.gref.plot_X_1d(*a, **kw) + def predict(self, Xnew, full_cov=False, Y_metadata=None, kern=None, Yindex=0): + """ + Prediction for data set Yindex[default=0]. + This predicts the output mean and variance for the dataset given in Ylist[Yindex] + """ + b = self.bgplvms[Yindex] + self.posterior = b.posterior + self.kern = b.kern + self.likelihood = b.likelihood + return super(MRD, self).predict(Xnew, full_cov, Y_metadata, kern) - def plot_X(self, fignum=None, ax=None): - fig = self._handle_plotting(fignum, ax, lambda i, g, ax: ax.imshow(g.X)) - return fig - - def plot_predict(self, fignum=None, ax=None, sharex=False, sharey=False, **kwargs): - fig = self._handle_plotting(fignum, - ax, - lambda i, g, ax: ax.imshow(g. predict(g.X)[0], **kwargs), - sharex=sharex, sharey=sharey) - return fig + #=============================================================================== + # TODO: Predict! Maybe even change to several bgplvms, which share an X? + #=============================================================================== + # def plot_predict(self, fignum=None, ax=None, sharex=False, sharey=False, **kwargs): + # fig = self._handle_plotting(fignum, + # ax, + # lambda i, g, ax: ax.imshow(g.predict(g.X)[0], **kwargs), + # sharex=sharex, sharey=sharey) + # return fig def plot_scales(self, fignum=None, ax=None, titles=None, sharex=False, sharey=True, *args, **kwargs): """ @@ -326,52 +281,61 @@ class MRD(Model): """ if titles is None: titles = [r'${}$'.format(name) for name in self.names] - ymax = reduce(max, [numpy.ceil(max(g.input_sensitivity())) for g in self.bgplvms]) - def plotf(i, g, axis): - axis.set_ylim([0,ymax]) - g.kern.plot_ARD(ax=axis, title=titles[i], *args, **kwargs) + ymax = reduce(max, [np.ceil(max(g.kern.input_sensitivity())) for g in self.bgplvms]) + def plotf(i, g, ax): + #ax.set_ylim([0,ymax]) + return g.kern.plot_ARD(ax=ax, title=titles[i], *args, **kwargs) fig = self._handle_plotting(fignum, ax, plotf, sharex=sharex, sharey=sharey) return fig - def plot_latent(self, fignum=None, ax=None, *args, **kwargs): - fig = self.gref.plot_latent(fignum=fignum, ax=ax, *args, **kwargs) # self._handle_plotting(fignum, ax, lambda i, g, ax: g.plot_latent(ax=ax, *args, **kwargs)) - return fig + def plot_latent(self, labels=None, which_indices=None, + resolution=50, ax=None, marker='o', s=40, + fignum=None, plot_inducing=True, legend=True, + plot_limits=None, + aspect='auto', updates=False, predict_kwargs={}, imshow_kwargs={}): + """ + see plotting.matplot_dep.dim_reduction_plots.plot_latent + if predict_kwargs is None, will plot latent spaces for 0th dataset (and kernel), otherwise give + predict_kwargs=dict(Yindex='index') for plotting only the latent space of dataset with 'index'. + """ + import sys + assert "matplotlib" in sys.modules, "matplotlib package has not been imported." + from matplotlib import pyplot as plt + from ..plotting.matplot_dep import dim_reduction_plots + if "Yindex" not in predict_kwargs: + predict_kwargs['Yindex'] = 0 - def _debug_plot(self): - self.plot_X_1d() - fig = pylab.figure("MRD DEBUG PLOT", figsize=(4 * len(self.bgplvms), 9)) - fig.clf() - axes = [fig.add_subplot(3, len(self.bgplvms), i + 1) for i in range(len(self.bgplvms))] - self.plot_X(ax=axes) - axes = [fig.add_subplot(3, len(self.bgplvms), i + len(self.bgplvms) + 1) for i in range(len(self.bgplvms))] - self.plot_latent(ax=axes) - axes = [fig.add_subplot(3, len(self.bgplvms), i + 2 * len(self.bgplvms) + 1) for i in range(len(self.bgplvms))] - self.plot_scales(ax=axes) - pylab.draw() - fig.tight_layout() - - def getstate(self): - return Model.getstate(self) + [self.names, - self.bgplvms, - self.gref, - self.nparams, - self.input_dim, - self.num_inducing, - self.num_data, - self.NQ, - self.MQ] - - def setstate(self, state): - self.MQ = state.pop() - self.NQ = state.pop() - self.num_data = state.pop() - self.num_inducing = state.pop() - self.input_dim = state.pop() - self.nparams = state.pop() - self.gref = state.pop() - self.bgplvms = state.pop() - self.names = state.pop() - Model.setstate(self, state) + Yindex = predict_kwargs['Yindex'] + if ax is None: + fig = plt.figure(num=fignum) + ax = fig.add_subplot(111) + else: + fig = ax.figure + self.kern = self.bgplvms[Yindex].kern + self.likelihood = self.bgplvms[Yindex].likelihood + plot = dim_reduction_plots.plot_latent(self, labels, which_indices, + resolution, ax, marker, s, + fignum, plot_inducing, legend, + plot_limits, aspect, updates, predict_kwargs, imshow_kwargs) + ax.set_title(self.bgplvms[Yindex].name) + try: + fig.tight_layout() + except: + pass + return plot + def __getstate__(self): + state = super(MRD, self).__getstate__() + if state.has_key('kern'): + del state['kern'] + if state.has_key('likelihood'): + del state['likelihood'] + return state + def __setstate__(self, state): + # TODO: + super(MRD, self).__setstate__(state) + self.kern = self.bgplvms[0].kern + self.likelihood = self.bgplvms[0].likelihood + self.parameters_changed() \ No newline at end of file diff --git a/GPy/models_modules/sparse_gp_classification.py b/GPy/models_modules/sparse_gp_classification.py index 9274aacc..e281a4b9 100644 --- a/GPy/models_modules/sparse_gp_classification.py +++ b/GPy/models_modules/sparse_gp_classification.py @@ -7,6 +7,7 @@ from ..core import SparseGP from .. import likelihoods from .. import kern from ..likelihoods import likelihood +from ..inference.latent_function_inference import expectation_propagation_dtc class SparseGPClassification(SparseGP): """ @@ -16,7 +17,7 @@ class SparseGPClassification(SparseGP): :param X: input observations :param Y: observed values - :param likelihood: a GPy likelihood, defaults to Bernoulli with probit link_function + :param likelihood: a GPy likelihood, defaults to Binomial with probit link_function :param kernel: a GPy kernel, defaults to rbf+white :param normalize_X: whether to normalize the input data before computing (predictions will be in original scales) :type normalize_X: False|True @@ -26,16 +27,14 @@ class SparseGPClassification(SparseGP): """ - def __init__(self, X, Y=None, likelihood=None, kernel=None, normalize_X=False, normalize_Y=False, Z=None, num_inducing=10): - if kernel is None: - kernel = kern.rbf(X.shape[1])# + kern.white(X.shape[1],1e-3) + #def __init__(self, X, Y=None, likelihood=None, kernel=None, normalize_X=False, normalize_Y=False, Z=None, num_inducing=10): + def __init__(self, X, Y=None, likelihood=None, kernel=None, Z=None, num_inducing=10, Y_metadata=None): - if likelihood is None: - noise_model = likelihoods.bernoulli() - likelihood = likelihoods.EP(Y, noise_model) - elif Y is not None: - if not all(Y.flatten() == likelihood.data.flatten()): - raise Warning, 'likelihood.data and Y are different.' + + if kernel is None: + kernel = kern.RBF(X.shape[1]) + + likelihood = likelihoods.Bernoulli() if Z is None: i = np.random.permutation(X.shape[0])[:num_inducing] @@ -43,14 +42,5 @@ class SparseGPClassification(SparseGP): else: assert Z.shape[1] == X.shape[1] - SparseGP.__init__(self, X, likelihood, kernel, Z=Z, normalize_X=normalize_X) - self.ensure_default_constraints() - - def getstate(self): - return SparseGP.getstate(self) - - - def setstate(self, state): - return SparseGP.setstate(self, state) - - pass + SparseGP.__init__(self, X, Y, Z, kernel, likelihood, inference_method=expectation_propagation_dtc.EPDTC(), name='SparseGPClassification',Y_metadata=Y_metadata) + #def __init__(self, X, Y, Z, kernel, likelihood, inference_method=None, name='sparse gp', Y_metadata=None): diff --git a/GPy/models_modules/sparse_gp_multioutput_regression.py b/GPy/models_modules/sparse_gp_multioutput_regression.py deleted file mode 100644 index d809610b..00000000 --- a/GPy/models_modules/sparse_gp_multioutput_regression.py +++ /dev/null @@ -1,80 +0,0 @@ -# Copyright (c) 2013, Ricardo Andrade -# Licensed under the BSD 3-clause license (see LICENSE.txt) - - -import numpy as np -from ..core import SparseGP -from .. import likelihoods -from .. import kern -from ..util import multioutput - -class SparseGPMultioutputRegression(SparseGP): - """ - Sparse multiple output Gaussian process with Gaussian noise - - This is a wrapper around the models.SparseGP class, with a set of sensible defaults - - :param X_list: input observations - :type X_list: list of numpy arrays (num_data_output_i x input_dim), one array per output - :param Y_list: observed values - :type Y_list: list of numpy arrays (num_data_output_i x 1), one array per output - :param kernel_list: GPy kernels, defaults to rbf - :type kernel_list: list of GPy kernels - :param noise_variance_list: noise parameters per output, defaults to 1.0 for every output - :type noise_variance_list: list of floats - :param normalize_X: whether to normalize the input data before computing (predictions will be in original scales) - :type normalize_X: False|True - :param normalize_Y: whether to normalize the input data before computing (predictions will be in original scales) - :type normalize_Y: False|True - :param Z_list: inducing inputs (optional) - :type Z_list: list of numpy arrays (num_inducing_output_i x input_dim), one array per output | empty list - :param num_inducing: number of inducing inputs per output, defaults to 10 (ignored if Z_list is not empty) - :type num_inducing: integer - :param rank: number tuples of the corregionalization parameters 'coregion_W' (see coregionalize kernel documentation) - :type rank: integer - """ - #NOTE not tested with uncertain inputs - def __init__(self,X_list,Y_list,kernel_list=None,noise_variance_list=None,normalize_X=False,normalize_Y=False,Z_list=[],num_inducing=10,rank=1): - - self.output_dim = len(Y_list) - assert len(X_list) == self.output_dim, 'Number of outputs do not match length of inputs list.' - - #Inducing inputs list - if len(Z_list): - assert len(Z_list) == self.output_dim, 'Number of outputs do not match length of inducing inputs list.' - else: - if isinstance(num_inducing,np.int): - num_inducing = [num_inducing] * self.output_dim - num_inducing = np.asarray(num_inducing) - assert num_inducing.size == self.output_dim, 'Number of outputs do not match length of inducing inputs list.' - for ni,X in zip(num_inducing,X_list): - i = np.random.permutation(X.shape[0])[:ni] - Z_list.append(X[i].copy()) - - #Inputs and inducing inputs indexing - i = 0 - index = [] - index_z = [] - for x,y,z in zip(X_list,Y_list,Z_list): - assert x.shape[0] == y.shape[0] - index.append(np.repeat(i,x.size)[:,None]) - index_z.append(np.repeat(i,z.size)[:,None]) - i += 1 - index = np.vstack(index) - index_z = np.vstack(index_z) - X = np.hstack([np.vstack(X_list),index]) - Z = np.hstack([np.vstack(Z_list),index_z]) - original_dim = X.shape[1] - 1 - - #Mixed noise likelihood definition - likelihood = likelihoods.Gaussian_Mixed_Noise(Y_list,noise_params=noise_variance_list,normalize=normalize_Y) - - #Coregionalization kernel definition - if kernel_list is None: - kernel_list = [kern.rbf(original_dim)] - mkernel = kern.build_lcm(input_dim=original_dim, output_dim=self.output_dim, kernel_list = kernel_list, rank=rank) - - self.multioutput = True - SparseGP.__init__(self, X, likelihood, mkernel, Z=Z, normalize_X=normalize_X) - self.constrain_fixed('.*iip_\d+_1') - self.ensure_default_constraints() diff --git a/GPy/models_modules/sparse_gp_regression.py b/GPy/models_modules/sparse_gp_regression.py index d2e23887..49c3914c 100644 --- a/GPy/models_modules/sparse_gp_regression.py +++ b/GPy/models_modules/sparse_gp_regression.py @@ -4,10 +4,14 @@ import numpy as np from ..core import SparseGP +from ..core.sparse_gp_mpi import SparseGP_MPI from .. import likelihoods from .. import kern +from ..inference.latent_function_inference import VarDTC +from ..core.parameterization.variational import NormalPosterior +from GPy.inference.latent_function_inference.var_dtc_parallel import VarDTC_minibatch -class SparseGPRegression(SparseGP): +class SparseGPRegression(SparseGP_MPI): """ Gaussian Process model for regression @@ -16,44 +20,90 @@ class SparseGPRegression(SparseGP): :param X: input observations :param Y: observed values :param kernel: a GPy kernel, defaults to rbf+white - :param normalize_X: whether to normalize the input data before computing (predictions will be in original scales) - :type normalize_X: False|True - :param normalize_Y: whether to normalize the input data before computing (predictions will be in original scales) - :type normalize_Y: False|True :param Z: inducing inputs (optional, see note) :type Z: np.ndarray (num_inducing x input_dim) | None + :param num_inducing: number of inducing points (ignored if Z is passed, see note) + :type num_inducing: int :rtype: model object - :param X_variance: The uncertainty in the measurements of X (Gaussian variance) - :type X_variance: np.ndarray (num_data x input_dim) | None + .. Note:: If no Z array is passed, num_inducing (default 10) points are selected from the data. Other wise num_inducing is ignored .. Note:: Multiple independent outputs are allowed using columns of Y """ - def __init__(self, X, Y, kernel=None, normalize_X=False, normalize_Y=False, Z=None, num_inducing=10, X_variance=None): + def __init__(self, X, Y, kernel=None, Z=None, num_inducing=10, X_variance=None, normalizer=None, mpi_comm=None): + num_data, input_dim = X.shape + # kern defaults to rbf (plus white for stability) if kernel is None: - kernel = kern.rbf(X.shape[1]) # + kern.white(X.shape[1], 1e-3) + kernel = kern.RBF(input_dim)# + kern.white(input_dim, variance=1e-3) # Z defaults to a subset of the data if Z is None: - i = np.random.permutation(X.shape[0])[:num_inducing] + i = np.random.permutation(num_data)[:min(num_inducing, num_data)] + Z = X.view(np.ndarray)[i].copy() + else: + assert Z.shape[1] == input_dim + + likelihood = likelihoods.Gaussian() + + if not (X_variance is None): + X = NormalPosterior(X,X_variance) + + if mpi_comm is not None: + from ..inference.latent_function_inference.var_dtc_parallel import VarDTC_minibatch + infr = VarDTC_minibatch(mpi_comm=mpi_comm) + else: + infr = VarDTC() + + SparseGP_MPI.__init__(self, X, Y, Z, kernel, likelihood, inference_method=infr, normalizer=normalizer, mpi_comm=mpi_comm) + + def parameters_changed(self): + from ..inference.latent_function_inference.var_dtc_parallel import update_gradients_sparsegp,VarDTC_minibatch + if isinstance(self.inference_method,VarDTC_minibatch): + update_gradients_sparsegp(self, mpi_comm=self.mpi_comm) + else: + super(SparseGPRegression, self).parameters_changed() + +class SparseGPRegressionUncertainInput(SparseGP): + """ + Gaussian Process model for regression with Gaussian variance on the inputs (X_variance) + + This is a thin wrapper around the SparseGP class, with a set of sensible defalts + + """ + + def __init__(self, X, X_variance, Y, kernel=None, Z=None, num_inducing=10, normalizer=None): + """ + :param X: input observations + :type X: np.ndarray (num_data x input_dim) + :param X_variance: The uncertainty in the measurements of X (Gaussian variance, optional) + :type X_variance: np.ndarray (num_data x input_dim) + :param Y: observed values + :param kernel: a GPy kernel, defaults to rbf+white + :param Z: inducing inputs (optional, see note) + :type Z: np.ndarray (num_inducing x input_dim) | None + :param num_inducing: number of inducing points (ignored if Z is passed, see note) + :type num_inducing: int + :rtype: model object + + .. Note:: If no Z array is passed, num_inducing (default 10) points are selected from the data. Other wise num_inducing is ignored + .. Note:: Multiple independent outputs are allowed using columns of Y + """ + num_data, input_dim = X.shape + + # kern defaults to rbf (plus white for stability) + if kernel is None: + kernel = kern.RBF(input_dim) + kern.White(input_dim, variance=1e-3) + + # Z defaults to a subset of the data + if Z is None: + i = np.random.permutation(num_data)[:min(num_inducing, num_data)] Z = X[i].copy() else: - assert Z.shape[1] == X.shape[1] + assert Z.shape[1] == input_dim - # likelihood defaults to Gaussian - likelihood = likelihoods.Gaussian(Y, normalize=normalize_Y) + likelihood = likelihoods.Gaussian() - SparseGP.__init__(self, X, likelihood, kernel, Z=Z, normalize_X=normalize_X, X_variance=X_variance) + SparseGP.__init__(self, X, Y, Z, kernel, likelihood, X_variance=X_variance, inference_method=VarDTC(), normalizer=normalizer) self.ensure_default_constraints() - pass - - def getstate(self): - return SparseGP.getstate(self) - - - def setstate(self, state): - return SparseGP.setstate(self, state) - - pass diff --git a/GPy/models_modules/sparse_gplvm.py b/GPy/models_modules/sparse_gplvm.py index 04d3415a..d1ad5884 100644 --- a/GPy/models_modules/sparse_gplvm.py +++ b/GPy/models_modules/sparse_gplvm.py @@ -3,12 +3,10 @@ import numpy as np -import pylab as pb -import sys, pdb -from sparse_gp_regression import SparseGPRegression -from gplvm import GPLVM, initialise_latent +import sys +from GPy.models.sparse_gp_regression import SparseGPRegression -class SparseGPLVM(SparseGPRegression, GPLVM): +class SparseGPLVM(SparseGPRegression): """ Sparse Gaussian Process Latent Variable Model @@ -20,48 +18,26 @@ class SparseGPLVM(SparseGPRegression, GPLVM): :type init: 'PCA'|'random' """ - def __init__(self, Y, input_dim, kernel=None, init='PCA', num_inducing=10): - X = initialise_latent(init, input_dim, Y) + def __init__(self, Y, input_dim, X=None, kernel=None, init='PCA', num_inducing=10): + if X is None: + from ..util.initialization import initialize_latent + X, fracs = initialize_latent(init, input_dim, Y) SparseGPRegression.__init__(self, X, Y, kernel=kernel, num_inducing=num_inducing) - self.ensure_default_constraints() - def getstate(self): - return SparseGPRegression.getstate(self) + def parameters_changed(self): + super(SparseGPLVM, self).parameters_changed() + self.X.gradient = self.kern.gradients_X_diag(self.grad_dict['dL_dKdiag'], self.X) + self.X.gradient += self.kern.gradients_X(self.grad_dict['dL_dKnm'], self.X, self.Z) + def plot_latent(self, labels=None, which_indices=None, + resolution=50, ax=None, marker='o', s=40, + fignum=None, plot_inducing=True, legend=True, + plot_limits=None, + aspect='auto', updates=False, predict_kwargs={}, imshow_kwargs={}): + assert "matplotlib" in sys.modules, "matplotlib package has not been imported." + from ..plotting.matplot_dep import dim_reduction_plots - def setstate(self, state): - return SparseGPRegression.setstate(self, state) - - - def _get_param_names(self): - return (sum([['X_%i_%i' % (n, q) for q in range(self.input_dim)] for n in range(self.num_data)], []) - + SparseGPRegression._get_param_names(self)) - - def _get_params(self): - return np.hstack((self.X.flatten(), SparseGPRegression._get_params(self))) - - def _set_params(self, x): - self.X = x[:self.X.size].reshape(self.num_data, self.input_dim).copy() - SparseGPRegression._set_params(self, x[self.X.size:]) - - def log_likelihood(self): - return SparseGPRegression.log_likelihood(self) - - def dL_dX(self): - dL_dX = self.kern.dKdiag_dX(self.dL_dpsi0, self.X) - dL_dX += self.kern.dK_dX(self.dL_dpsi1, self.X, self.Z) - - return dL_dX - - def _log_likelihood_gradients(self): - return np.hstack((self.dL_dX().flatten(), SparseGPRegression._log_likelihood_gradients(self))) - - def plot(self): - GPLVM.plot(self) - # passing Z without a small amout of jitter will induce the white kernel where we don;t want it! - mu, var, upper, lower = SparseGPRegression.predict(self, self.Z + np.random.randn(*self.Z.shape) * 0.0001) - pb.plot(mu[:, 0] , mu[:, 1], 'ko') - - def plot_latent(self, *args, **kwargs): - GPLVM.plot_latent(self, *args, **kwargs) - #pb.plot(self.Z[:, input_1], self.Z[:, input_2], '^w') + return dim_reduction_plots.plot_latent(self, labels, which_indices, + resolution, ax, marker, s, + fignum, plot_inducing, legend, + plot_limits, aspect, updates, predict_kwargs, imshow_kwargs) diff --git a/GPy/models_modules/svigp_regression.py b/GPy/models_modules/svigp_regression.py deleted file mode 100644 index e826bf35..00000000 --- a/GPy/models_modules/svigp_regression.py +++ /dev/null @@ -1,52 +0,0 @@ -# Copyright (c) 2012, James Hensman -# Licensed under the BSD 3-clause license (see LICENSE.txt) - -import numpy as np -from ..core import SVIGP -from .. import likelihoods -from .. import kern - -class SVIGPRegression(SVIGP): - """ - Gaussian Process model for regression - - This is a thin wrapper around the SVIGP class, with a set of sensible defalts - - :param X: input observations - :param Y: observed values - :param kernel: a GPy kernel, defaults to rbf+white - :param normalize_X: whether to normalize the input data before computing (predictions will be in original scales) - :type normalize_X: False|True - :param normalize_Y: whether to normalize the input data before computing (predictions will be in original scales) - :type normalize_Y: False|True - :rtype: model object - - .. Note:: Multiple independent outputs are allowed using columns of Y - - """ - - def __init__(self, X, Y, kernel=None, Z=None, num_inducing=10, q_u=None, batchsize=10, normalize_Y=False): - # kern defaults to rbf (plus white for stability) - if kernel is None: - kernel = kern.rbf(X.shape[1], variance=1., lengthscale=4.) + kern.white(X.shape[1], 1e-3) - - # Z defaults to a subset of the data - if Z is None: - i = np.random.permutation(X.shape[0])[:num_inducing] - Z = X[i].copy() - else: - assert Z.shape[1] == X.shape[1] - - # likelihood defaults to Gaussian - likelihood = likelihoods.Gaussian(Y, normalize=normalize_Y) - - SVIGP.__init__(self, X, likelihood, kernel, Z, q_u=q_u, batchsize=batchsize) - self.load_batch() - - def getstate(self): - return GPBase.getstate(self) - - - def setstate(self, state): - return GPBase.setstate(self, state) - diff --git a/GPy/models_modules/warped_gp.py b/GPy/models_modules/warped_gp.py index 260139a6..4b982ed2 100644 --- a/GPy/models_modules/warped_gp.py +++ b/GPy/models_modules/warped_gp.py @@ -30,14 +30,6 @@ class WarpedGP(GP): GP.__init__(self, X, likelihood, kernel, normalize_X=normalize_X) self._set_params(self._get_params()) - def getstate(self): - return GP.getstate(self) - - - def setstate(self, state): - return GP.setstate(self, state) - - def _scale_data(self, Y): self._Ymax = Y.max() self._Ymin = Y.min() diff --git a/GPy/notes.txt b/GPy/notes.txt deleted file mode 100644 index 768701f2..00000000 --- a/GPy/notes.txt +++ /dev/null @@ -1,80 +0,0 @@ -Prod.py kernel could also take a list of kernels rather than two arguments for kernels. -transformations.py should have limits on what is fed into exp() particularly for the negative log logistic (done -neil). - -Load in a model with mlp kernel, plot it, change a parameter, plot it again. It doesn't update the plot. - -Tests for kernels which work directly on the kernel implementation (not through GP). - -Should stationary covariances have their own kernpart type, I think so, also inner product kernels. That way the caching so carefully constructed for RBF or linear could be shared. - -Where do we declare default kernel parameters. In constructors.py or in the definition file for the kernel? - -When printing to stdout, can we check that our approach is also working nicely for the ipython notebook? I like the way our optimization ticks over, but at the moment this doesn't seem to work in the ipython notebook, it would be nice if it did. My problems may be due to using ipython 0.12, I've had a poke around at fixing this and I can't do it for 0.12. - -When we print a model should we also include information such as number of inputs and number of outputs? - -Let's not use N for giving the number of data in the model. When it pops up as a help tip it's not as clear as num_samples or num_data. Prefer the second, but oddly I've been using first. - -Loving the fact that the * has been overloaded on the kernels (oddly never thought to check this before). Although naming can be a bit confusing. Can we think how to deal with the names in a clearer way when we use a kernel like this one: -kern = GPy.kern.rbf(30)*(GPy.kern.mlp(30)+GPy.kern.poly(30, degree=5)) + GPy.kern.bias(30). There seems to be some tieing of parameters going on ... should there be? (you can try it as the kernel for the robot wireless model). - -Can we comment up some of the list incomprehensions in hierarchical.py?? - -Need to tidy up classification.py, -many examples include help that doesn't apply -(it is suggested that you can try different approximation types) - -Shall we overload the ** operator to have tensor products? (I've done this now we can see if we like it) - -People aren't filling the doc strings in as they go *everyone* needs to get in the habit of this (and modifying them as they edit, or correcting them when there is a problem). - -Need some nice way of explaining how to compile documentation and run the unit tests, could this be in a readme or FAQ somewhere? Maybe it's there already somewhere and I've missed it. - -Shouldn't EP be in the inference package (not likelihoods)? - -When using bfgs in ipython notebook, text appears in the original console, not in the notebook. - -In sparse GPs wouldn't it be clearer to call Z inducing? - -In coregionalisation matrix, setting the W to all ones will (surely?) ensure that symmetry isn't broken. Also, but allowing it to scale like that, the output variance increases as rank is increased (and if user sets rank to more than output dim they could get very different results). - -We are inconsistent about our use of ise and ize e.g. optimize and normalize_X, but coregionalise, we should choose one and stick to it. Suggest -ize. Neil- I'm imposing the US spellings to keep things consistent, so -ize it is. - -Exceptions: we need to provide a list of exceptions we throw and specify what is thrown where. - -Why is it get_params() but it's getstate()? Should be get_state(). Why is it get_gradient instead of get_gradients? Need to be consistent!! Doesn't matter which way we choose as long as it's consistent. - -In likelihood Nparams should be num_params - -In likelihood N should be num_data - -The Gaussian target in likelihood should be F What is V doing here? - -Need to check for nan values in likelihoods. These should be treated as missing values. If the likelihood can't handle the missing value an error should be throw. - - -Sometimes you want to print kernpart objects, for diagnosis etc. This isn't possible currently. - -Why do likelihoods still have YYT everywhere, didn't we agree to set observed data to Y and latent function to F? - -For some reason a stub of _get_param_names(self) wasn't available in the Parameterized base class. Have put it in (is this right?) - -Is there a quick FAQ or something on how to build the documentation? I did it once, but can't remember! Have started a FAQ.txt file where we can add this type of information. - -Similar for the nosetests ... even ran them last week but can't remember the command! - -Now added Gaussian priors to GPLVM latent variables by default. When running the GPy.examples.dimensionality_reduction.stick() example the print out from print model has the same value for the prior+likelihood as for the prior. - -For the back constrained GP-LVM need priors to be on the Xs not on the model parameters (because they aren't parameters, they are constraints). Need to work out how to do this, perhaps by creating the full GP-LVM model then constraining around it, rather than overriding inside the GP-LVM model. - - -This code fails: - -kern = GPy.kern.rbf(2) -GPy.kern.Kern_check_dK_dX(kern, X=np.random.randn(10, 2), X2=None).checkgrad(verbose=True) - -because X2 is now equal to X, so there is a factor of 2 missing. Does this every come up? Yes, in the GP-LVM, (gplvm.py, line 64) where it is called with a corrective factor of 2! And on line 241 of sparse_gp where it is also called with a corrective factor of 2! In original matlab GPLVM, didn't allow gradients with respect to X alone, and multiplied by 2 in base code, but then add diagonal across those elements. This is missing in the new code. - - -In white.py, line 41, Need to check here if X and X2 refer to the same reference too ... becaue up the pipeline somewhere someone may have set X2=X when X2 arrived originally equal to None. - diff --git a/GPy/testing/bcgplvm_tests.py b/GPy/old_tests/bcgplvm_tests.py similarity index 100% rename from GPy/testing/bcgplvm_tests.py rename to GPy/old_tests/bcgplvm_tests.py diff --git a/GPy/testing/cgd_tests.py b/GPy/old_tests/cgd_tests.py similarity index 94% rename from GPy/testing/cgd_tests.py rename to GPy/old_tests/cgd_tests.py index 82041c9f..c2653ea5 100644 --- a/GPy/testing/cgd_tests.py +++ b/GPy/old_tests/cgd_tests.py @@ -5,10 +5,10 @@ Created on 26 Apr 2013 ''' import unittest import numpy -from GPy.inference.conjugate_gradient_descent import CGD, RUNNING +from GPy.inference.optimization.conjugate_gradient_descent import CGD, RUNNING import pylab from scipy.optimize.optimize import rosen, rosen_der -from GPy.inference.gradient_descent_update_rules import PolakRibiere +from GPy.inference.optimization.gradient_descent_update_rules import PolakRibiere class Test(unittest.TestCase): @@ -30,7 +30,7 @@ class Test(unittest.TestCase): assert numpy.allclose(res[0], 0, atol=1e-5) break except AssertionError: - import ipdb;ipdb.set_trace() + import pdb;pdb.set_trace() # RESTART pass else: @@ -108,4 +108,3 @@ if __name__ == "__main__": res[0] = opt.opt(f, df, x0.copy(), callback, messages=True, maxiter=1000, report_every=7, gtol=1e-12, update_rule=PolakRibiere) - pass diff --git a/GPy/testing/gp_transformation_tests.py b/GPy/old_tests/gp_transformation_tests.py similarity index 100% rename from GPy/testing/gp_transformation_tests.py rename to GPy/old_tests/gp_transformation_tests.py diff --git a/GPy/testing/gplvm_tests.py b/GPy/old_tests/gplvm_tests.py similarity index 78% rename from GPy/testing/gplvm_tests.py rename to GPy/old_tests/gplvm_tests.py index 6223d833..a605a96c 100644 --- a/GPy/testing/gplvm_tests.py +++ b/GPy/old_tests/gplvm_tests.py @@ -9,10 +9,10 @@ class GPLVMTests(unittest.TestCase): def test_bias_kern(self): num_data, num_inducing, input_dim, output_dim = 10, 3, 2, 4 X = np.random.rand(num_data, input_dim) - k = GPy.kern.rbf(input_dim) + GPy.kern.white(input_dim, 0.00001) + k = GPy.kern.RBF(input_dim) + GPy.kern.White(input_dim, 0.00001) K = k.K(X) Y = np.random.multivariate_normal(np.zeros(num_data),K,output_dim).T - k = GPy.kern.bias(input_dim) + GPy.kern.white(input_dim, 0.00001) + k = GPy.kern.Bias(input_dim) + GPy.kern.White(input_dim, 0.00001) m = GPy.models.GPLVM(Y, input_dim, kernel = k) m.randomize() self.assertTrue(m.checkgrad()) @@ -20,10 +20,10 @@ class GPLVMTests(unittest.TestCase): def test_linear_kern(self): num_data, num_inducing, input_dim, output_dim = 10, 3, 2, 4 X = np.random.rand(num_data, input_dim) - k = GPy.kern.rbf(input_dim) + GPy.kern.white(input_dim, 0.00001) + k = GPy.kern.RBF(input_dim) + GPy.kern.White(input_dim, 0.00001) K = k.K(X) Y = np.random.multivariate_normal(np.zeros(num_data),K,output_dim).T - k = GPy.kern.linear(input_dim) + GPy.kern.white(input_dim, 0.00001) + k = GPy.kern.Linear(input_dim) + GPy.kern.White(input_dim, 0.00001) m = GPy.models.GPLVM(Y, input_dim, kernel = k) m.randomize() self.assertTrue(m.checkgrad()) @@ -31,10 +31,10 @@ class GPLVMTests(unittest.TestCase): def test_rbf_kern(self): num_data, num_inducing, input_dim, output_dim = 10, 3, 2, 4 X = np.random.rand(num_data, input_dim) - k = GPy.kern.rbf(input_dim) + GPy.kern.white(input_dim, 0.00001) + k = GPy.kern.RBF(input_dim) + GPy.kern.White(input_dim, 0.00001) K = k.K(X) Y = np.random.multivariate_normal(np.zeros(num_data),K,output_dim).T - k = GPy.kern.rbf(input_dim) + GPy.kern.white(input_dim, 0.00001) + k = GPy.kern.RBF(input_dim) + GPy.kern.White(input_dim, 0.00001) m = GPy.models.GPLVM(Y, input_dim, kernel = k) m.randomize() self.assertTrue(m.checkgrad()) diff --git a/GPy/testing/mapping_tests.py b/GPy/old_tests/mapping_tests.py similarity index 96% rename from GPy/testing/mapping_tests.py rename to GPy/old_tests/mapping_tests.py index cd28e71a..d501df1d 100644 --- a/GPy/testing/mapping_tests.py +++ b/GPy/old_tests/mapping_tests.py @@ -4,7 +4,7 @@ import unittest import numpy as np import GPy - + class MappingTests(unittest.TestCase): @@ -23,12 +23,11 @@ class MappingTests(unittest.TestCase): def test_mlpmapping(self): verbose = False - mapping = GPy.mappings.MLP(input_dim=2, hidden_dim=[3, 4, 8, 2], output_dim=2) + mapping = GPy.mappings.MLP(input_dim=2, hidden_dim=[3, 4, 8, 2], output_dim=2) self.assertTrue(GPy.core.Mapping_check_df_dtheta(mapping=mapping).checkgrad(verbose=verbose)) self.assertTrue(GPy.core.Mapping_check_df_dX(mapping=mapping).checkgrad(verbose=verbose)) - if __name__ == "__main__": print "Running unit tests, please be (very) patient..." unittest.main() diff --git a/GPy/testing/psi_stat_expectation_tests.py b/GPy/old_tests/psi_stat_expectation_tests.py similarity index 53% rename from GPy/testing/psi_stat_expectation_tests.py rename to GPy/old_tests/psi_stat_expectation_tests.py index 90252197..ffbde37c 100644 --- a/GPy/testing/psi_stat_expectation_tests.py +++ b/GPy/old_tests/psi_stat_expectation_tests.py @@ -9,9 +9,10 @@ import numpy as np from GPy import testing import sys import numpy -from GPy.kern.parts.rbf import RBF -from GPy.kern.parts.linear import Linear +from GPy.kern import RBF +from GPy.kern import Linear from copy import deepcopy +from GPy.core.parameterization.variational import NormalPosterior __test__ = lambda: 'deep' in sys.argv # np.random.seed(0) @@ -28,53 +29,21 @@ def ard(p): class Test(unittest.TestCase): input_dim = 9 num_inducing = 13 - N = 300 + N = 1000 Nsamples = 1e6 def setUp(self): - i_s_dim_list = [2,4,3] - indices = numpy.cumsum(i_s_dim_list).tolist() - input_slices = [slice(a,b) for a,b in zip([None]+indices, indices)] - #input_slices[2] = deepcopy(input_slices[1]) - input_slice_kern = GPy.kern.kern(9, - [ - RBF(i_s_dim_list[0], np.random.rand(), np.random.rand(i_s_dim_list[0]), ARD=True), - RBF(i_s_dim_list[1], np.random.rand(), np.random.rand(i_s_dim_list[1]), ARD=True), - Linear(i_s_dim_list[2], np.random.rand(i_s_dim_list[2]), ARD=True) - ], - input_slices = input_slices - ) self.kerns = ( -# input_slice_kern, -# (GPy.kern.rbf(self.input_dim, ARD=True) + -# GPy.kern.linear(self.input_dim, ARD=True) + -# GPy.kern.bias(self.input_dim) + -# GPy.kern.white(self.input_dim)), - (#GPy.kern.rbf(self.input_dim, np.random.rand(), np.random.rand(self.input_dim), ARD=True) - GPy.kern.linear(self.input_dim, np.random.rand(self.input_dim), ARD=True) - +GPy.kern.rbf(self.input_dim, np.random.rand(), np.random.rand(self.input_dim), ARD=True) -# +GPy.kern.bias(self.input_dim) -# +GPy.kern.white(self.input_dim)), - ), -# (GPy.kern.rbf(self.input_dim, np.random.rand(), np.random.rand(self.input_dim), ARD=True) + -# GPy.kern.bias(self.input_dim, np.random.rand())), -# (GPy.kern.rbf(self.input_dim, np.random.rand(), np.random.rand(self.input_dim), ARD=True) -# +GPy.kern.rbf(self.input_dim, np.random.rand(), np.random.rand(self.input_dim), ARD=True) -# #+GPy.kern.bias(self.input_dim, np.random.rand()) -# #+GPy.kern.white(self.input_dim, np.random.rand())), -# ), -# GPy.kern.white(self.input_dim, np.random.rand())), -# GPy.kern.rbf(self.input_dim), GPy.kern.rbf(self.input_dim, ARD=True), -# GPy.kern.linear(self.input_dim, ARD=False), GPy.kern.linear(self.input_dim, ARD=True), -# GPy.kern.linear(self.input_dim) + GPy.kern.bias(self.input_dim), -# GPy.kern.rbf(self.input_dim) + GPy.kern.bias(self.input_dim), -# GPy.kern.linear(self.input_dim) + GPy.kern.bias(self.input_dim) + GPy.kern.white(self.input_dim), -# GPy.kern.rbf(self.input_dim) + GPy.kern.bias(self.input_dim) + GPy.kern.white(self.input_dim), -# GPy.kern.bias(self.input_dim), GPy.kern.white(self.input_dim), + #GPy.kern.RBF([0,1,2], ARD=True)+GPy.kern.Bias(self.input_dim)+GPy.kern.White(self.input_dim), + #GPy.kern.RBF(self.input_dim)+GPy.kern.Bias(self.input_dim)+GPy.kern.White(self.input_dim), + #GPy.kern.Linear(self.input_dim) + GPy.kern.Bias(self.input_dim) + GPy.kern.White(self.input_dim), + #GPy.kern.Linear(self.input_dim, ARD=True) + GPy.kern.Bias(self.input_dim) + GPy.kern.White(self.input_dim), + GPy.kern.Linear([1,3,6,7], ARD=True) + GPy.kern.RBF([0,5,8], ARD=True) + GPy.kern.White(self.input_dim), ) - self.q_x_mean = np.random.randn(self.input_dim) - self.q_x_variance = np.exp(np.random.randn(self.input_dim)) + self.q_x_mean = np.random.randn(self.input_dim)[None] + self.q_x_variance = np.exp(.5*np.random.randn(self.input_dim))[None] self.q_x_samples = np.random.randn(self.Nsamples, self.input_dim) * np.sqrt(self.q_x_variance) + self.q_x_mean + self.q_x = NormalPosterior(self.q_x_mean, self.q_x_variance) self.Z = np.random.randn(self.num_inducing, self.input_dim) self.q_x_mean.shape = (1, self.input_dim) self.q_x_variance.shape = (1, self.input_dim) @@ -114,8 +83,9 @@ class Test(unittest.TestCase): def test_psi2(self): for kern in self.kerns: + kern.randomize() Nsamples = int(np.floor(self.Nsamples/self.N)) - psi2 = kern.psi2(self.Z, self.q_x_mean, self.q_x_variance) + psi2 = kern.psi2(self.Z, self.q_x) K_ = np.zeros((self.num_inducing, self.num_inducing)) diffs = [] for i, q_x_sample_stripe in enumerate(np.array_split(self.q_x_samples, self.Nsamples / Nsamples)): @@ -130,8 +100,8 @@ class Test(unittest.TestCase): pylab.figure(msg) pylab.plot(diffs, marker='x', mew=.2) # print msg, np.allclose(psi2.squeeze(), K_, rtol=1e-1, atol=.1) - self.assertTrue(np.allclose(psi2.squeeze(), K_), - #rtol=1e-1, atol=.1), + self.assertTrue(np.allclose(psi2.squeeze(), K_, + atol=.1, rtol=1), msg=msg + ": not matching") # sys.stdout.write(".") except: diff --git a/GPy/testing/psi_stat_gradient_tests.py b/GPy/old_tests/psi_stat_gradient_tests.py similarity index 58% rename from GPy/testing/psi_stat_gradient_tests.py rename to GPy/old_tests/psi_stat_gradient_tests.py index e373aaa3..d51cd913 100644 --- a/GPy/testing/psi_stat_gradient_tests.py +++ b/GPy/old_tests/psi_stat_gradient_tests.py @@ -9,42 +9,46 @@ import numpy import GPy import itertools from GPy.core import Model +from GPy.core.parameterization.param import Param +from GPy.core.parameterization.transformations import Logexp +from GPy.core.parameterization.variational import NormalPosterior class PsiStatModel(Model): def __init__(self, which, X, X_variance, Z, num_inducing, kernel): + super(PsiStatModel, self).__init__(name='psi stat test') self.which = which - self.X = X - self.X_variance = X_variance - self.Z = Z + self.X = Param("X", X) + self.X_variance = Param('X_variance', X_variance, Logexp()) + self.q = NormalPosterior(self.X, self.X_variance) + self.Z = Param("Z", Z) self.N, self.input_dim = X.shape self.num_inducing, input_dim = Z.shape assert self.input_dim == input_dim, "shape missmatch: Z:{!s} X:{!s}".format(Z.shape, X.shape) self.kern = kernel - super(PsiStatModel, self).__init__() - self.psi_ = self.kern.__getattribute__(self.which)(self.Z, self.X, self.X_variance) - def _get_param_names(self): - Xnames = ["{}_{}_{}".format(what, i, j) for what, i, j in itertools.product(['X', 'X_variance'], range(self.N), range(self.input_dim))] - Znames = ["Z_{}_{}".format(i, j) for i, j in itertools.product(range(self.num_inducing), range(self.input_dim))] - return Xnames + Znames + self.kern._get_param_names() - def _get_params(self): - return numpy.hstack([self.X.flatten(), self.X_variance.flatten(), self.Z.flatten(), self.kern._get_params()]) - def _set_params(self, x, save_old=True, save_count=0): - start, end = 0, self.X.size - self.X = x[start:end].reshape(self.N, self.input_dim) - start, end = end, end + self.X_variance.size - self.X_variance = x[start: end].reshape(self.N, self.input_dim) - start, end = end, end + self.Z.size - self.Z = x[start: end].reshape(self.num_inducing, self.input_dim) - self.kern._set_params(x[end:]) + self.psi_ = self.kern.__getattribute__(self.which)(self.Z, self.q) + self.add_parameters(self.q, self.Z, self.kern) + def log_likelihood(self): return self.kern.__getattribute__(self.which)(self.Z, self.X, self.X_variance).sum() - def _log_likelihood_gradients(self): - psimu, psiS = self.kern.__getattribute__("d" + self.which + "_dmuS")(numpy.ones_like(self.psi_), self.Z, self.X, self.X_variance) + + def parameters_changed(self): + psimu, psiS = self.kern.__getattribute__("d" + self.which + "_dmuS")(numpy.ones_like(self.psi_), self.Z, self.q) + self.X.gradient = psimu + self.X_variance.gradient = psiS #psimu, psiS = numpy.ones(self.N * self.input_dim), numpy.ones(self.N * self.input_dim) - psiZ = self.kern.__getattribute__("d" + self.which + "_dZ")(numpy.ones_like(self.psi_), self.Z, self.X, self.X_variance) + try: psiZ = self.kern.__getattribute__("d" + self.which + "_dZ")(numpy.ones_like(self.psi_), self.Z, self.q) + except AttributeError: psiZ = numpy.zeros_like(self.Z) + self.Z.gradient = psiZ #psiZ = numpy.ones(self.num_inducing * self.input_dim) - thetagrad = self.kern.__getattribute__("d" + self.which + "_dtheta")(numpy.ones_like(self.psi_), self.Z, self.X, self.X_variance).flatten() - return numpy.hstack((psimu.flatten(), psiS.flatten(), psiZ.flatten(), thetagrad)) + N,M = self.X.shape[0], self.Z.shape[0] + dL_dpsi0, dL_dpsi1, dL_dpsi2 = numpy.zeros([N]), numpy.zeros([N,M]), numpy.zeros([N,M,M]) + if self.which == 'psi0': dL_dpsi0 += 1 + if self.which == 'psi1': dL_dpsi1 += 1 + if self.which == 'psi2': dL_dpsi2 += 1 + self.kern.update_gradients_variational(numpy.zeros([1,1]), + dL_dpsi0, + dL_dpsi1, + dL_dpsi2, self.X, self.X_variance, self.Z) class DPsiStatTest(unittest.TestCase): input_dim = 5 @@ -55,63 +59,60 @@ class DPsiStatTest(unittest.TestCase): X_var = .5 * numpy.ones_like(X) + .4 * numpy.clip(numpy.random.randn(*X.shape), 0, 1) Z = numpy.random.permutation(X)[:num_inducing] Y = X.dot(numpy.random.randn(input_dim, input_dim)) -# kernels = [GPy.kern.linear(input_dim, ARD=True, variances=numpy.random.rand(input_dim)), GPy.kern.rbf(input_dim, ARD=True), GPy.kern.bias(input_dim)] +# kernels = [GPy.kern.Linear(input_dim, ARD=True, variances=numpy.random.rand(input_dim)), GPy.kern.RBF(input_dim, ARD=True), GPy.kern.Bias(input_dim)] - kernels = [GPy.kern.linear(input_dim), GPy.kern.rbf(input_dim), GPy.kern.bias(input_dim), - GPy.kern.linear(input_dim) + GPy.kern.bias(input_dim), - GPy.kern.rbf(input_dim) + GPy.kern.bias(input_dim)] + kernels = [ + GPy.kern.Linear(input_dim), + GPy.kern.RBF(input_dim), + #GPy.kern.Bias(input_dim), + #GPy.kern.Linear(input_dim) + GPy.kern.Bias(input_dim), + #GPy.kern.RBF(input_dim) + GPy.kern.Bias(input_dim) + ] def testPsi0(self): for k in self.kernels: m = PsiStatModel('psi0', X=self.X, X_variance=self.X_var, Z=self.Z,\ num_inducing=self.num_inducing, kernel=k) - m.ensure_default_constraints() m.randomize() - assert m.checkgrad(), "{} x psi0".format("+".join(map(lambda x: x.name, k.parts))) - + assert m.checkgrad(), "{} x psi0".format("+".join(map(lambda x: x.name, k._parameters_))) + def testPsi1(self): for k in self.kernels: m = PsiStatModel('psi1', X=self.X, X_variance=self.X_var, Z=self.Z, num_inducing=self.num_inducing, kernel=k) - m.ensure_default_constraints() m.randomize() - assert m.checkgrad(), "{} x psi1".format("+".join(map(lambda x: x.name, k.parts))) + assert m.checkgrad(), "{} x psi1".format("+".join(map(lambda x: x.name, k._parameters_))) def testPsi2_lin(self): k = self.kernels[0] m = PsiStatModel('psi2', X=self.X, X_variance=self.X_var, Z=self.Z, num_inducing=self.num_inducing, kernel=k) - m.ensure_default_constraints() m.randomize() - assert m.checkgrad(), "{} x psi2".format("+".join(map(lambda x: x.name, k.parts))) + assert m.checkgrad(), "{} x psi2".format("+".join(map(lambda x: x.name, k._parameters_))) def testPsi2_lin_bia(self): k = self.kernels[3] m = PsiStatModel('psi2', X=self.X, X_variance=self.X_var, Z=self.Z, num_inducing=self.num_inducing, kernel=k) - m.ensure_default_constraints() m.randomize() - assert m.checkgrad(), "{} x psi2".format("+".join(map(lambda x: x.name, k.parts))) + assert m.checkgrad(), "{} x psi2".format("+".join(map(lambda x: x.name, k._parameters_))) def testPsi2_rbf(self): k = self.kernels[1] m = PsiStatModel('psi2', X=self.X, X_variance=self.X_var, Z=self.Z, num_inducing=self.num_inducing, kernel=k) - m.ensure_default_constraints() m.randomize() - assert m.checkgrad(), "{} x psi2".format("+".join(map(lambda x: x.name, k.parts))) + assert m.checkgrad(), "{} x psi2".format("+".join(map(lambda x: x.name, k._parameters_))) def testPsi2_rbf_bia(self): k = self.kernels[-1] m = PsiStatModel('psi2', X=self.X, X_variance=self.X_var, Z=self.Z, num_inducing=self.num_inducing, kernel=k) - m.ensure_default_constraints() m.randomize() - assert m.checkgrad(), "{} x psi2".format("+".join(map(lambda x: x.name, k.parts))) + assert m.checkgrad(), "{} x psi2".format("+".join(map(lambda x: x.name, k._parameters_))) def testPsi2_bia(self): k = self.kernels[2] m = PsiStatModel('psi2', X=self.X, X_variance=self.X_var, Z=self.Z, num_inducing=self.num_inducing, kernel=k) - m.ensure_default_constraints() m.randomize() - assert m.checkgrad(), "{} x psi2".format("+".join(map(lambda x: x.name, k.parts))) + assert m.checkgrad(), "{} x psi2".format("+".join(map(lambda x: x.name, k._parameters_))) if __name__ == "__main__": @@ -120,11 +121,11 @@ if __name__ == "__main__": if interactive: # N, num_inducing, input_dim, input_dim = 30, 5, 4, 30 # X = numpy.random.rand(N, input_dim) -# k = GPy.kern.linear(input_dim) + GPy.kern.bias(input_dim) + GPy.kern.white(input_dim, 0.00001) +# k = GPy.kern.Linear(input_dim) + GPy.kern.Bias(input_dim) + GPy.kern.White(input_dim, 0.00001) # K = k.K(X) # Y = numpy.random.multivariate_normal(numpy.zeros(N), K, input_dim).T # Y -= Y.mean(axis=0) -# k = GPy.kern.linear(input_dim) + GPy.kern.bias(input_dim) + GPy.kern.white(input_dim, 0.00001) +# k = GPy.kern.Linear(input_dim) + GPy.kern.Bias(input_dim) + GPy.kern.White(input_dim, 0.00001) # m = GPy.models.Bayesian_GPLVM(Y, input_dim, kernel=k, num_inducing=num_inducing) # m.randomize() # # self.assertTrue(m.checkgrad()) @@ -137,11 +138,11 @@ if __name__ == "__main__": X_var = .5 * numpy.ones_like(X) + .1 * numpy.clip(numpy.random.randn(*X.shape), 0, 1) Z = numpy.random.permutation(X)[:num_inducing] Y = X.dot(numpy.random.randn(input_dim, D)) -# kernel = GPy.kern.bias(input_dim) +# kernel = GPy.kern.Bias(input_dim) # -# kernels = [GPy.kern.linear(input_dim), GPy.kern.rbf(input_dim), GPy.kern.bias(input_dim), -# GPy.kern.linear(input_dim) + GPy.kern.bias(input_dim), -# GPy.kern.rbf(input_dim) + GPy.kern.bias(input_dim)] +# kernels = [GPy.kern.Linear(input_dim), GPy.kern.RBF(input_dim), GPy.kern.Bias(input_dim), +# GPy.kern.Linear(input_dim) + GPy.kern.Bias(input_dim), +# GPy.kern.RBF(input_dim) + GPy.kern.Bias(input_dim)] # for k in kernels: # m = PsiStatModel('psi1', X=X, X_variance=X_var, Z=Z, @@ -149,34 +150,34 @@ if __name__ == "__main__": # assert m.checkgrad(), "{} x psi1".format("+".join(map(lambda x: x.name, k.parts))) # m0 = PsiStatModel('psi0', X=X, X_variance=X_var, Z=Z, - num_inducing=num_inducing, kernel=GPy.kern.rbf(input_dim)+GPy.kern.bias(input_dim)) + num_inducing=num_inducing, kernel=GPy.kern.RBF(input_dim)+GPy.kern.Bias(input_dim)) # m1 = PsiStatModel('psi1', X=X, X_variance=X_var, Z=Z, # num_inducing=num_inducing, kernel=kernel) # m1 = PsiStatModel('psi1', X=X, X_variance=X_var, Z=Z, # num_inducing=num_inducing, kernel=kernel) # m2 = PsiStatModel('psi2', X=X, X_variance=X_var, Z=Z, -# num_inducing=num_inducing, kernel=GPy.kern.rbf(input_dim)) +# num_inducing=num_inducing, kernel=GPy.kern.RBF(input_dim)) # m3 = PsiStatModel('psi2', X=X, X_variance=X_var, Z=Z, -# num_inducing=num_inducing, kernel=GPy.kern.linear(input_dim, ARD=True, variances=numpy.random.rand(input_dim))) - # + GPy.kern.bias(input_dim)) +# num_inducing=num_inducing, kernel=GPy.kern.Linear(input_dim, ARD=True, variances=numpy.random.rand(input_dim))) + # + GPy.kern.Bias(input_dim)) # m = PsiStatModel('psi2', X=X, X_variance=X_var, Z=Z, -# num_inducing=num_inducing, +# num_inducing=num_inducing, # kernel=( -# GPy.kern.rbf(input_dim, ARD=1) -# +GPy.kern.linear(input_dim, ARD=1) -# +GPy.kern.bias(input_dim)) +# GPy.kern.RBF(input_dim, ARD=1) +# +GPy.kern.Linear(input_dim, ARD=1) +# +GPy.kern.Bias(input_dim)) # ) # m.ensure_default_constraints() m2 = PsiStatModel('psi2', X=X, X_variance=X_var, Z=Z, num_inducing=num_inducing, kernel=( - GPy.kern.rbf(input_dim, numpy.random.rand(), numpy.random.rand(input_dim), ARD=1) - #+GPy.kern.linear(input_dim, numpy.random.rand(input_dim), ARD=1) - #+GPy.kern.rbf(input_dim, numpy.random.rand(), numpy.random.rand(input_dim), ARD=1) - #+GPy.kern.rbf(input_dim, numpy.random.rand(), numpy.random.rand(), ARD=0) - +GPy.kern.bias(input_dim) - +GPy.kern.white(input_dim) + GPy.kern.RBF(input_dim, numpy.random.rand(), numpy.random.rand(input_dim), ARD=1) + #+GPy.kern.Linear(input_dim, numpy.random.rand(input_dim), ARD=1) + #+GPy.kern.RBF(input_dim, numpy.random.rand(), numpy.random.rand(input_dim), ARD=1) + #+GPy.kern.RBF(input_dim, numpy.random.rand(), numpy.random.rand(), ARD=0) + +GPy.kern.Bias(input_dim) + +GPy.kern.White(input_dim) ) ) - m2.ensure_default_constraints() + #m2.ensure_default_constraints() else: unittest.main() diff --git a/GPy/testing/sparse_gplvm_tests.py b/GPy/old_tests/sparse_gplvm_tests.py similarity index 78% rename from GPy/testing/sparse_gplvm_tests.py rename to GPy/old_tests/sparse_gplvm_tests.py index c3942b95..eb8ccb9c 100644 --- a/GPy/testing/sparse_gplvm_tests.py +++ b/GPy/old_tests/sparse_gplvm_tests.py @@ -10,10 +10,10 @@ class sparse_GPLVMTests(unittest.TestCase): def test_bias_kern(self): N, num_inducing, input_dim, D = 10, 3, 2, 4 X = np.random.rand(N, input_dim) - k = GPy.kern.rbf(input_dim) + GPy.kern.white(input_dim, 0.00001) + k = GPy.kern.RBF(input_dim) + GPy.kern.White(input_dim, 0.00001) K = k.K(X) Y = np.random.multivariate_normal(np.zeros(N),K,input_dim).T - k = GPy.kern.bias(input_dim) + GPy.kern.white(input_dim, 0.00001) + k = GPy.kern.Bias(input_dim) + GPy.kern.White(input_dim, 0.00001) m = SparseGPLVM(Y, input_dim, kernel=k, num_inducing=num_inducing) m.randomize() self.assertTrue(m.checkgrad()) @@ -21,10 +21,10 @@ class sparse_GPLVMTests(unittest.TestCase): def test_linear_kern(self): N, num_inducing, input_dim, D = 10, 3, 2, 4 X = np.random.rand(N, input_dim) - k = GPy.kern.rbf(input_dim) + GPy.kern.white(input_dim, 0.00001) + k = GPy.kern.RBF(input_dim) + GPy.kern.White(input_dim, 0.00001) K = k.K(X) Y = np.random.multivariate_normal(np.zeros(N),K,input_dim).T - k = GPy.kern.linear(input_dim) + GPy.kern.white(input_dim, 0.00001) + k = GPy.kern.Linear(input_dim) + GPy.kern.White(input_dim, 0.00001) m = SparseGPLVM(Y, input_dim, kernel=k, num_inducing=num_inducing) m.randomize() self.assertTrue(m.checkgrad()) @@ -32,10 +32,10 @@ class sparse_GPLVMTests(unittest.TestCase): def test_rbf_kern(self): N, num_inducing, input_dim, D = 10, 3, 2, 4 X = np.random.rand(N, input_dim) - k = GPy.kern.rbf(input_dim) + GPy.kern.white(input_dim, 0.00001) + k = GPy.kern.RBF(input_dim) + GPy.kern.White(input_dim, 0.00001) K = k.K(X) Y = np.random.multivariate_normal(np.zeros(N),K,input_dim).T - k = GPy.kern.rbf(input_dim) + GPy.kern.white(input_dim, 0.00001) + k = GPy.kern.RBF(input_dim) + GPy.kern.White(input_dim, 0.00001) m = SparseGPLVM(Y, input_dim, kernel=k, num_inducing=num_inducing) m.randomize() self.assertTrue(m.checkgrad()) diff --git a/GPy/plotting/__init__.py b/GPy/plotting/__init__.py new file mode 100644 index 00000000..d3a96914 --- /dev/null +++ b/GPy/plotting/__init__.py @@ -0,0 +1,7 @@ +# Copyright (c) 2014, GPy authors (see AUTHORS.txt). +# Licensed under the BSD 3-clause license (see LICENSE.txt) + +try: + import matplot_dep +except (ImportError, NameError): + print 'Fail to load GPy.plotting.matplot_dep.' \ No newline at end of file diff --git a/GPy/util/Tango.py b/GPy/plotting/matplot_dep/Tango.py similarity index 100% rename from GPy/util/Tango.py rename to GPy/plotting/matplot_dep/Tango.py diff --git a/GPy/plotting/matplot_dep/__init__.py b/GPy/plotting/matplot_dep/__init__.py new file mode 100644 index 00000000..4c4402ce --- /dev/null +++ b/GPy/plotting/matplot_dep/__init__.py @@ -0,0 +1,18 @@ +# Copyright (c) 2014, GPy authors (see AUTHORS.txt). +# Licensed under the BSD 3-clause license (see LICENSE.txt) + +import base_plots +import models_plots +import priors_plots +import variational_plots +import kernel_plots +import dim_reduction_plots +import mapping_plots +import Tango +import visualize +import latent_space_visualizations +import netpbmfile +import inference_plots +import maps +import img_plots +from ssgplvm import SSGPLVM_plot diff --git a/GPy/util/plot.py b/GPy/plotting/matplot_dep/base_plots.py similarity index 78% rename from GPy/util/plot.py rename to GPy/plotting/matplot_dep/base_plots.py index f44864f3..b4142342 100644 --- a/GPy/util/plot.py +++ b/GPy/plotting/matplot_dep/base_plots.py @@ -2,41 +2,63 @@ # Licensed under the BSD 3-clause license (see LICENSE.txt) -import Tango -import pylab as pb +try: + import Tango + import pylab as pb +except: + pass import numpy as np -def gpplot(x,mu,lower,upper,edgecol=Tango.colorsHex['darkBlue'],fillcol=Tango.colorsHex['lightBlue'],axes=None,**kwargs): - if axes is None: - axes = pb.gca() +def ax_default(fignum, ax): + if ax is None: + fig = pb.figure(fignum) + ax = fig.add_subplot(111) + else: + fig = ax.figure + return fig, ax + +def meanplot(x, mu, color=Tango.colorsHex['darkBlue'], ax=None, fignum=None, linewidth=2,**kw): + _, axes = ax_default(fignum, ax) + return axes.plot(x,mu,color=color,linewidth=linewidth,**kw) + +def gpplot(x, mu, lower, upper, edgecol=Tango.colorsHex['darkBlue'], fillcol=Tango.colorsHex['lightBlue'], ax=None, fignum=None, **kwargs): + _, axes = ax_default(fignum, ax) + mu = mu.flatten() x = x.flatten() lower = lower.flatten() upper = upper.flatten() + plots = [] + #here's the mean - axes.plot(x,mu,color=edgecol,linewidth=2) + plots.append(meanplot(x, mu, edgecol, axes)) #here's the box kwargs['linewidth']=0.5 if not 'alpha' in kwargs.keys(): kwargs['alpha'] = 0.3 - axes.fill(np.hstack((x,x[::-1])),np.hstack((upper,lower[::-1])),color=fillcol,**kwargs) + plots.append(axes.fill(np.hstack((x,x[::-1])),np.hstack((upper,lower[::-1])),color=fillcol,**kwargs)) #this is the edge: - axes.plot(x,upper,color=edgecol,linewidth=0.2) - axes.plot(x,lower,color=edgecol,linewidth=0.2) + plots.append(meanplot(x, upper,color=edgecol,linewidth=0.2,ax=axes)) + plots.append(meanplot(x, lower,color=edgecol,linewidth=0.2,ax=axes)) + + return plots + def removeRightTicks(ax=None): ax = ax or pb.gca() for i, line in enumerate(ax.get_yticklines()): if i%2 == 1: # odd indices line.set_visible(False) + def removeUpperTicks(ax=None): ax = ax or pb.gca() for i, line in enumerate(ax.get_xticklines()): if i%2 == 1: # odd indices line.set_visible(False) + def fewerXticks(ax=None,divideby=2): ax = ax or pb.gca() ax.set_xticks(ax.get_xticks()[::divideby]) @@ -71,8 +93,8 @@ def align_subplots(N,M,xlim=None, ylim=None): removeUpperTicks() def align_subplot_array(axes,xlim=None, ylim=None): - """make all of the axes in the array hae the same limits, turn off unnecessary ticks - + """ + Make all of the axes in the array hae the same limits, turn off unnecessary ticks use pb.subplots() to get an array of axes """ #find sensible xlim,ylim diff --git a/GPy/plotting/matplot_dep/dim_reduction_plots.py b/GPy/plotting/matplot_dep/dim_reduction_plots.py new file mode 100644 index 00000000..1398b40c --- /dev/null +++ b/GPy/plotting/matplot_dep/dim_reduction_plots.py @@ -0,0 +1,338 @@ +# Copyright (c) 2012, GPy authors (see AUTHORS.txt). +# Licensed under the BSD 3-clause license (see LICENSE.txt) + +import numpy as np +from latent_space_visualizations.controllers.imshow_controller import ImshowController,ImAnnotateController +from ...core.parameterization.variational import VariationalPosterior +from .base_plots import x_frame2D +import itertools +try: + import Tango + from matplotlib.cm import get_cmap + import pylab as pb +except: + pass + +def most_significant_input_dimensions(model, which_indices): + """ + Determine which dimensions should be plotted + """ + if which_indices is None: + if model.input_dim == 1: + input_1 = 0 + input_2 = None + if model.input_dim == 2: + input_1, input_2 = 0, 1 + else: + try: + input_1, input_2 = np.argsort(model.input_sensitivity())[::-1][:2] + except: + raise ValueError, "cannot automatically determine which dimensions to plot, please pass 'which_indices'" + else: + input_1, input_2 = which_indices + return input_1, input_2 + +def plot_latent(model, labels=None, which_indices=None, + resolution=50, ax=None, marker='o', s=40, + fignum=None, plot_inducing=False, legend=True, + plot_limits=None, + aspect='auto', updates=False, predict_kwargs={}, imshow_kwargs={}): + """ + :param labels: a np.array of size model.num_data containing labels for the points (can be number, strings, etc) + :param resolution: the resolution of the grid on which to evaluate the predictive variance + """ + if ax is None: + fig = pb.figure(num=fignum) + ax = fig.add_subplot(111) + else: + fig = ax.figure + Tango.reset() + + if labels is None: + labels = np.ones(model.num_data) + + input_1, input_2 = most_significant_input_dimensions(model, which_indices) + + #fethch the data points X that we'd like to plot + X = model.X + if isinstance(X, VariationalPosterior): + X = X.mean + else: + X = X + + + if X.shape[0] > 1000: + print "Warning: subsampling X, as it has more samples then 1000. X.shape={!s}".format(X.shape) + subsample = np.random.choice(X.shape[0], size=1000, replace=False) + X = X[subsample] + labels = labels[subsample] + #======================================================================= + # <<>> + # <<>> + # plt.close('all') + # fig, ax = plt.subplots(1,1) + # from GPy.plotting.matplot_dep.dim_reduction_plots import most_significant_input_dimensions + # import matplotlib.patches as mpatches + # i1, i2 = most_significant_input_dimensions(m, None) + # xmin, xmax = 100, -100 + # ymin, ymax = 100, -100 + # legend_handles = [] + # + # X = m.X.mean[:, [i1, i2]] + # X = m.X.variance[:, [i1, i2]] + # + # xmin = X[:,0].min(); xmax = X[:,0].max() + # ymin = X[:,1].min(); ymax = X[:,1].max() + # range_ = [[xmin, xmax], [ymin, ymax]] + # ul = np.unique(labels) + # + # for i, l in enumerate(ul): + # #cdict = dict(red =[(0., colors[i][0], colors[i][0]), (1., colors[i][0], colors[i][0])], + # # green=[(0., colors[i][0], colors[i][1]), (1., colors[i][1], colors[i][1])], + # # blue =[(0., colors[i][0], colors[i][2]), (1., colors[i][2], colors[i][2])], + # # alpha=[(0., 0., .0), (.5, .5, .5), (1., .5, .5)]) + # #cmap = LinearSegmentedColormap('{}'.format(l), cdict) + # cmap = LinearSegmentedColormap.from_list('cmap_{}'.format(str(l)), [colors[i], colors[i]], 255) + # cmap._init() + # #alphas = .5*(1+scipy.special.erf(np.linspace(-2,2, cmap.N+3)))#np.log(np.linspace(np.exp(0), np.exp(1.), cmap.N+3)) + # alphas = (scipy.special.erf(np.linspace(0,2.4, cmap.N+3)))#np.log(np.linspace(np.exp(0), np.exp(1.), cmap.N+3)) + # cmap._lut[:, -1] = alphas + # print l + # x, y = X[labels==l].T + # + # heatmap, xedges, yedges = np.histogram2d(x, y, bins=300, range=range_) + # #heatmap, xedges, yedges = np.histogram2d(x, y, bins=100) + # + # im = ax.imshow(heatmap, extent=[xedges[0], xedges[-1], yedges[0], yedges[-1]], cmap=cmap, aspect='auto', interpolation='nearest', label=str(l)) + # legend_handles.append(mpatches.Patch(color=colors[i], label=l)) + # ax.set_xlim(xmin, xmax) + # ax.set_ylim(ymin, ymax) + # plt.legend(legend_handles, [l.get_label() for l in legend_handles]) + # plt.draw() + # plt.show() + #======================================================================= + + # create a function which computes the shading of latent space according to the output variance + def plot_function(x): + Xtest_full = np.zeros((x.shape[0], model.X.shape[1])) + Xtest_full[:, [input_1, input_2]] = x + _, var = model.predict(Xtest_full, **predict_kwargs) + var = var[:, :1] + return np.log(var) + + #Create an IMshow controller that can re-plot the latent space shading at a good resolution + if plot_limits is None: + xmin, ymin = X[:, [input_1, input_2]].min(0) + xmax, ymax = X[:, [input_1, input_2]].max(0) + x_r, y_r = xmax-xmin, ymax-ymin + xmin -= .1*x_r + xmax += .1*x_r + ymin -= .1*y_r + ymax += .1*y_r + else: + try: + xmin, xmax, ymin, ymax = plot_limits + except (TypeError, ValueError) as e: + raise e.__class__, "Wrong plot limits: {} given -> need (xmin, xmax, ymin, ymax)".format(plot_limits) + view = ImshowController(ax, plot_function, + (xmin, ymin, xmax, ymax), + resolution, aspect=aspect, interpolation='bilinear', + cmap=pb.cm.binary, **imshow_kwargs) + + # make sure labels are in order of input: + labels = np.asarray(labels) + ulabels = [] + for lab in labels: + if not lab in ulabels: + ulabels.append(lab) + + marker = itertools.cycle(list(marker)) + + for i, ul in enumerate(ulabels): + if type(ul) is np.string_: + this_label = ul + elif type(ul) is np.int64: + this_label = 'class %i' % ul + else: + this_label = unicode(ul) + m = marker.next() + + index = np.nonzero(labels == ul)[0] + if model.input_dim == 1: + x = X[index, input_1] + y = np.zeros(index.size) + else: + x = X[index, input_1] + y = X[index, input_2] + ax.scatter(x, y, marker=m, s=s, c=Tango.nextMedium(), label=this_label, linewidth=.2, edgecolor='k', alpha=.9) + + ax.set_xlabel('latent dimension %i' % input_1) + ax.set_ylabel('latent dimension %i' % input_2) + + if not np.all(labels == 1.) and legend: + ax.legend(loc=0, numpoints=1) + + ax.grid(b=False) # remove the grid if present, it doesn't look good + ax.set_aspect('auto') # set a nice aspect ratio + + if plot_inducing: + Z = model.Z + ax.scatter(Z[:, input_1], Z[:, input_2], c='w', s=14, marker="^", edgecolor='k', linewidth=.3, alpha=.6) + + ax.set_xlim((xmin, xmax)) + ax.set_ylim((ymin, ymax)) + + try: + fig.canvas.draw() + fig.tight_layout() + fig.canvas.draw() + except Exception as e: + print "Could not invoke tight layout: {}".format(e) + pass + + if updates: + try: + ax.figure.canvas.show() + except Exception as e: + print "Could not invoke show: {}".format(e) + raw_input('Enter to continue') + view.deactivate() + return ax + +def plot_magnification(model, labels=None, which_indices=None, + resolution=60, ax=None, marker='o', s=40, + fignum=None, plot_inducing=False, legend=True, + aspect='auto', updates=False): + """ + :param labels: a np.array of size model.num_data containing labels for the points (can be number, strings, etc) + :param resolution: the resolution of the grid on which to evaluate the predictive variance + """ + if ax is None: + fig = pb.figure(num=fignum) + ax = fig.add_subplot(111) + Tango.reset() + + if labels is None: + labels = np.ones(model.num_data) + + input_1, input_2 = most_significant_input_dimensions(model, which_indices) + + # first, plot the output variance as a function of the latent space + Xtest, xx, yy, xmin, xmax = x_frame2D(model.X[:, [input_1, input_2]], resolution=resolution) + Xtest_full = np.zeros((Xtest.shape[0], model.X.shape[1])) + + def plot_function(x): + Xtest_full[:, [input_1, input_2]] = x + mf=model.magnification(Xtest_full) + return mf + + view = ImshowController(ax, plot_function, + tuple(model.X.min(0)[:, [input_1, input_2]]) + tuple(model.X.max(0)[:, [input_1, input_2]]), + resolution, aspect=aspect, interpolation='bilinear', + cmap=pb.cm.gray) + + # make sure labels are in order of input: + ulabels = [] + for lab in labels: + if not lab in ulabels: + ulabels.append(lab) + + marker = itertools.cycle(list(marker)) + + for i, ul in enumerate(ulabels): + if type(ul) is np.string_: + this_label = ul + elif type(ul) is np.int64: + this_label = 'class %i' % ul + else: + this_label = 'class %i' % i + m = marker.next() + + index = np.nonzero(labels == ul)[0] + if model.input_dim == 1: + x = model.X[index, input_1] + y = np.zeros(index.size) + else: + x = model.X[index, input_1] + y = model.X[index, input_2] + ax.scatter(x, y, marker=m, s=s, color=Tango.nextMedium(), label=this_label) + + ax.set_xlabel('latent dimension %i' % input_1) + ax.set_ylabel('latent dimension %i' % input_2) + + if not np.all(labels == 1.) and legend: + ax.legend(loc=0, numpoints=1) + + ax.set_xlim(xmin[0], xmax[0]) + ax.set_ylim(xmin[1], xmax[1]) + ax.grid(b=False) # remove the grid if present, it doesn't look good + ax.set_aspect('auto') # set a nice aspect ratio + + if plot_inducing: + ax.plot(model.Z[:, input_1], model.Z[:, input_2], '^w') + + if updates: + fig.canvas.show() + raw_input('Enter to continue') + + pb.title('Magnification Factor') + return ax + + +def plot_steepest_gradient_map(model, fignum=None, ax=None, which_indices=None, labels=None, data_labels=None, data_marker='o', data_s=40, resolution=20, aspect='auto', updates=False, ** kwargs): + + input_1, input_2 = significant_dims = most_significant_input_dimensions(model, which_indices) + + X = np.zeros((resolution ** 2, model.input_dim)) + indices = np.r_[:X.shape[0]] + if labels is None: + labels = range(model.output_dim) + + def plot_function(x): + X[:, significant_dims] = x + dmu_dX = model.dmu_dXnew(X) + argmax = np.argmax(dmu_dX, 1) + return dmu_dX[indices, argmax], np.array(labels)[argmax] + + if ax is None: + fig = pb.figure(num=fignum) + ax = fig.add_subplot(111) + + if data_labels is None: + data_labels = np.ones(model.num_data) + ulabels = [] + for lab in data_labels: + if not lab in ulabels: + ulabels.append(lab) + marker = itertools.cycle(list(data_marker)) + for i, ul in enumerate(ulabels): + if type(ul) is np.string_: + this_label = ul + elif type(ul) is np.int64: + this_label = 'class %i' % ul + else: + this_label = 'class %i' % i + m = marker.next() + index = np.nonzero(data_labels == ul)[0] + x = model.X[index, input_1] + y = model.X[index, input_2] + ax.scatter(x, y, marker=m, s=data_s, color=Tango.nextMedium(), label=this_label) + + ax.set_xlabel('latent dimension %i' % input_1) + ax.set_ylabel('latent dimension %i' % input_2) + + controller = ImAnnotateController(ax, + plot_function, + tuple(model.X.min(0)[:, significant_dims]) + tuple(model.X.max(0)[:, significant_dims]), + resolution=resolution, + aspect=aspect, + cmap=get_cmap('jet'), + **kwargs) + ax.legend() + ax.figure.tight_layout() + if updates: + pb.show() + clear = raw_input('Enter to continue') + if clear.lower() in 'yes' or clear == '': + controller.deactivate() + return controller.view diff --git a/GPy/plotting/matplot_dep/img_plots.py b/GPy/plotting/matplot_dep/img_plots.py new file mode 100644 index 00000000..453a904d --- /dev/null +++ b/GPy/plotting/matplot_dep/img_plots.py @@ -0,0 +1,58 @@ +# Copyright (c) 2012, GPy authors (see AUTHORS.txt). +# Licensed under the BSD 3-clause license (see LICENSE.txt) +""" +The module contains the tools for ploting 2D image visualizations +""" + +import numpy as np +from matplotlib.cm import jet + +width_max = 15 +height_max = 12 + +def _calculateFigureSize(x_size, y_size, fig_ncols, fig_nrows, pad): + width = (x_size*fig_ncols+pad*(fig_ncols-1)) + height = (y_size*fig_nrows+pad*(fig_nrows-1)) + if width > float(height)/height_max*width_max: + return (width_max, float(width_max)/width*height) + else: + return (float(height_max)/height*width, height_max) + +def plot_2D_images(figure, arr, symmetric=False, pad=None, zoom=None, mode=None, interpolation='nearest'): + ax = figure.add_subplot(111) + if len(arr.shape)==2: + arr = arr.reshape(*((1,)+arr.shape)) + fig_num = arr.shape[0] + y_size = arr.shape[1] + x_size = arr.shape[2] + fig_ncols = int(np.ceil(np.sqrt(fig_num))) + fig_nrows = int(np.ceil((float)(fig_num)/fig_ncols)) + if pad==None: + pad = max(int(min(y_size,x_size)/10),1) + + figsize = _calculateFigureSize(x_size, y_size, fig_ncols, fig_nrows, pad) + #figure.set_size_inches(figsize,forward=True) + #figure.subplots_adjust(left=0.05, bottom=0.05, right=0.95, top=0.95) + + if symmetric: + # symmetric around zero: fix zero as the middle color + mval = max(abs(arr.max()),abs(arr.min())) + arr = arr/(2.*mval)+0.5 + else: + minval,maxval = arr.min(),arr.max() + arr = (arr-minval)/(maxval-minval) + + if mode=='L': + arr_color = np.empty(arr.shape+(3,)) + arr_color[:] = arr.reshape(*(arr.shape+(1,))) + elif mode==None or mode=='jet': + arr_color = jet(arr) + + buf = np.ones((y_size*fig_nrows+pad*(fig_nrows-1), x_size*fig_ncols+pad*(fig_ncols-1), 3),dtype=arr.dtype) + + for y in xrange(fig_nrows): + for x in xrange(fig_ncols): + if y*fig_ncols+x 1: + mode = 'expand' + ax.legend(bbox_to_anchor=(0., 1.02, 1., 1.02), loc=3, + ncol=len(bars), mode=mode, borderaxespad=0.) + fig.tight_layout(rect=(0, 0, 1, .9)) + else: + ax.legend() + return ax + + + +def plot(kernel,x=None, fignum=None, ax=None, title=None, plot_limits=None, resolution=None, **mpl_kwargs): + """ + plot a kernel. + :param x: the value to use for the other kernel argument (kernels are a function of two variables!) + :param fignum: figure number of the plot + :param ax: matplotlib axis to plot on + :param title: the matplotlib title + :param plot_limits: the range over which to plot the kernel + :resolution: the resolution of the lines used in plotting + :mpl_kwargs avalid keyword arguments to pass through to matplotlib (e.g. lw=7) + """ + fig, ax = ax_default(fignum,ax) + + if title is None: + ax.set_title('%s kernel' % kernel.name) + else: + ax.set_title(title) + + + if kernel.input_dim == 1: + if x is None: + x = np.zeros((1, 1)) + else: + x = np.asarray(x) + assert x.size == 1, "The size of the fixed variable x is not 1" + x = x.reshape((1, 1)) + + if plot_limits == None: + xmin, xmax = (x - 5).flatten(), (x + 5).flatten() + elif len(plot_limits) == 2: + xmin, xmax = plot_limits + else: + raise ValueError, "Bad limits for plotting" + + Xnew = np.linspace(xmin, xmax, resolution or 201)[:, None] + Kx = kernel.K(Xnew, x) + ax.plot(Xnew, Kx, **mpl_kwargs) + ax.set_xlim(xmin, xmax) + ax.set_xlabel("x") + ax.set_ylabel("k(x,%0.1f)" % x) + + elif kernel.input_dim == 2: + if x is None: + x = np.zeros((1, 2)) + else: + x = np.asarray(x) + assert x.size == 2, "The size of the fixed variable x is not 2" + x = x.reshape((1, 2)) + + if plot_limits is None: + xmin, xmax = (x - 5).flatten(), (x + 5).flatten() + elif len(plot_limits) == 2: + xmin, xmax = plot_limits + else: + raise ValueError, "Bad limits for plotting" + + resolution = resolution or 51 + xx, yy = np.mgrid[xmin[0]:xmax[0]:1j * resolution, xmin[1]:xmax[1]:1j * resolution] + Xnew = np.vstack((xx.flatten(), yy.flatten())).T + Kx = kernel.K(Xnew, x) + Kx = Kx.reshape(resolution, resolution).T + ax.contour(xx, yy, Kx, vmin=Kx.min(), vmax=Kx.max(), cmap=pb.cm.jet, **mpl_kwargs) # @UndefinedVariable + ax.set_xlim(xmin[0], xmax[0]) + ax.set_ylim(xmin[1], xmax[1]) + ax.set_xlabel("x1") + ax.set_ylabel("x2") + ax.set_title("k(x1,x2 ; %0.1f,%0.1f)" % (x[0, 0], x[0, 1])) + else: + raise NotImplementedError, "Cannot plot a kernel with more than two input dimensions" diff --git a/GPy/util/latent_space_visualizations/__init__.py b/GPy/plotting/matplot_dep/latent_space_visualizations/__init__.py similarity index 100% rename from GPy/util/latent_space_visualizations/__init__.py rename to GPy/plotting/matplot_dep/latent_space_visualizations/__init__.py diff --git a/GPy/util/latent_space_visualizations/controllers/__init__.py b/GPy/plotting/matplot_dep/latent_space_visualizations/controllers/__init__.py similarity index 100% rename from GPy/util/latent_space_visualizations/controllers/__init__.py rename to GPy/plotting/matplot_dep/latent_space_visualizations/controllers/__init__.py diff --git a/GPy/util/latent_space_visualizations/controllers/axis_event_controller.py b/GPy/plotting/matplot_dep/latent_space_visualizations/controllers/axis_event_controller.py similarity index 78% rename from GPy/util/latent_space_visualizations/controllers/axis_event_controller.py rename to GPy/plotting/matplot_dep/latent_space_visualizations/controllers/axis_event_controller.py index 67e7a797..62b622c5 100644 --- a/GPy/util/latent_space_visualizations/controllers/axis_event_controller.py +++ b/GPy/plotting/matplot_dep/latent_space_visualizations/controllers/axis_event_controller.py @@ -28,15 +28,14 @@ class AxisChangedController(AxisEventController): ''' _changing = False - def __init__(self, ax, plot_limits=None, update_lim=None): + def __init__(self, ax, update_lim=None): ''' Constructor ''' super(AxisChangedController, self).__init__(ax) - self._lim_ratio_threshold = update_lim or .8 - if plot_limits is not None: - self._x_lim = [plot_limits[0], plot_limits[2]] - self._y_lim = [plot_limits[0], plot_limits[2]] + self._lim_ratio_threshold = update_lim or .95 + self._x_lim = self.ax.get_xlim() + self._y_lim = self.ax.get_ylim() def update(self, ax): pass @@ -81,23 +80,28 @@ class AxisChangedController(AxisEventController): class BufferedAxisChangedController(AxisChangedController): def __init__(self, ax, plot_function, plot_limits, resolution=50, update_lim=None, **kwargs): """ - :param plot_function: + Buffered axis changed controller. Controls the buffer and handles update events for when the axes changed. + + Updated plotting will be after first reload (first time will be within plot limits, after that the limits will be buffered) + + :param plot_function: function to use for creating image for plotting (return ndarray-like) plot_function gets called with (2D!) Xtest grid if replotting required :type plot_function: function :param plot_limits: beginning plot limits [xmin, ymin, xmax, ymax] - + :param kwargs: additional kwargs are for pyplot.imshow(**kwargs) """ - super(BufferedAxisChangedController, self).__init__(ax, plot_limits, update_lim=update_lim) + super(BufferedAxisChangedController, self).__init__(ax, update_lim=update_lim) self.plot_function = plot_function - #xmin, xmax = self._x_lim # self._compute_buffered(*self._x_lim) - #ymin, ymax = self._y_lim # self._compute_buffered(*self._y_lim) - xmin, ymin, xmax, ymax = plot_limits + xmin, ymin, xmax, ymax = plot_limits#self._x_lim # self._compute_buffered(*self._x_lim) + # imshow acts on the limits of the plot, this is why we need to override the limits here, to make sure the right plot limits are used: + self._x_lim = xmin, xmax + self._y_lim = ymin, ymax self.resolution = resolution self._not_init = False - self.view = self._init_view(self.ax, self.recompute_X(), xmin, xmax, ymin, ymax, **kwargs) + self.view = self._init_view(self.ax, self.recompute_X(buffered=False), xmin, xmax, ymin, ymax, **kwargs) self._not_init = True def update(self, ax): @@ -113,18 +117,16 @@ class BufferedAxisChangedController(AxisChangedController): def update_view(self, view, X, xmin, xmax, ymin, ymax): raise NotImplementedError('update view given in here') - def get_grid(self): - if self._not_init: - xmin, xmax = self._compute_buffered(*self._x_lim) - ymin, ymax = self._compute_buffered(*self._y_lim) - else: - xmin, xmax = self._x_lim - ymin, ymax = self._y_lim + def get_grid(self, buffered=True): + if buffered: comp = self._compute_buffered + else: comp = lambda a,b: (a,b) + xmin, xmax = comp(*self._x_lim) + ymin, ymax = comp(*self._y_lim) x, y = numpy.mgrid[xmin:xmax:1j * self.resolution, ymin:ymax:1j * self.resolution] return numpy.hstack((x.flatten()[:, None], y.flatten()[:, None])) - def recompute_X(self): - X = self.plot_function(self.get_grid()) + def recompute_X(self, buffered=True): + X = self.plot_function(self.get_grid(buffered)) if isinstance(X, (tuple, list)): for x in X: x.shape = [self.resolution, self.resolution] @@ -143,6 +145,3 @@ class BufferedAxisChangedController(AxisChangedController): except: buffersize = .4 return buffersize - - - diff --git a/GPy/util/latent_space_visualizations/controllers/imshow_controller.py b/GPy/plotting/matplot_dep/latent_space_visualizations/controllers/imshow_controller.py similarity index 94% rename from GPy/util/latent_space_visualizations/controllers/imshow_controller.py rename to GPy/plotting/matplot_dep/latent_space_visualizations/controllers/imshow_controller.py index f0ede360..de1114a2 100644 --- a/GPy/util/latent_space_visualizations/controllers/imshow_controller.py +++ b/GPy/plotting/matplot_dep/latent_space_visualizations/controllers/imshow_controller.py @@ -3,7 +3,7 @@ Created on 24 Jul 2013 @author: maxz ''' -from GPy.util.latent_space_visualizations.controllers.axis_event_controller import BufferedAxisChangedController +from axis_event_controller import BufferedAxisChangedController import itertools import numpy @@ -11,13 +11,13 @@ import numpy class ImshowController(BufferedAxisChangedController): def __init__(self, ax, plot_function, plot_limits, resolution=50, update_lim=.8, **kwargs): """ - :param plot_function: + :param plot_function: function to use for creating image for plotting (return ndarray-like) plot_function gets called with (2D!) Xtest grid if replotting required :type plot_function: function :param plot_limits: beginning plot limits [xmin, ymin, xmax, ymax] - + :param kwargs: additional kwargs are for pyplot.imshow(**kwargs) """ super(ImshowController, self).__init__(ax, plot_function, plot_limits, resolution, update_lim, **kwargs) @@ -36,7 +36,7 @@ class ImshowController(BufferedAxisChangedController): class ImAnnotateController(ImshowController): def __init__(self, ax, plot_function, plot_limits, resolution=20, update_lim=.99, **kwargs): """ - :param plot_function: + :param plot_function: function to use for creating image for plotting (return ndarray-like) plot_function gets called with (2D!) Xtest grid if replotting required :type plot_function: function diff --git a/GPy/plotting/matplot_dep/mapping_plots.py b/GPy/plotting/matplot_dep/mapping_plots.py new file mode 100644 index 00000000..6156687d --- /dev/null +++ b/GPy/plotting/matplot_dep/mapping_plots.py @@ -0,0 +1,84 @@ +# Copyright (c) 2012, GPy authors (see AUTHORS.txt). +# Licensed under the BSD 3-clause license (see LICENSE.txt) + +import numpy as np +try: + import Tango + import pylab as pb +except: + pass +from base_plots import x_frame1D, x_frame2D + + +def plot_mapping(self, plot_limits=None, which_data='all', which_parts='all', resolution=None, levels=20, samples=0, fignum=None, ax=None, fixed_inputs=[], linecol=Tango.colorsHex['darkBlue']): + """ + Plots the mapping associated with the model. + - In one dimension, the function is plotted. + - In two dimsensions, a contour-plot shows the function + - In higher dimensions, we've not implemented this yet !TODO! + + Can plot only part of the data and part of the posterior functions + using which_data and which_functions + + :param plot_limits: The limits of the plot. If 1D [xmin,xmax], if 2D [[xmin,ymin],[xmax,ymax]]. Defaluts to data limits + :type plot_limits: np.array + :param which_data: which if the training data to plot (default all) + :type which_data: 'all' or a slice object to slice self.X, self.Y + :param which_parts: which of the kernel functions to plot (additively) + :type which_parts: 'all', or list of bools + :param resolution: the number of intervals to sample the GP on. Defaults to 200 in 1D and 50 (a 50x50 grid) in 2D + :type resolution: int + :param levels: number of levels to plot in a contour plot. + :type levels: int + :param samples: the number of a posteriori samples to plot + :type samples: int + :param fignum: figure to plot on. + :type fignum: figure number + :param ax: axes to plot on. + :type ax: axes handle + :param fixed_inputs: a list of tuple [(i,v), (i,v)...], specifying that input index i should be set to value v. + :type fixed_inputs: a list of tuples + :param linecol: color of line to plot. + :type linecol: + :param levels: for 2D plotting, the number of contour levels to use is ax is None, create a new figure + + """ + # TODO include samples + if which_data == 'all': + which_data = slice(None) + + if ax is None: + fig = pb.figure(num=fignum) + ax = fig.add_subplot(111) + + plotdims = self.input_dim - len(fixed_inputs) + + if plotdims == 1: + + Xu = self.X * self._Xscale + self._Xoffset # NOTE self.X are the normalized values now + + fixed_dims = np.array([i for i,v in fixed_inputs]) + freedim = np.setdiff1d(np.arange(self.input_dim),fixed_dims) + + Xnew, xmin, xmax = x_frame1D(Xu[:,freedim], plot_limits=plot_limits) + Xgrid = np.empty((Xnew.shape[0],self.input_dim)) + Xgrid[:,freedim] = Xnew + for i,v in fixed_inputs: + Xgrid[:,i] = v + + f = self.predict(Xgrid, which_parts=which_parts) + for d in range(y.shape[1]): + ax.plot(Xnew, f[:, d], edgecol=linecol) + + elif self.X.shape[1] == 2: + resolution = resolution or 50 + Xnew, _, _, xmin, xmax = x_frame2D(self.X, plot_limits, resolution) + x, y = np.linspace(xmin[0], xmax[0], resolution), np.linspace(xmin[1], xmax[1], resolution) + f = self.predict(Xnew, which_parts=which_parts) + m = m.reshape(resolution, resolution).T + ax.contour(x, y, f, levels, vmin=m.min(), vmax=m.max(), cmap=pb.cm.jet) # @UndefinedVariable + ax.set_xlim(xmin[0], xmax[0]) + ax.set_ylim(xmin[1], xmax[1]) + + else: + raise NotImplementedError, "Cannot define a frame with more than two input dimensions" diff --git a/GPy/plotting/matplot_dep/maps.py b/GPy/plotting/matplot_dep/maps.py new file mode 100644 index 00000000..fcb03b38 --- /dev/null +++ b/GPy/plotting/matplot_dep/maps.py @@ -0,0 +1,175 @@ +# Copyright (c) 2012, GPy authors (see AUTHORS.txt). +# Licensed under the BSD 3-clause license (see LICENSE.txt) +import numpy as np +try: + import pylab as pb + from matplotlib.patches import Polygon + from matplotlib.collections import PatchCollection + #from matplotlib import cm + pb.ion() +except: + pass +import re + +def plot(shape_records,facecolor='w',edgecolor='k',linewidths=.5, ax=None,xlims=None,ylims=None): + """ + Plot the geometry of a shapefile + + :param shape_records: geometry and attributes list + :type shape_records: ShapeRecord object (output of a shapeRecords() method) + :param facecolor: color to be used to fill in polygons + :param edgecolor: color to be used for lines + :param ax: axes to plot on. + :type ax: axes handle + """ + #Axes handle + if ax is None: + fig = pb.figure() + ax = fig.add_subplot(111) + + #Iterate over shape_records + for srec in shape_records: + points = np.vstack(srec.shape.points) + sparts = srec.shape.parts + par = list(sparts) + [points.shape[0]] + + polygs = [] + for pj in xrange(len(sparts)): + polygs.append(Polygon(points[par[pj]:par[pj+1]])) + ax.add_collection(PatchCollection(polygs,facecolor=facecolor,edgecolor=edgecolor, linewidths=linewidths)) + + #Plot limits + _box = np.vstack([srec.shape.bbox for srec in shape_records]) + minx,miny = np.min(_box[:,:2],0) + maxx,maxy = np.max(_box[:,2:],0) + + if xlims is not None: + minx,maxx = xlims + if ylims is not None: + miny,maxy = ylims + ax.set_xlim(minx,maxx) + ax.set_ylim(miny,maxy) + + +def string_match(sf,regex,field=2): + """ + Return the geometry and attributes of a shapefile whose fields match a regular expression given + + :param sf: shapefile + :type sf: shapefile object + :regex: regular expression to match + :type regex: string + :field: field number to be matched with the regex + :type field: integer + """ + index = [] + shape_records = [] + for rec in enumerate(sf.shapeRecords()): + m = re.search(regex,rec[1].record[field]) + if m is not None: + index.append(rec[0]) + shape_records.append(rec[1]) + return index,shape_records + +def bbox_match(sf,bbox,inside_only=True): + """ + Return the geometry and attributes of a shapefile that lie within (or intersect) a bounding box + + :param sf: shapefile + :type sf: shapefile object + :param bbox: bounding box + :type bbox: list of floats [x_min,y_min,x_max,y_max] + :inside_only: True if the objects returned are those that lie within the bbox and False if the objects returned are any that intersect the bbox + :type inside_only: Boolean + """ + A,B,C,D = bbox + index = [] + shape_records = [] + for rec in enumerate(sf.shapeRecords()): + a,b,c,d = rec[1].shape.bbox + if inside_only: + if A <= a and B <= b and C >= c and D >= d: + index.append(rec[0]) + shape_records.append(rec[1]) + else: + cond1 = A <= a and B <= b and C >= a and D >= b + cond2 = A <= c and B <= d and C >= c and D >= d + cond3 = A <= a and D >= d and C >= a and B <= d + cond4 = A <= c and D >= b and C >= c and B <= b + cond5 = a <= C and b <= B and d >= D + cond6 = c <= A and b <= B and d >= D + cond7 = d <= B and a <= A and c >= C + cond8 = b <= D and a <= A and c >= C + if cond1 or cond2 or cond3 or cond4 or cond5 or cond6 or cond7 or cond8: + index.append(rec[0]) + shape_records.append(rec[1]) + return index,shape_records + + +def plot_bbox(sf,bbox,inside_only=True): + """ + Plot the geometry of a shapefile within a bbox + + :param sf: shapefile + :type sf: shapefile object + :param bbox: bounding box + :type bbox: list of floats [x_min,y_min,x_max,y_max] + :inside_only: True if the objects returned are those that lie within the bbox and False if the objects returned are any that intersect the bbox + :type inside_only: Boolean + """ + index,shape_records = bbox_match(sf,bbox,inside_only) + A,B,C,D = bbox + plot(shape_records,xlims=[bbox[0],bbox[2]],ylims=[bbox[1],bbox[3]]) + +def plot_string_match(sf,regex,field,**kwargs): + """ + Plot the geometry of a shapefile whose fields match a regular expression given + + :param sf: shapefile + :type sf: shapefile object + :regex: regular expression to match + :type regex: string + :field: field number to be matched with the regex + :type field: integer + """ + index,shape_records = string_match(sf,regex,field) + plot(shape_records,**kwargs) + + +def new_shape_string(sf,name,regex,field=2,type=None): + import shapefile + if type is None: + type = shapefile.POINT + newshp = shapefile.Writer(shapeType = sf.shapeType) + newshp.autoBalance = 1 + + index,shape_records = string_match(sf,regex,field) + + _fi = [sf.fields[j] for j in index] + for f in _fi: + newshp.field(name=f[0],fieldType=f[1],size=f[2],decimal=f[3]) + + _shre = shape_records + for sr in _shre: + _points = [] + _parts = [] + for point in sr.shape.points: + _points.append(point) + _parts.append(_points) + + newshp.line(parts=_parts) + newshp.records.append(sr.record) + print len(sr.record) + + newshp.save(name) + print index + +def apply_bbox(sf,ax): + """ + Use bbox as xlim and ylim in ax + """ + limits = sf.bbox + xlim = limits[0],limits[2] + ylim = limits[1],limits[3] + ax.set_xlim(xlim) + ax.set_ylim(ylim) diff --git a/GPy/plotting/matplot_dep/models_plots.py b/GPy/plotting/matplot_dep/models_plots.py new file mode 100644 index 00000000..ed024c0a --- /dev/null +++ b/GPy/plotting/matplot_dep/models_plots.py @@ -0,0 +1,188 @@ +# Copyright (c) 2012, GPy authors (see AUTHORS.txt). +# Licensed under the BSD 3-clause license (see LICENSE.txt) + +try: + import Tango + import pylab as pb +except: + pass +import numpy as np +from base_plots import gpplot, x_frame1D, x_frame2D +from ...models.gp_coregionalized_regression import GPCoregionalizedRegression +from ...models.sparse_gp_coregionalized_regression import SparseGPCoregionalizedRegression +from scipy import sparse + +def plot_fit(model, plot_limits=None, which_data_rows='all', + which_data_ycols='all', fixed_inputs=[], + levels=20, samples=0, fignum=None, ax=None, resolution=None, + plot_raw=False, + linecol=Tango.colorsHex['darkBlue'],fillcol=Tango.colorsHex['lightBlue'], Y_metadata=None, data_symbol='kx'): + """ + Plot the posterior of the GP. + - In one dimension, the function is plotted with a shaded region identifying two standard deviations. + - In two dimsensions, a contour-plot shows the mean predicted function + - In higher dimensions, use fixed_inputs to plot the GP with some of the inputs fixed. + + Can plot only part of the data and part of the posterior functions + using which_data_rowsm which_data_ycols. + + :param plot_limits: The limits of the plot. If 1D [xmin,xmax], if 2D [[xmin,ymin],[xmax,ymax]]. Defaluts to data limits + :type plot_limits: np.array + :param which_data_rows: which of the training data to plot (default all) + :type which_data_rows: 'all' or a slice object to slice model.X, model.Y + :param which_data_ycols: when the data has several columns (independant outputs), only plot these + :type which_data_rows: 'all' or a list of integers + :param fixed_inputs: a list of tuple [(i,v), (i,v)...], specifying that input index i should be set to value v. + :type fixed_inputs: a list of tuples + :param resolution: the number of intervals to sample the GP on. Defaults to 200 in 1D and 50 (a 50x50 grid) in 2D + :type resolution: int + :param levels: number of levels to plot in a contour plot. + :type levels: int + :param samples: the number of a posteriori samples to plot + :type samples: int + :param fignum: figure to plot on. + :type fignum: figure number + :param ax: axes to plot on. + :type ax: axes handle + :type output: integer (first output is 0) + :param linecol: color of line to plot. + :type linecol: + :param fillcol: color of fill + :param levels: for 2D plotting, the number of contour levels to use is ax is None, create a new figure + """ + #deal with optional arguments + if which_data_rows == 'all': + which_data_rows = slice(None) + if which_data_ycols == 'all': + which_data_ycols = np.arange(model.output_dim) + #if len(which_data_ycols)==0: + #raise ValueError('No data selected for plotting') + if ax is None: + fig = pb.figure(num=fignum) + ax = fig.add_subplot(111) + + if hasattr(model, 'has_uncertain_inputs') and model.has_uncertain_inputs(): + X = model.X.mean + X_variance = model.X.variance + else: + X = model.X + Y = model.Y + if sparse.issparse(Y): Y = Y.todense().view(np.ndarray) + + if hasattr(model, 'Z'): Z = model.Z + + #work out what the inputs are for plotting (1D or 2D) + fixed_dims = np.array([i for i,v in fixed_inputs]) + free_dims = np.setdiff1d(np.arange(model.input_dim),fixed_dims) + plots = {} + #one dimensional plotting + if len(free_dims) == 1: + + #define the frame on which to plot + Xnew, xmin, xmax = x_frame1D(X[:,free_dims], plot_limits=plot_limits, resolution=resolution or 200) + Xgrid = np.empty((Xnew.shape[0],model.input_dim)) + Xgrid[:,free_dims] = Xnew + for i,v in fixed_inputs: + Xgrid[:,i] = v + + #make a prediction on the frame and plot it + if plot_raw: + m, v = model._raw_predict(Xgrid) + lower = m - 2*np.sqrt(v) + upper = m + 2*np.sqrt(v) + else: + if isinstance(model,GPCoregionalizedRegression) or isinstance(model,SparseGPCoregionalizedRegression): + meta = {'output_index': Xgrid[:,-1:].astype(np.int)} + else: + meta = None + m, v = model.predict(Xgrid, full_cov=False, Y_metadata=meta) + lower, upper = model.predict_quantiles(Xgrid, Y_metadata=meta) + + + for d in which_data_ycols: + plots['gpplot'] = gpplot(Xnew, m[:, d], lower[:, d], upper[:, d], ax=ax, edgecol=linecol, fillcol=fillcol) + if not plot_raw: plots['dataplot'] = ax.plot(X[which_data_rows,free_dims], Y[which_data_rows, d], data_symbol, mew=1.5) + + #optionally plot some samples + if samples: #NOTE not tested with fixed_inputs + Ysim = model.posterior_samples(Xgrid, samples) + for yi in Ysim.T: + plots['posterior_samples'] = ax.plot(Xnew, yi[:,None], Tango.colorsHex['darkBlue'], linewidth=0.25) + #ax.plot(Xnew, yi[:,None], marker='x', linestyle='--',color=Tango.colorsHex['darkBlue']) #TODO apply this line for discrete outputs. + + + #add error bars for uncertain (if input uncertainty is being modelled) + if hasattr(model,"has_uncertain_inputs") and model.has_uncertain_inputs(): + plots['xerrorbar'] = ax.errorbar(X[which_data_rows, free_dims].flatten(), Y[which_data_rows, which_data_ycols].flatten(), + xerr=2 * np.sqrt(X_variance[which_data_rows, free_dims].flatten()), + ecolor='k', fmt=None, elinewidth=.5, alpha=.5) + + + #set the limits of the plot to some sensible values + ymin, ymax = min(np.append(Y[which_data_rows, which_data_ycols].flatten(), lower)), max(np.append(Y[which_data_rows, which_data_ycols].flatten(), upper)) + ymin, ymax = ymin - 0.1 * (ymax - ymin), ymax + 0.1 * (ymax - ymin) + ax.set_xlim(xmin, xmax) + ax.set_ylim(ymin, ymax) + + #add inducing inputs (if a sparse model is used) + if hasattr(model,"Z"): + #Zu = model.Z[:,free_dims] * model._Xscale[:,free_dims] + model._Xoffset[:,free_dims] + if isinstance(model,SparseGPCoregionalizedRegression): + Z = Z[Z[:,-1] == Y_metadata['output_index'],:] + Zu = Z[:,free_dims] + z_height = ax.get_ylim()[0] + plots['inducing_inputs'] = ax.plot(Zu, np.zeros_like(Zu) + z_height, 'r|', mew=1.5, markersize=12) + + + + #2D plotting + elif len(free_dims) == 2: + + #define the frame for plotting on + resolution = resolution or 50 + Xnew, _, _, xmin, xmax = x_frame2D(X[:,free_dims], plot_limits, resolution) + Xgrid = np.empty((Xnew.shape[0],model.input_dim)) + Xgrid[:,free_dims] = Xnew + for i,v in fixed_inputs: + Xgrid[:,i] = v + x, y = np.linspace(xmin[0], xmax[0], resolution), np.linspace(xmin[1], xmax[1], resolution) + + #predict on the frame and plot + if plot_raw: + m, _ = model._raw_predict(Xgrid) + else: + if isinstance(model,GPCoregionalizedRegression) or isinstance(model,SparseGPCoregionalizedRegression): + meta = {'output_index': Xgrid[:,-1:].astype(np.int)} + else: + meta = None + m, v = model.predict(Xgrid, full_cov=False, Y_metadata=meta) + for d in which_data_ycols: + m_d = m[:,d].reshape(resolution, resolution).T + plots['contour'] = ax.contour(x, y, m_d, levels, vmin=m.min(), vmax=m.max(), cmap=pb.cm.jet) + if not plot_raw: plots['dataplot'] = ax.scatter(X[which_data_rows, free_dims[0]], X[which_data_rows, free_dims[1]], 40, Y[which_data_rows, d], cmap=pb.cm.jet, vmin=m.min(), vmax=m.max(), linewidth=0.) + + #set the limits of the plot to some sensible values + ax.set_xlim(xmin[0], xmax[0]) + ax.set_ylim(xmin[1], xmax[1]) + + if samples: + warnings.warn("Samples are rather difficult to plot for 2D inputs...") + + #add inducing inputs (if a sparse model is used) + if hasattr(model,"Z"): + #Zu = model.Z[:,free_dims] * model._Xscale[:,free_dims] + model._Xoffset[:,free_dims] + Zu = Z[:,free_dims] + plots['inducing_inputs'] = ax.plot(Zu[:,free_dims[0]], Zu[:,free_dims[1]], 'wo') + + else: + raise NotImplementedError, "Cannot define a frame with more than two input dimensions" + return plots + +def plot_fit_f(model, *args, **kwargs): + """ + Plot the GP's view of the world, where the data is normalized and before applying a likelihood. + + All args and kwargs are passed on to models_plots.plot. + """ + kwargs['plot_raw'] = True + plot_fit(model,*args, **kwargs) diff --git a/GPy/plotting/matplot_dep/netpbmfile.py b/GPy/plotting/matplot_dep/netpbmfile.py new file mode 100644 index 00000000..030bd574 --- /dev/null +++ b/GPy/plotting/matplot_dep/netpbmfile.py @@ -0,0 +1,331 @@ +#!/usr/bin/env python +# -*- coding: utf-8 -*- +# netpbmfile.py + +# Copyright (c) 2011-2013, Christoph Gohlke +# Copyright (c) 2011-2013, The Regents of the University of California +# Produced at the Laboratory for Fluorescence Dynamics. +# All rights reserved. +# +# Redistribution and use in source and binary forms, with or without +# modification, are permitted provided that the following conditions are met: +# +# * Redistributions of source code must retain the above copyright +# notice, this list of conditions and the following disclaimer. +# * Redistributions in binary form must reproduce the above copyright +# notice, this list of conditions and the following disclaimer in the +# documentation and/or other materials provided with the distribution. +# * Neither the name of the copyright holders nor the names of any +# contributors may be used to endorse or promote products derived +# from this software without specific prior written permission. +# +# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" +# AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE +# IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE +# ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE +# LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR +# CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF +# SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS +# INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN +# CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) +# ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE +# POSSIBILITY OF SUCH DAMAGE. + +"""Read and write image data from respectively to Netpbm files. + +This implementation follows the Netpbm format specifications at +http://netpbm.sourceforge.net/doc/. No gamma correction is performed. + +The following image formats are supported: PBM (bi-level), PGM (grayscale), +PPM (color), PAM (arbitrary), XV thumbnail (RGB332, read-only). + +:Author: + `Christoph Gohlke `_ + +:Organization: + Laboratory for Fluorescence Dynamics, University of California, Irvine + +:Version: 2013.01.18 + +Requirements +------------ +* `CPython 2.7, 3.2 or 3.3 `_ +* `Numpy 1.7 `_ +* `Matplotlib 1.2 `_ (optional for plotting) + +Examples +-------- +>>> im1 = numpy.array([[0, 1],[65534, 65535]], dtype=numpy.uint16) +>>> imsave('_tmp.pgm', im1) +>>> im2 = imread('_tmp.pgm') +>>> assert numpy.all(im1 == im2) + +""" + +from __future__ import division, print_function + +import sys +import re +import math +from copy import deepcopy + +import numpy + +__version__ = '2013.01.18' +__docformat__ = 'restructuredtext en' +__all__ = ['imread', 'imsave', 'NetpbmFile'] + + +def imread(filename, *args, **kwargs): + """Return image data from Netpbm file as numpy array. + + `args` and `kwargs` are arguments to NetpbmFile.asarray(). + + Examples + -------- + >>> image = imread('_tmp.pgm') + + """ + try: + netpbm = NetpbmFile(filename) + image = netpbm.asarray() + finally: + netpbm.close() + return image + + +def imsave(filename, data, maxval=None, pam=False): + """Write image data to Netpbm file. + + Examples + -------- + >>> image = numpy.array([[0, 1],[65534, 65535]], dtype=numpy.uint16) + >>> imsave('_tmp.pgm', image) + + """ + try: + netpbm = NetpbmFile(data, maxval=maxval) + netpbm.write(filename, pam=pam) + finally: + netpbm.close() + + +class NetpbmFile(object): + """Read and write Netpbm PAM, PBM, PGM, PPM, files.""" + + _types = {b'P1': b'BLACKANDWHITE', b'P2': b'GRAYSCALE', b'P3': b'RGB', + b'P4': b'BLACKANDWHITE', b'P5': b'GRAYSCALE', b'P6': b'RGB', + b'P7 332': b'RGB', b'P7': b'RGB_ALPHA'} + + def __init__(self, arg=None, **kwargs): + """Initialize instance from filename, open file, or numpy array.""" + for attr in ('header', 'magicnum', 'width', 'height', 'maxval', + 'depth', 'tupltypes', '_filename', '_fh', '_data'): + setattr(self, attr, None) + if arg is None: + self._fromdata([], **kwargs) + elif isinstance(arg, basestring): + self._fh = open(arg, 'rb') + self._filename = arg + self._fromfile(self._fh, **kwargs) + elif hasattr(arg, 'seek'): + self._fromfile(arg, **kwargs) + self._fh = arg + else: + self._fromdata(arg, **kwargs) + + def asarray(self, copy=True, cache=False, **kwargs): + """Return image data from file as numpy array.""" + data = self._data + if data is None: + data = self._read_data(self._fh, **kwargs) + if cache: + self._data = data + else: + return data + return deepcopy(data) if copy else data + + def write(self, arg, **kwargs): + """Write instance to file.""" + if hasattr(arg, 'seek'): + self._tofile(arg, **kwargs) + else: + with open(arg, 'wb') as fid: + self._tofile(fid, **kwargs) + + def close(self): + """Close open file. Future asarray calls might fail.""" + if self._filename and self._fh: + self._fh.close() + self._fh = None + + def __del__(self): + self.close() + + def _fromfile(self, fh): + """Initialize instance from open file.""" + fh.seek(0) + data = fh.read(4096) + if (len(data) < 7) or not (b'0' < data[1:2] < b'8'): + raise ValueError("Not a Netpbm file:\n%s" % data[:32]) + try: + self._read_pam_header(data) + except Exception: + try: + self._read_pnm_header(data) + except Exception: + raise ValueError("Not a Netpbm file:\n%s" % data[:32]) + + def _read_pam_header(self, data): + """Read PAM header and initialize instance.""" + regroups = re.search( + b"(^P7[\n\r]+(?:(?:[\n\r]+)|(?:#.*)|" + b"(HEIGHT\s+\d+)|(WIDTH\s+\d+)|(DEPTH\s+\d+)|(MAXVAL\s+\d+)|" + b"(?:TUPLTYPE\s+\w+))*ENDHDR\n)", data).groups() + self.header = regroups[0] + self.magicnum = b'P7' + for group in regroups[1:]: + key, value = group.split() + setattr(self, unicode(key).lower(), int(value)) + matches = re.findall(b"(TUPLTYPE\s+\w+)", self.header) + self.tupltypes = [s.split(None, 1)[1] for s in matches] + + def _read_pnm_header(self, data): + """Read PNM header and initialize instance.""" + bpm = data[1:2] in b"14" + regroups = re.search(b"".join(( + b"(^(P[123456]|P7 332)\s+(?:#.*[\r\n])*", + b"\s*(\d+)\s+(?:#.*[\r\n])*", + b"\s*(\d+)\s+(?:#.*[\r\n])*" * (not bpm), + b"\s*(\d+)\s(?:\s*#.*[\r\n]\s)*)")), data).groups() + (1, ) * bpm + self.header = regroups[0] + self.magicnum = regroups[1] + self.width = int(regroups[2]) + self.height = int(regroups[3]) + self.maxval = int(regroups[4]) + self.depth = 3 if self.magicnum in b"P3P6P7 332" else 1 + self.tupltypes = [self._types[self.magicnum]] + + def _read_data(self, fh, byteorder='>'): + """Return image data from open file as numpy array.""" + fh.seek(len(self.header)) + data = fh.read() + dtype = 'u1' if self.maxval < 256 else byteorder + 'u2' + depth = 1 if self.magicnum == b"P7 332" else self.depth + shape = [-1, self.height, self.width, depth] + size = numpy.prod(shape[1:]) + if self.magicnum in b"P1P2P3": + data = numpy.array(data.split(None, size)[:size], dtype) + data = data.reshape(shape) + elif self.maxval == 1: + shape[2] = int(math.ceil(self.width / 8)) + data = numpy.frombuffer(data, dtype).reshape(shape) + data = numpy.unpackbits(data, axis=-2)[:, :, :self.width, :] + else: + data = numpy.frombuffer(data, dtype) + data = data[:size * (data.size // size)].reshape(shape) + if data.shape[0] < 2: + data = data.reshape(data.shape[1:]) + if data.shape[-1] < 2: + data = data.reshape(data.shape[:-1]) + if self.magicnum == b"P7 332": + rgb332 = numpy.array(list(numpy.ndindex(8, 8, 4)), numpy.uint8) + rgb332 *= [36, 36, 85] + data = numpy.take(rgb332, data, axis=0) + return data + + def _fromdata(self, data, maxval=None): + """Initialize instance from numpy array.""" + data = numpy.array(data, ndmin=2, copy=True) + if data.dtype.kind not in "uib": + raise ValueError("not an integer type: %s" % data.dtype) + if data.dtype.kind == 'i' and numpy.min(data) < 0: + raise ValueError("data out of range: %i" % numpy.min(data)) + if maxval is None: + maxval = numpy.max(data) + maxval = 255 if maxval < 256 else 65535 + if maxval < 0 or maxval > 65535: + raise ValueError("data out of range: %i" % maxval) + data = data.astype('u1' if maxval < 256 else '>u2') + self._data = data + if data.ndim > 2 and data.shape[-1] in (3, 4): + self.depth = data.shape[-1] + self.width = data.shape[-2] + self.height = data.shape[-3] + self.magicnum = b'P7' if self.depth == 4 else b'P6' + else: + self.depth = 1 + self.width = data.shape[-1] + self.height = data.shape[-2] + self.magicnum = b'P5' if maxval > 1 else b'P4' + self.maxval = maxval + self.tupltypes = [self._types[self.magicnum]] + self.header = self._header() + + def _tofile(self, fh, pam=False): + """Write Netbm file.""" + fh.seek(0) + fh.write(self._header(pam)) + data = self.asarray(copy=False) + if self.maxval == 1: + data = numpy.packbits(data, axis=-1) + data.tofile(fh) + + def _header(self, pam=False): + """Return file header as byte string.""" + if pam or self.magicnum == b'P7': + header = "\n".join(( + "P7", + "HEIGHT %i" % self.height, + "WIDTH %i" % self.width, + "DEPTH %i" % self.depth, + "MAXVAL %i" % self.maxval, + "\n".join("TUPLTYPE %s" % unicode(i) for i in self.tupltypes), + "ENDHDR\n")) + elif self.maxval == 1: + header = "P4 %i %i\n" % (self.width, self.height) + elif self.depth == 1: + header = "P5 %i %i %i\n" % (self.width, self.height, self.maxval) + else: + header = "P6 %i %i %i\n" % (self.width, self.height, self.maxval) + if sys.version_info[0] > 2: + header = bytes(header, 'ascii') + return header + + def __str__(self): + """Return information about instance.""" + return unicode(self.header) + + +if sys.version_info[0] > 2: + basestring = str + unicode = lambda x: str(x, 'ascii') + +if __name__ == "__main__": + # Show images specified on command line or all images in current directory + from glob import glob + from matplotlib import pyplot + files = sys.argv[1:] if len(sys.argv) > 1 else glob('*.p*m') + for fname in files: + try: + pam = NetpbmFile(fname) + img = pam.asarray(copy=False) + if False: + pam.write('_tmp.pgm.out', pam=True) + img2 = imread('_tmp.pgm.out') + assert numpy.all(img == img2) + imsave('_tmp.pgm.out', img) + img2 = imread('_tmp.pgm.out') + assert numpy.all(img == img2) + pam.close() + except ValueError as e: + print(fname, e) + continue + _shape = img.shape + if img.ndim > 3 or (img.ndim > 2 and img.shape[-1] not in (3, 4)): + img = img[0] + cmap = 'gray' if pam.maxval > 1 else 'binary' + pyplot.imshow(img, cmap, interpolation='nearest') + pyplot.title("%s %s %s %s" % (fname, unicode(pam.magicnum), + _shape, img.dtype)) + pyplot.show() diff --git a/GPy/plotting/matplot_dep/priors_plots.py b/GPy/plotting/matplot_dep/priors_plots.py new file mode 100644 index 00000000..8f02a03b --- /dev/null +++ b/GPy/plotting/matplot_dep/priors_plots.py @@ -0,0 +1,32 @@ +# Copyright (c) 2012, GPy authors (see AUTHORS.txt). +# Licensed under the BSD 3-clause license (see LICENSE.txt) + + +import numpy as np +try: + import pylab as pb +except: + pass + + +def univariate_plot(prior): + rvs = prior.rvs(1000) + pb.hist(rvs, 100, normed=True) + xmin, xmax = pb.xlim() + xx = np.linspace(xmin, xmax, 1000) + pb.plot(xx, prior.pdf(xx), 'r', linewidth=2) + +def plot(prior): + + if prior.input_dim == 2: + rvs = prior.rvs(200) + pb.plot(rvs[:, 0], rvs[:, 1], 'kx', mew=1.5) + xmin, xmax = pb.xlim() + ymin, ymax = pb.ylim() + xx, yy = np.mgrid[xmin:xmax:100j, ymin:ymax:100j] + xflat = np.vstack((xx.flatten(), yy.flatten())).T + zz = prior.pdf(xflat).reshape(100, 100) + pb.contour(xx, yy, zz, linewidths=2) + + else: + raise NotImplementedError, "Cannot define a frame with more than two input dimensions" diff --git a/GPy/plotting/matplot_dep/ssgplvm.py b/GPy/plotting/matplot_dep/ssgplvm.py new file mode 100644 index 00000000..ef45a759 --- /dev/null +++ b/GPy/plotting/matplot_dep/ssgplvm.py @@ -0,0 +1,28 @@ +""" +The module plotting results for SSGPLVM +""" + +import pylab + +from ...models import SSGPLVM +from img_plots import plot_2D_images + +class SSGPLVM_plot(object): + def __init__(self,model, imgsize): + assert isinstance(model,SSGPLVM) + self.model = model + self.imgsize= imgsize + assert model.Y.shape[1] == imgsize[0]*imgsize[1] + + def plot_inducing(self): + fig1 = pylab.figure() + mean = self.model.posterior.mean + arr = mean.reshape(*(mean.shape[0],self.imgsize[1],self.imgsize[0])) + plot_2D_images(fig1, arr) + fig1.gca().set_title('The mean of inducing points') + + fig2 = pylab.figure() + covar = self.model.posterior.covariance + plot_2D_images(fig2, covar) + fig2.gca().set_title('The variance of inducing points') + diff --git a/GPy/plotting/matplot_dep/svig_plots.py b/GPy/plotting/matplot_dep/svig_plots.py new file mode 100644 index 00000000..95344643 --- /dev/null +++ b/GPy/plotting/matplot_dep/svig_plots.py @@ -0,0 +1,43 @@ +# Copyright (c) 2012, James Hensman and Nicolo' Fusi +# Licensed under the BSD 3-clause license (see LICENSE.txt) + +import numpy as np +import pylab as pb + + +def plot(model, ax=None, fignum=None, Z_height=None, **kwargs): + + if ax is None: + fig = pb.figure(num=fignum) + ax = fig.add_subplot(111) + + #horrible hack here: + data = model.likelihood.data.copy() + model.likelihood.data = model.Y + GP.plot(model, ax=ax, **kwargs) + model.likelihood.data = data + + Zu = model.Z * model._Xscale + model._Xoffset + if model.input_dim==1: + ax.plot(model.X_batch, model.likelihood.data, 'gx',mew=2) + if Z_height is None: + Z_height = ax.get_ylim()[0] + ax.plot(Zu, np.zeros_like(Zu) + Z_height, 'r|', mew=1.5, markersize=12) + + if model.input_dim==2: + ax.scatter(model.X[:,0], model.X[:,1], 20., model.Y[:,0], linewidth=0, cmap=pb.cm.jet) # @UndefinedVariable + ax.plot(Zu[:,0], Zu[:,1], 'w^') + +def plot_traces(model): + + pb.figure() + t = np.array(model._param_trace) + pb.subplot(2,1,1) + for l,ti in zip(model._get_param_names(),t.T): + if not l[:3]=='iip': + pb.plot(ti,label=l) + pb.legend(loc=0) + + pb.subplot(2,1,2) + pb.plot(np.asarray(model._ll_trace),label='stochastic likelihood') + pb.legend(loc=0) diff --git a/GPy/plotting/matplot_dep/variational_plots.py b/GPy/plotting/matplot_dep/variational_plots.py new file mode 100644 index 00000000..5cced10d --- /dev/null +++ b/GPy/plotting/matplot_dep/variational_plots.py @@ -0,0 +1,100 @@ +import pylab as pb, numpy as np + +def plot(parameterized, fignum=None, ax=None, colors=None): + """ + Plot latent space X in 1D: + + - if fig is given, create input_dim subplots in fig and plot in these + - if ax is given plot input_dim 1D latent space plots of X into each `axis` + - if neither fig nor ax is given create a figure with fignum and plot in there + + colors: + colors of different latent space dimensions input_dim + + """ + if ax is None: + fig = pb.figure(num=fignum, figsize=(8, min(12, (2 * parameterized.mean.shape[1])))) + if colors is None: + colors = pb.gca()._get_lines.color_cycle + pb.clf() + else: + colors = iter(colors) + plots = [] + means, variances = parameterized.mean, parameterized.variance + x = np.arange(means.shape[0]) + for i in range(means.shape[1]): + if ax is None: + a = fig.add_subplot(means.shape[1], 1, i + 1) + elif isinstance(ax, (tuple, list)): + a = ax[i] + else: + raise ValueError("Need one ax per latent dimension input_dim") + a.plot(means, c='k', alpha=.3) + plots.extend(a.plot(x, means.T[i], c=colors.next(), label=r"$\mathbf{{X_{{{}}}}}$".format(i))) + a.fill_between(x, + means.T[i] - 2 * np.sqrt(variances.T[i]), + means.T[i] + 2 * np.sqrt(variances.T[i]), + facecolor=plots[-1].get_color(), + alpha=.3) + a.legend(borderaxespad=0.) + a.set_xlim(x.min(), x.max()) + if i < means.shape[1] - 1: + a.set_xticklabels('') + pb.draw() + fig.tight_layout(h_pad=.01) # , rect=(0, 0, 1, .95)) + return fig + +def plot_SpikeSlab(parameterized, fignum=None, ax=None, colors=None, side_by_side=True): + """ + Plot latent space X in 1D: + + - if fig is given, create input_dim subplots in fig and plot in these + - if ax is given plot input_dim 1D latent space plots of X into each `axis` + - if neither fig nor ax is given create a figure with fignum and plot in there + + colors: + colors of different latent space dimensions input_dim + + """ + if ax is None: + if side_by_side: + fig = pb.figure(num=fignum, figsize=(16, min(12, (2 * parameterized.mean.shape[1])))) + else: + fig = pb.figure(num=fignum, figsize=(8, min(12, (2 * parameterized.mean.shape[1])))) + if colors is None: + colors = pb.gca()._get_lines.color_cycle + pb.clf() + else: + colors = iter(colors) + plots = [] + means, variances, gamma = parameterized.mean, parameterized.variance, parameterized.binary_prob + x = np.arange(means.shape[0]) + for i in range(means.shape[1]): + if side_by_side: + sub1 = (means.shape[1],2,2*i+1) + sub2 = (means.shape[1],2,2*i+2) + else: + sub1 = (means.shape[1]*2,1,2*i+1) + sub2 = (means.shape[1]*2,1,2*i+2) + + # mean and variance plot + a = fig.add_subplot(*sub1) + a.plot(means, c='k', alpha=.3) + plots.extend(a.plot(x, means.T[i], c=colors.next(), label=r"$\mathbf{{X_{{{}}}}}$".format(i))) + a.fill_between(x, + means.T[i] - 2 * np.sqrt(variances.T[i]), + means.T[i] + 2 * np.sqrt(variances.T[i]), + facecolor=plots[-1].get_color(), + alpha=.3) + a.legend(borderaxespad=0.) + a.set_xlim(x.min(), x.max()) + if i < means.shape[1] - 1: + a.set_xticklabels('') + # binary prob plot + a = fig.add_subplot(*sub2) + a.bar(x,gamma[:,i],bottom=0.,linewidth=0,width=1.0,align='center') + a.set_xlim(x.min(), x.max()) + a.set_ylim([0.,1.]) + pb.draw() + fig.tight_layout(h_pad=.01) # , rect=(0, 0, 1, .95)) + return fig diff --git a/GPy/util/visualize.py b/GPy/plotting/matplot_dep/visualize.py similarity index 83% rename from GPy/util/visualize.py rename to GPy/plotting/matplot_dep/visualize.py index 7645ec40..9ff41730 100644 --- a/GPy/util/visualize.py +++ b/GPy/plotting/matplot_dep/visualize.py @@ -4,6 +4,7 @@ import GPy import numpy as np import matplotlib as mpl import time +from GPy.core.parameterization.variational import VariationalPosterior try: import visual visual_available = True @@ -72,17 +73,21 @@ class vector_show(matplotlib_show): """ def __init__(self, vals, axes=None): matplotlib_show.__init__(self, vals, axes) - self.handle = self.axes.plot(np.arange(0, len(vals))[:, None], self.vals.T)[0] + #assert vals.ndim == 2, "Please give a vector in [n x 1] to plot" + #assert vals.shape[1] == 1, "only showing a vector in one dimension" + self.size = vals.size + self.handle = self.axes.plot(np.arange(0, vals.size)[:, None], vals)[0] def modify(self, vals): self.vals = vals.copy() xdata, ydata = self.handle.get_data() - self.handle.set_data(xdata, self.vals.T) + assert vals.size == self.size, "values passed into modify changed size! vals.size:{} != in.size:{}".format(vals.size, self.size) + self.handle.set_data(xdata, self.vals) self.axes.figure.canvas.draw() class lvm(matplotlib_show): - def __init__(self, vals, model, data_visualize, latent_axes=None, sense_axes=None, latent_index=[0,1]): + def __init__(self, vals, model, data_visualize, latent_axes=None, sense_axes=None, latent_index=[0,1], disable_drag=False): """Visualize a latent variable model :param model: the latent variable model to visualize. @@ -90,19 +95,25 @@ class lvm(matplotlib_show): :type data_visualize: visualize.data_show type. :param latent_axes: the axes where the latent visualization should be plotted. """ - if vals == None: - vals = model.X[0] - + if vals is None: + if isinstance(model.X, VariationalPosterior): + vals = model.X.mean.values + else: + vals = model.X.values + if len(vals.shape)==1: + vals = vals[None,:] matplotlib_show.__init__(self, vals, axes=latent_axes) if isinstance(latent_axes,mpl.axes.Axes): self.cid = latent_axes.figure.canvas.mpl_connect('button_press_event', self.on_click) - self.cid = latent_axes.figure.canvas.mpl_connect('motion_notify_event', self.on_move) + if not disable_drag: + self.cid = latent_axes.figure.canvas.mpl_connect('motion_notify_event', self.on_move) self.cid = latent_axes.figure.canvas.mpl_connect('axes_leave_event', self.on_leave) self.cid = latent_axes.figure.canvas.mpl_connect('axes_enter_event', self.on_enter) else: self.cid = latent_axes[0].figure.canvas.mpl_connect('button_press_event', self.on_click) - self.cid = latent_axes[0].figure.canvas.mpl_connect('motion_notify_event', self.on_move) + if not disable_drag: + self.cid = latent_axes[0].figure.canvas.mpl_connect('motion_notify_event', self.on_move) self.cid = latent_axes[0].figure.canvas.mpl_connect('axes_leave_event', self.on_leave) self.cid = latent_axes[0].figure.canvas.mpl_connect('axes_enter_event', self.on_enter) @@ -114,6 +125,7 @@ class lvm(matplotlib_show): self.move_on = False self.latent_index = latent_index self.latent_dim = model.input_dim + self.disable_drag = disable_drag # The red cross which shows current latent point. self.latent_values = vals @@ -123,10 +135,10 @@ class lvm(matplotlib_show): def modify(self, vals): """When latent values are modified update the latent representation and ulso update the output visualization.""" - self.vals = vals.copy() + self.vals = vals.view(np.ndarray).copy() y = self.model.predict(self.vals)[0] self.data_visualize.modify(y) - self.latent_handle.set_data(self.vals[self.latent_index[0]], self.vals[self.latent_index[1]]) + self.latent_handle.set_data(self.vals[0,self.latent_index[0]], self.vals[0,self.latent_index[1]]) self.axes.figure.canvas.draw() @@ -137,15 +149,20 @@ class lvm(matplotlib_show): def on_click(self, event): if event.inaxes!=self.latent_axes: return - self.move_on = not self.move_on - self.called = True + if self.disable_drag: + self.move_on = True + self.called = True + self.on_move(event) + else: + self.move_on = not self.move_on + self.called = True def on_move(self, event): if event.inaxes!=self.latent_axes: return if self.called and self.move_on: # Call modify code on move - self.latent_values[self.latent_index[0]]=event.xdata - self.latent_values[self.latent_index[1]]=event.ydata + self.latent_values[:, self.latent_index[0]]=event.xdata + self.latent_values[:, self.latent_index[1]]=event.ydata self.modify(self.latent_values) def show_sensitivities(self): @@ -175,7 +192,7 @@ class lvm_subplots(lvm): assert len(latent_axes)==self.nplots if vals==None: vals = Model.X[0, :] - self.latent_values = vals + self.latent_values = vals for i, axis in enumerate(latent_axes): if i == self.nplots-1: @@ -193,7 +210,7 @@ class lvm_dimselect(lvm): A visualizer for latent variable models which allows selection of the latent dimensions to use by clicking on a bar chart of their length scales. For an example of the visualizer's use try: - + GPy.examples.dimensionality_reduction.BGPVLM_oil() """ @@ -208,20 +225,20 @@ class lvm_dimselect(lvm): self.labels = labels lvm.__init__(self,vals,model,data_visualize,latent_axes,sense_axes,latent_index) self.show_sensitivities() - print "use left and right mouse butons to select dimensions" + print self.latent_values + print "use left and right mouse buttons to select dimensions" def on_click(self, event): - if event.inaxes==self.sense_axes: new_index = max(0,min(int(np.round(event.xdata-0.5)),self.model.input_dim-1)) if event.button == 1: # Make it red if and y-axis (red=port=left) if it is a left button click - self.latent_index[1] = new_index + self.latent_index[1] = new_index else: # Make it green and x-axis (green=starboard=right) if it is a right button click self.latent_index[0] = new_index - + self.show_sensitivities() self.latent_axes.cla() @@ -238,6 +255,7 @@ class lvm_dimselect(lvm): def on_leave(self,event): + print type(self.latent_values) latent_values = self.latent_values.copy() y = self.model.predict(latent_values[None,:])[0] self.data_visualize.modify(y) @@ -263,8 +281,11 @@ class image_show(matplotlib_show): :param preset_mean: the preset mean of a scaled image. :type preset_mean: double :param preset_std: the preset standard deviation of a scaled image. - :type preset_std: double""" - def __init__(self, vals, axes=None, dimensions=(16,16), transpose=False, order='C', invert=False, scale=False, palette=[], preset_mean = 0., preset_std = -1., select_image=0): + :type preset_std: double + :param cmap: the colormap for image visualization + :type cmap: matplotlib.cm""" + + def __init__(self, vals, axes=None, dimensions=(16,16), transpose=False, order='C', invert=False, scale=False, palette=[], preset_mean=0., preset_std=1., select_image=0, cmap=None): matplotlib_show.__init__(self, vals, axes) self.dimensions = dimensions self.transpose = transpose @@ -279,14 +300,16 @@ class image_show(matplotlib_show): self.set_image(self.vals) if not self.palette == []: # Can just show the image (self.set_image() took care of setting the palette) self.handle = self.axes.imshow(self.vals, interpolation='nearest') - else: # Use a boring gray map. - self.handle = self.axes.imshow(self.vals, cmap=plt.cm.gray, interpolation='nearest') # @UndefinedVariable + elif cmap==None: # Use a jet map. + self.handle = self.axes.imshow(self.vals, cmap=plt.cm.jet, interpolation='nearest') # @UndefinedVariable + else: # Use the selected map. + self.handle = self.axes.imshow(self.vals, cmap=cmap, interpolation='nearest') # @UndefinedVariable plt.show() def modify(self, vals): self.set_image(vals.copy()) self.handle.set_array(self.vals) - self.axes.figure.canvas.draw() + self.axes.figure.canvas.draw() def set_image(self, vals): dim = self.dimensions[0] * self.dimensions[1] @@ -304,7 +327,7 @@ class image_show(matplotlib_show): last_col = (iC+1)*self.dimensions[1] self.vals[first_row:last_row, first_col:last_col] = cur_img - else: + else: self.vals = np.reshape(vals[0,dim*self.select_image+np.array(range(dim))], self.dimensions, order=self.order) if self.transpose: self.vals = self.vals.T @@ -314,13 +337,12 @@ class image_show(matplotlib_show): self.vals = -self.vals # un-normalizing, for visualisation purposes: - if self.preset_std >= 0: # The Mean is assumed to be in the range (0,255) - self.vals = self.vals*self.preset_std + self.preset_mean - # Clipping the values: - self.vals[self.vals < 0] = 0 - self.vals[self.vals > 255] = 255 - else: - self.vals = 255*(self.vals - self.vals.min())/(self.vals.max() - self.vals.min()) + self.vals = self.vals*self.preset_std + self.preset_mean + # Clipping the values: + #self.vals[self.vals < 0] = 0 + #self.vals[self.vals > 255] = 255 + #else: + #self.vals = 255*(self.vals - self.vals.min())/(self.vals.max() - self.vals.min()) if not self.palette == []: # applying using an image palette (e.g. if the image has been quantized) from PIL import Image self.vals = Image.fromarray(self.vals.astype('uint8')) @@ -358,7 +380,7 @@ class mocap_data_show_vpython(vpython_show): def modify_edges(self): self.line_handle = [] - if not self.connect==None: + if not self.connect==None: self.I, self.J = np.nonzero(self.connect) for rod, i, j in zip(self.rods, self.I, self.J): rod.pos, rod.axis = self.pos_axis(i, j) @@ -383,14 +405,13 @@ class mocap_data_show_vpython(vpython_show): def process_values(self): raise NotImplementedError, "this needs to be implemented to use the data_show class" - class mocap_data_show(matplotlib_show): """Base class for visualizing motion capture data.""" def __init__(self, vals, axes=None, connect=None): if axes==None: fig = plt.figure() - axes = fig.add_subplot(111, projection='3d') + axes = fig.add_subplot(111, projection='3d', aspect='equal') matplotlib_show.__init__(self, vals, axes) self.connect = connect @@ -403,7 +424,7 @@ class mocap_data_show(matplotlib_show): def draw_vertices(self): self.points_handle = self.axes.scatter(self.vals[:, 0], self.vals[:, 1], self.vals[:, 2]) - + def draw_edges(self): self.line_handle = [] if not self.connect==None: @@ -422,12 +443,13 @@ class mocap_data_show(matplotlib_show): z.append(self.vals[j, 2]) z.append(np.NaN) self.line_handle = self.axes.plot(np.array(x), np.array(y), np.array(z), 'b-') - + def modify(self, vals): self.vals = vals.copy() self.process_values() self.initialize_axes_modify() self.draw_vertices() + self.initialize_axes() self.finalize_axes_modify() self.draw_edges() self.axes.figure.canvas.draw() @@ -435,11 +457,12 @@ class mocap_data_show(matplotlib_show): def process_values(self): raise NotImplementedError, "this needs to be implemented to use the data_show class" - def initialize_axes(self): + def initialize_axes(self, boundary=0.05): """Set up the axes with the right limits and scaling.""" - self.x_lim = np.array([self.vals[:, 0].min(), self.vals[:, 0].max()]) - self.y_lim = np.array([self.vals[:, 1].min(), self.vals[:, 1].max()]) - self.z_lim = np.array([self.vals[:, 2].min(), self.vals[:, 2].max()]) + bs = [(self.vals[:, i].max()-self.vals[:, i].min())*boundary for i in xrange(3)] + self.x_lim = np.array([self.vals[:, 0].min()-bs[0], self.vals[:, 0].max()+bs[0]]) + self.y_lim = np.array([self.vals[:, 1].min()-bs[1], self.vals[:, 1].max()+bs[1]]) + self.z_lim = np.array([self.vals[:, 2].min()-bs[2], self.vals[:, 2].max()+bs[2]]) def initialize_axes_modify(self): self.points_handle.remove() @@ -449,44 +472,46 @@ class mocap_data_show(matplotlib_show): self.axes.set_xlim(self.x_lim) self.axes.set_ylim(self.y_lim) self.axes.set_zlim(self.z_lim) - self.axes.auto_scale_xyz([-1., 1.], [-1., 1.], [-1.5, 1.5]) - - #self.axes.set_aspect('equal') - self.axes.autoscale(enable=False) + self.axes.auto_scale_xyz([-1., 1.], [-1., 1.], [-1., 1.]) + +# self.axes.set_aspect('equal') +# self.axes.autoscale(enable=False) def finalize_axes_modify(self): self.axes.set_xlim(self.x_lim) self.axes.set_ylim(self.y_lim) self.axes.set_zlim(self.z_lim) -class stick_show(mocap_data_show_vpython): +class stick_show(mocap_data_show): """Show a three dimensional point cloud as a figure. Connect elements of the figure together using the matrix connect.""" - def __init__(self, vals, connect=None, scene=None): - mocap_data_show_vpython.__init__(self, vals, scene=scene, connect=connect, radius=0.04) + def __init__(self, vals, connect=None, axes=None): + if len(vals.shape)==1: + vals = vals[None,:] + mocap_data_show.__init__(self, vals, axes=axes, connect=connect) def process_values(self): self.vals = self.vals.reshape((3, self.vals.shape[1]/3)).T -class skeleton_show(mocap_data_show_vpython): +class skeleton_show(mocap_data_show): """data_show class for visualizing motion capture data encoded as a skeleton with angles.""" - def __init__(self, vals, skel, scene=None, padding=0): + def __init__(self, vals, skel, axes=None, padding=0): """data_show class for visualizing motion capture data encoded as a skeleton with angles. :param vals: set of modeled angles to use for printing in the axis when it's first created. :type vals: np.array :param skel: skeleton object that has the parameters of the motion capture skeleton associated with it. - :type skel: mocap.skeleton object + :type skel: mocap.skeleton object :param padding: :type int """ self.skel = skel self.padding = padding connect = skel.connection_matrix() - mocap_data_show_vpython.__init__(self, vals, scene=scene, connect=connect, radius=0.4) + mocap_data_show.__init__(self, vals, axes=axes, connect=connect) def process_values(self): """Takes a set of angles and converts them to the x,y,z coordinates in the internal prepresentation of the class, ready for plotting. :param vals: the values that are being modelled.""" - + if self.padding>0: channels = np.zeros((self.vals.shape[0], self.vals.shape[1]+self.padding)) channels[:, 0:self.vals.shape[0]] = self.vals @@ -498,7 +523,7 @@ class skeleton_show(mocap_data_show_vpython): self.vals[:, 0] = vals_mat[:, 0].copy() self.vals[:, 1] = vals_mat[:, 2].copy() self.vals[:, 2] = vals_mat[:, 1].copy() - + def wrap_around(self, lim, connect): quot = lim[1] - lim[0] self.vals = rem(self.vals, quot)+lim[0] @@ -520,7 +545,7 @@ def data_play(Y, visualizer, frame_rate=30): Example usage: This example loads in the CMU mocap database (http://mocap.cs.cmu.edu) subject number 35 motion number 01. It then plays it using the mocap_show visualize object. - + .. code-block:: python data = GPy.util.datasets.cmu_mocap(subject='35', train_motions=['01']) @@ -530,7 +555,7 @@ def data_play(Y, visualizer, frame_rate=30): GPy.util.visualize.data_play(Y, visualize) """ - + for y in Y: visualizer.modify(y[None, :]) diff --git a/GPy/testing/__init__.py b/GPy/testing/__init__.py index f5a4c54f..2e64d90e 100644 --- a/GPy/testing/__init__.py +++ b/GPy/testing/__init__.py @@ -1,3 +1,5 @@ +# Copyright (c) 2014, Max Zwiessele +# Licensed under the BSD 3-clause license (see LICENSE.txt) """ MaxZ diff --git a/GPy/testing/bgplvm_tests.py b/GPy/testing/bgplvm_tests.py deleted file mode 100644 index 1192448a..00000000 --- a/GPy/testing/bgplvm_tests.py +++ /dev/null @@ -1,85 +0,0 @@ -# Copyright (c) 2012, Nicolo Fusi -# Licensed under the BSD 3-clause license (see LICENSE.txt) - -import unittest -import numpy as np -import GPy -from ..models import BayesianGPLVM - -class BGPLVMTests(unittest.TestCase): - def test_bias_kern(self): - N, num_inducing, input_dim, D = 10, 3, 2, 4 - X = np.random.rand(N, input_dim) - k = GPy.kern.rbf(input_dim) + GPy.kern.white(input_dim, 0.00001) - K = k.K(X) - Y = np.random.multivariate_normal(np.zeros(N),K,input_dim).T - Y -= Y.mean(axis=0) - k = GPy.kern.bias(input_dim) + GPy.kern.white(input_dim, 0.00001) - m = BayesianGPLVM(Y, input_dim, kernel=k, num_inducing=num_inducing) - m.randomize() - self.assertTrue(m.checkgrad()) - - def test_linear_kern(self): - N, num_inducing, input_dim, D = 10, 3, 2, 4 - X = np.random.rand(N, input_dim) - k = GPy.kern.rbf(input_dim) + GPy.kern.white(input_dim, 0.00001) - K = k.K(X) - Y = np.random.multivariate_normal(np.zeros(N),K,input_dim).T - Y -= Y.mean(axis=0) - k = GPy.kern.linear(input_dim) + GPy.kern.white(input_dim, 0.00001) - m = BayesianGPLVM(Y, input_dim, kernel=k, num_inducing=num_inducing) - m.randomize() - self.assertTrue(m.checkgrad()) - - def test_rbf_kern(self): - N, num_inducing, input_dim, D = 10, 3, 2, 4 - X = np.random.rand(N, input_dim) - k = GPy.kern.rbf(input_dim) + GPy.kern.white(input_dim, 0.00001) - K = k.K(X) - Y = np.random.multivariate_normal(np.zeros(N),K,input_dim).T - Y -= Y.mean(axis=0) - k = GPy.kern.rbf(input_dim) + GPy.kern.white(input_dim, 0.00001) - m = BayesianGPLVM(Y, input_dim, kernel=k, num_inducing=num_inducing) - m.randomize() - self.assertTrue(m.checkgrad()) - - def test_rbf_bias_kern(self): - N, num_inducing, input_dim, D = 10, 3, 2, 4 - X = np.random.rand(N, input_dim) - k = GPy.kern.rbf(input_dim) + GPy.kern.bias(input_dim) + GPy.kern.white(input_dim, 0.00001) - K = k.K(X) - Y = np.random.multivariate_normal(np.zeros(N),K,input_dim).T - Y -= Y.mean(axis=0) - k = GPy.kern.rbf(input_dim) + GPy.kern.bias(input_dim) + GPy.kern.white(input_dim, 0.00001) - m = BayesianGPLVM(Y, input_dim, kernel=k, num_inducing=num_inducing) - m.randomize() - self.assertTrue(m.checkgrad()) - - def test_rbf_line_kern(self): - N, num_inducing, input_dim, D = 10, 3, 2, 4 - X = np.random.rand(N, input_dim) - k = GPy.kern.rbf(input_dim) + GPy.kern.linear(input_dim) + GPy.kern.white(input_dim, 0.00001) - K = k.K(X) - Y = np.random.multivariate_normal(np.zeros(N),K,input_dim).T - Y -= Y.mean(axis=0) - k = GPy.kern.rbf(input_dim) + GPy.kern.bias(input_dim) + GPy.kern.white(input_dim, 0.00001) - m = BayesianGPLVM(Y, input_dim, kernel=k, num_inducing=num_inducing) - m.randomize() - self.assertTrue(m.checkgrad()) - - def test_linear_bias_kern(self): - N, num_inducing, input_dim, D = 30, 5, 4, 30 - X = np.random.rand(N, input_dim) - k = GPy.kern.linear(input_dim) + GPy.kern.bias(input_dim) + GPy.kern.white(input_dim, 0.00001) - K = k.K(X) - Y = np.random.multivariate_normal(np.zeros(N),K,input_dim).T - Y -= Y.mean(axis=0) - k = GPy.kern.linear(input_dim) + GPy.kern.bias(input_dim) + GPy.kern.white(input_dim, 0.00001) - m = BayesianGPLVM(Y, input_dim, kernel=k, num_inducing=num_inducing) - m.randomize() - self.assertTrue(m.checkgrad()) - - -if __name__ == "__main__": - print "Running unit tests, please be (very) patient..." - unittest.main() diff --git a/GPy/testing/fitc.py b/GPy/testing/fitc.py new file mode 100644 index 00000000..58f009d2 --- /dev/null +++ b/GPy/testing/fitc.py @@ -0,0 +1,34 @@ +# Copyright (c) 2014, James Hensman +# Licensed under the BSD 3-clause license (see LICENSE.txt) + +import unittest +import numpy as np +import GPy + +class FITCtest(unittest.TestCase): + def setUp(self): + ###################################### + # # 1 dimensional example + + N = 20 + # sample inputs and outputs + self.X1D = np.random.uniform(-3., 3., (N, 1)) + self.Y1D = np.sin(self.X1D) + np.random.randn(N, 1) * 0.05 + + ###################################### + # # 2 dimensional example + + # sample inputs and outputs + self.X2D = np.random.uniform(-3., 3., (N, 2)) + self.Y2D = np.sin(self.X2D[:, 0:1]) * np.sin(self.X2D[:, 1:2]) + np.random.randn(N, 1) * 0.05 + + def test_fitc_1d(self): + m = GPy.models.SparseGPRegression(self.X1D, self.Y1D) + m.inference_method=GPy.inference.latent_function_inference.FITC() + self.assertTrue(m.checkgrad()) + + def test_fitc_2d(self): + m = GPy.models.SparseGPRegression(self.X2D, self.Y2D) + m.inference_method=GPy.inference.latent_function_inference.FITC() + self.assertTrue(m.checkgrad()) + diff --git a/GPy/testing/index_operations_tests.py b/GPy/testing/index_operations_tests.py new file mode 100644 index 00000000..e5c2011a --- /dev/null +++ b/GPy/testing/index_operations_tests.py @@ -0,0 +1,135 @@ +# Copyright (c) 2014, Max Zwiessele +# Licensed under the BSD 3-clause license (see LICENSE.txt) + +import unittest +import numpy as np +from GPy.core.parameterization.index_operations import ParameterIndexOperations,\ + ParameterIndexOperationsView + +one, two, three = 'one', 'two', 'three' + +class Test(unittest.TestCase): + + def setUp(self): + self.param_index = ParameterIndexOperations() + self.param_index.add(one, [3,9]) + self.param_index.add(two, [0,5]) + self.param_index.add(three, [2,4,7,10]) + self.view = ParameterIndexOperationsView(self.param_index, 2, 6) + + def test_clear(self): + self.param_index.clear() + self.assertDictEqual(self.param_index._properties, {}) + + def test_remove(self): + removed = self.param_index.remove(three, np.r_[3:13]) + self.assertListEqual(removed.tolist(), [4,7,10]) + self.assertListEqual(self.param_index[three].tolist(), [2]) + removed = self.param_index.remove(one, [1]) + self.assertListEqual(removed.tolist(), []) + self.assertListEqual(self.param_index[one].tolist(), [3,9]) + self.assertListEqual(self.param_index.remove('not in there', []).tolist(), []) + removed = self.param_index.remove(one, [9]) + self.assertListEqual(removed.tolist(), [9]) + self.assertListEqual(self.param_index[one].tolist(), [3]) + self.assertListEqual(self.param_index.remove('not in there', [2,3,4]).tolist(), []) + self.assertListEqual(self.view.remove('not in there', [2,3,4]).tolist(), []) + + def test_shift_left(self): + self.view.shift_left(0, 2) + self.assertListEqual(self.param_index[three].tolist(), [2,5,8]) + self.assertListEqual(self.param_index[two].tolist(), [0,3]) + self.assertListEqual(self.param_index[one].tolist(), [7]) + #======================================================================= + # 0 1 2 3 4 5 6 7 8 9 10 + # one + # two two + # three three three + # view: [0 1 2 3 4 5 ] + #======================================================================= + self.assertListEqual(self.view[three].tolist(), [0,3]) + self.assertListEqual(self.view[two].tolist(), [1]) + self.assertListEqual(self.view[one].tolist(), [5]) + self.param_index.shift_left(7, 1) + #======================================================================= + # 0 1 2 3 4 5 6 7 8 9 10 + # + # two two + # three three three + # view: [0 1 2 3 4 5 ] + #======================================================================= + self.assertListEqual(self.param_index[three].tolist(), [2,5,7]) + self.assertListEqual(self.param_index[two].tolist(), [0,3]) + self.assertListEqual(self.param_index[one].tolist(), []) + self.assertListEqual(self.view[three].tolist(), [0,3,5]) + self.assertListEqual(self.view[two].tolist(), [1]) + self.assertListEqual(self.view[one].tolist(), []) + + def test_shift_right(self): + self.view.shift_right(3, 2) + self.assertListEqual(self.param_index[three].tolist(), [2,4,9,12]) + self.assertListEqual(self.param_index[two].tolist(), [0,7]) + self.assertListEqual(self.param_index[one].tolist(), [3,11]) + + def test_index_view(self): + #======================================================================= + # 0 1 2 3 4 5 6 7 8 9 10 + # one one + # two two + # three three three three + # view: [0 1 2 3 4 5 ] + #======================================================================= + self.view = ParameterIndexOperationsView(self.param_index, 2, 6) + self.assertSetEqual(set(self.view.properties()), set([one, two, three])) + for v,p in zip(self.view.properties_for(np.r_[:6]), self.param_index.properties_for(np.r_[2:2+6])): + self.assertEqual(v, p) + self.assertSetEqual(set(self.view[two]), set([3])) + self.assertSetEqual(set(self.param_index[two]), set([0, 5])) + self.view.add(two, np.array([0])) + self.assertSetEqual(set(self.view[two]), set([0,3])) + self.assertSetEqual(set(self.param_index[two]), set([0, 2, 5])) + self.view.clear() + for v,p in zip(self.view.properties_for(np.r_[:6]), self.param_index.properties_for(np.r_[2:2+6])): + self.assertEqual(v, p) + self.assertEqual(v, []) + param_index = ParameterIndexOperations() + param_index.add(one, [3,9]) + param_index.add(two, [0,5]) + param_index.add(three, [2,4,7,10]) + view2 = ParameterIndexOperationsView(param_index, 2, 8) + self.view.update(view2) + for [i,v],[i2,v2] in zip(sorted(param_index.items()), sorted(self.param_index.items())): + self.assertEqual(i, i2) + np.testing.assert_equal(v, v2) + + def test_view_of_view(self): + #======================================================================= + # 0 1 2 3 4 5 6 7 8 9 10 + # one one + # two two + # three three three three + # view: [0 1 2 3 4 5 ] + # view2: [0 1 2 3 4 5 ] + #======================================================================= + view2 = ParameterIndexOperationsView(self.view, 2, 6) + view2.shift_right(0, 2) + + def test_indexview_remove(self): + removed = self.view.remove(two, [3]) + self.assertListEqual(removed.tolist(), [3]) + removed = self.view.remove(three, np.r_[:5]) + self.assertListEqual(removed.tolist(), [0, 2]) + + def test_misc(self): + for k,v in self.param_index.copy()._properties.iteritems(): + self.assertListEqual(self.param_index[k].tolist(), v.tolist()) + self.assertEqual(self.param_index.size, 8) + self.assertEqual(self.view.size, 5) + + def test_print(self): + print self.param_index + print self.view + +if __name__ == "__main__": + #import sys;sys.argv = ['', 'Test.test_index_view'] + unittest.main() diff --git a/GPy/testing/inference_tests.py b/GPy/testing/inference_tests.py new file mode 100644 index 00000000..ac92c519 --- /dev/null +++ b/GPy/testing/inference_tests.py @@ -0,0 +1,84 @@ +# Copyright (c) 2014, Max Zwiessele +# Licensed under the BSD 3-clause license (see LICENSE.txt) + +""" +The test cases for various inference algorithms +""" + +import unittest, itertools +import numpy as np +import GPy + + +class InferenceXTestCase(unittest.TestCase): + + def genData(self): + D1,D2,N = 12,12,50 + np.random.seed(1234) + + x = np.linspace(0, 4 * np.pi, N)[:, None] + s1 = np.vectorize(lambda x: np.sin(x)) + s2 = np.vectorize(lambda x: np.cos(x)**2) + s3 = np.vectorize(lambda x:-np.exp(-np.cos(2 * x))) + sS = np.vectorize(lambda x: np.cos(x)) + + s1 = s1(x) + s2 = s2(x) + s3 = s3(x) + sS = sS(x) + + s1 -= s1.mean(); s1 /= s1.std(0) + s2 -= s2.mean(); s2 /= s2.std(0) + s3 -= s3.mean(); s3 /= s3.std(0) + sS -= sS.mean(); sS /= sS.std(0) + + S1 = np.hstack([s1, sS]) + S2 = np.hstack([s3, sS]) + + P1 = np.random.randn(S1.shape[1], D1) + P2 = np.random.randn(S2.shape[1], D2) + + Y1 = S1.dot(P1) + Y2 = S2.dot(P2) + + Y1 += .01 * np.random.randn(*Y1.shape) + Y2 += .01 * np.random.randn(*Y2.shape) + + Y1 -= Y1.mean(0) + Y2 -= Y2.mean(0) + Y1 /= Y1.std(0) + Y2 /= Y2.std(0) + + slist = [s1, s2, s3, sS] + slist_names = ["s1", "s2", "s3", "sS"] + Ylist = [Y1, Y2] + + return Ylist + + def test_inferenceX_BGPLVM(self): + Ys = self.genData() + m = GPy.models.BayesianGPLVM(Ys[0],5,kernel=GPy.kern.Linear(5,ARD=True)) + + x,mi = m.infer_newX(m.Y, optimize=False) + self.assertTrue(mi.checkgrad()) + + m.optimize(max_iters=10000) + x,mi = m.infer_newX(m.Y) + + self.assertTrue(np.allclose(m.X.mean, mi.X.mean)) + self.assertTrue(np.allclose(m.X.variance, mi.X.variance)) + + def test_inferenceX_GPLVM(self): + Ys = self.genData() + m = GPy.models.GPLVM(Ys[0],3,kernel=GPy.kern.RBF(3,ARD=True)) + + x,mi = m.infer_newX(m.Y, optimize=False) + self.assertTrue(mi.checkgrad()) + +# m.optimize(max_iters=10000) +# x,mi = m.infer_newX(m.Y) +# self.assertTrue(np.allclose(m.X, x)) + + +if __name__ == "__main__": + unittest.main() diff --git a/GPy/testing/kernel_tests.py b/GPy/testing/kernel_tests.py index 0fceac60..c1bb9265 100644 --- a/GPy/testing/kernel_tests.py +++ b/GPy/testing/kernel_tests.py @@ -4,118 +4,426 @@ import unittest import numpy as np import GPy +import sys +from GPy.core.parameterization.param import Param -verbose = False - -try: - import sympy - SYMPY_AVAILABLE=True -except ImportError: - SYMPY_AVAILABLE=False +verbose = 0 -class KernelTests(unittest.TestCase): - def test_kerneltie(self): - K = GPy.kern.rbf(5, ARD=True) - K.tie_params('.*[01]') - K.constrain_fixed('2') - X = np.random.rand(5,5) - Y = np.ones((5,1)) - m = GPy.models.GPRegression(X,Y,K) - self.assertTrue(m.checkgrad()) +class Kern_check_model(GPy.core.Model): + """ + This is a dummy model class used as a base class for checking that the + gradients of a given kernel are implemented correctly. It enables + checkgrad() to be called independently on a kernel. + """ + def __init__(self, kernel=None, dL_dK=None, X=None, X2=None): + GPy.core.Model.__init__(self, 'kernel_test_model') + if kernel==None: + kernel = GPy.kern.RBF(1) + kernel.randomize(loc=1, scale=0.1) + if X is None: + X = np.random.randn(20, kernel.input_dim) + if dL_dK is None: + if X2 is None: + dL_dK = np.ones((X.shape[0], X.shape[0])) + else: + dL_dK = np.ones((X.shape[0], X2.shape[0])) - def test_rbfkernel(self): - kern = GPy.kern.rbf(5) - self.assertTrue(GPy.kern.kern_test(kern, verbose=verbose)) + self.kernel = kernel + self.X = X + self.X2 = X2 + self.dL_dK = dL_dK - def test_rbf_sympykernel(self): - if SYMPY_AVAILABLE: - kern = GPy.kern.rbf_sympy(5) - self.assertTrue(GPy.kern.kern_test(kern, verbose=verbose)) + def is_positive_semi_definite(self): + v = np.linalg.eig(self.kernel.K(self.X))[0] + if any(v.real<=-1e-10): + print v.real.min() + return False + else: + return True - def test_eq_sympykernel(self): - if SYMPY_AVAILABLE: - kern = GPy.kern.eq_sympy(5, 3) - self.assertTrue(GPy.kern.kern_test(kern, output_ind=4, verbose=verbose)) + def log_likelihood(self): + return np.sum(self.dL_dK*self.kernel.K(self.X, self.X2)) - def test_ode1_eqkernel(self): - if SYMPY_AVAILABLE: - kern = GPy.kern.ode1_eq(3) - self.assertTrue(GPy.kern.kern_test(kern, output_ind=1, verbose=verbose, X_positive=True)) +class Kern_check_dK_dtheta(Kern_check_model): + """ + This class allows gradient checks for the gradient of a kernel with + respect to parameters. + """ + def __init__(self, kernel=None, dL_dK=None, X=None, X2=None): + Kern_check_model.__init__(self,kernel=kernel,dL_dK=dL_dK, X=X, X2=X2) + self.link_parameter(self.kernel) - def test_rbf_invkernel(self): - kern = GPy.kern.rbf_inv(5) - self.assertTrue(GPy.kern.kern_test(kern, verbose=verbose)) + def parameters_changed(self): + return self.kernel.update_gradients_full(self.dL_dK, self.X, self.X2) - def test_Matern32kernel(self): - kern = GPy.kern.Matern32(5) - self.assertTrue(GPy.kern.kern_test(kern, verbose=verbose)) - def test_Matern52kernel(self): - kern = GPy.kern.Matern52(5) - self.assertTrue(GPy.kern.kern_test(kern, verbose=verbose)) +class Kern_check_dKdiag_dtheta(Kern_check_model): + """ + This class allows gradient checks of the gradient of the diagonal of a + kernel with respect to the parameters. + """ + def __init__(self, kernel=None, dL_dK=None, X=None): + Kern_check_model.__init__(self,kernel=kernel,dL_dK=dL_dK, X=X, X2=None) + self.link_parameter(self.kernel) - def test_linearkernel(self): - kern = GPy.kern.linear(5) - self.assertTrue(GPy.kern.kern_test(kern, verbose=verbose)) + def log_likelihood(self): + return (np.diag(self.dL_dK)*self.kernel.Kdiag(self.X)).sum() - def test_periodic_exponentialkernel(self): - kern = GPy.kern.periodic_exponential(1) - self.assertTrue(GPy.kern.kern_test(kern, verbose=verbose)) + def parameters_changed(self): + self.kernel.update_gradients_diag(np.diag(self.dL_dK), self.X) - def test_periodic_Matern32kernel(self): - kern = GPy.kern.periodic_Matern32(1) - self.assertTrue(GPy.kern.kern_test(kern, verbose=verbose)) +class Kern_check_dK_dX(Kern_check_model): + """This class allows gradient checks for the gradient of a kernel with respect to X. """ + def __init__(self, kernel=None, dL_dK=None, X=None, X2=None): + Kern_check_model.__init__(self,kernel=kernel,dL_dK=dL_dK, X=X, X2=X2) + self.X = Param('X',X) + self.link_parameter(self.X) - def test_periodic_Matern52kernel(self): - kern = GPy.kern.periodic_Matern52(1) - self.assertTrue(GPy.kern.kern_test(kern, verbose=verbose)) + def parameters_changed(self): + self.X.gradient[:] = self.kernel.gradients_X(self.dL_dK, self.X, self.X2) - def test_rational_quadratickernel(self): - kern = GPy.kern.rational_quadratic(1) - self.assertTrue(GPy.kern.kern_test(kern, verbose=verbose)) +class Kern_check_dKdiag_dX(Kern_check_dK_dX): + """This class allows gradient checks for the gradient of a kernel diagonal with respect to X. """ + def __init__(self, kernel=None, dL_dK=None, X=None, X2=None): + Kern_check_dK_dX.__init__(self,kernel=kernel,dL_dK=dL_dK, X=X, X2=None) - def test_gibbskernel(self): - kern = GPy.kern.gibbs(5, mapping=GPy.mappings.Linear(5, 1)) - self.assertTrue(GPy.kern.kern_test(kern, verbose=verbose)) + def log_likelihood(self): + return (np.diag(self.dL_dK)*self.kernel.Kdiag(self.X)).sum() - def test_heterokernel(self): - kern = GPy.kern.hetero(5, mapping=GPy.mappings.Linear(5, 1), transform=GPy.core.transformations.logexp()) - self.assertTrue(GPy.kern.kern_test(kern, verbose=verbose)) + def parameters_changed(self): + self.X.gradient[:] = self.kernel.gradients_X_diag(self.dL_dK.diagonal(), self.X) - def test_mlpkernel(self): - kern = GPy.kern.mlp(5) - self.assertTrue(GPy.kern.kern_test(kern, verbose=verbose)) - def test_polykernel(self): - kern = GPy.kern.poly(5, degree=4) - self.assertTrue(GPy.kern.kern_test(kern, verbose=verbose)) - def test_fixedkernel(self): - """ - Fixed effect kernel test - """ - X = np.random.rand(30, 4) - K = np.dot(X, X.T) - kernel = GPy.kern.fixed(4, K) - kern = GPy.kern.poly(5, degree=4) - self.assertTrue(GPy.kern.kern_test(kern, verbose=verbose)) +def check_kernel_gradient_functions(kern, X=None, X2=None, output_ind=None, verbose=False, fixed_X_dims=None): + """ + This function runs on kernels to check the correctness of their + implementation. It checks that the covariance function is positive definite + for a randomly generated data set. + + :param kern: the kernel to be tested. + :type kern: GPy.kern.Kernpart + :param X: X input values to test the covariance function. + :type X: ndarray + :param X2: X2 input values to test the covariance function. + :type X2: ndarray + + """ + pass_checks = True + if X is None: + X = np.random.randn(10, kern.input_dim) + if output_ind is not None: + X[:, output_ind] = np.random.randint(kern.output_dim, X.shape[0]) + if X2 is None: + X2 = np.random.randn(20, kern.input_dim) + if output_ind is not None: + X2[:, output_ind] = np.random.randint(kern.output_dim, X2.shape[0]) + + if verbose: + print("Checking covariance function is positive definite.") + result = Kern_check_model(kern, X=X).is_positive_semi_definite() + if result and verbose: + print("Check passed.") + if not result: + print("Positive definite check failed for " + kern.name + " covariance function.") + pass_checks = False + assert(result) + return False + + if verbose: + print("Checking gradients of K(X, X) wrt theta.") + result = Kern_check_dK_dtheta(kern, X=X, X2=None).checkgrad(verbose=verbose) + if result and verbose: + print("Check passed.") + if not result: + print("Gradient of K(X, X) wrt theta failed for " + kern.name + " covariance function. Gradient values as follows:") + Kern_check_dK_dtheta(kern, X=X, X2=None).checkgrad(verbose=True) + pass_checks = False + assert(result) + return False + + if verbose: + print("Checking gradients of K(X, X2) wrt theta.") + result = Kern_check_dK_dtheta(kern, X=X, X2=X2).checkgrad(verbose=verbose) + if result and verbose: + print("Check passed.") + if not result: + print("Gradient of K(X, X) wrt theta failed for " + kern.name + " covariance function. Gradient values as follows:") + Kern_check_dK_dtheta(kern, X=X, X2=X2).checkgrad(verbose=True) + pass_checks = False + assert(result) + return False + + if verbose: + print("Checking gradients of Kdiag(X) wrt theta.") + try: + result = Kern_check_dKdiag_dtheta(kern, X=X).checkgrad(verbose=verbose) + except NotImplementedError: + result=True + if verbose: + print("update_gradients_diag not implemented for " + kern.name) + if result and verbose: + print("Check passed.") + if not result: + print("Gradient of Kdiag(X) wrt theta failed for " + kern.name + " covariance function. Gradient values as follows:") + Kern_check_dKdiag_dtheta(kern, X=X).checkgrad(verbose=True) + pass_checks = False + assert(result) + return False + + if verbose: + print("Checking gradients of K(X, X) wrt X.") + try: + testmodel = Kern_check_dK_dX(kern, X=X, X2=None) + if fixed_X_dims is not None: + testmodel.X[:,fixed_X_dims].fix() + result = testmodel.checkgrad(verbose=verbose) + except NotImplementedError: + result=True + if verbose: + print("gradients_X not implemented for " + kern.name) + if result and verbose: + print("Check passed.") + if not result: + print("Gradient of K(X, X) wrt X failed for " + kern.name + " covariance function. Gradient values as follows:") + testmodel.checkgrad(verbose=True) + import ipdb;ipdb.set_trace() + assert(result) + pass_checks = False + return False + + if verbose: + print("Checking gradients of K(X, X2) wrt X.") + try: + testmodel = Kern_check_dK_dX(kern, X=X, X2=X2) + if fixed_X_dims is not None: + testmodel.X[:,fixed_X_dims].fix() + result = testmodel.checkgrad(verbose=verbose) + except NotImplementedError: + result=True + if verbose: + print("gradients_X not implemented for " + kern.name) + if result and verbose: + print("Check passed.") + if not result: + print("Gradient of K(X, X2) wrt X failed for " + kern.name + " covariance function. Gradient values as follows:") + testmodel.checkgrad(verbose=True) + assert(result) + pass_checks = False + return False + + if verbose: + print("Checking gradients of Kdiag(X) wrt X.") + try: + testmodel = Kern_check_dKdiag_dX(kern, X=X) + if fixed_X_dims is not None: + testmodel.X[:,fixed_X_dims].fix() + result = testmodel.checkgrad(verbose=verbose) + except NotImplementedError: + result=True + if verbose: + print("gradients_X not implemented for " + kern.name) + if result and verbose: + print("Check passed.") + if not result: + print("Gradient of Kdiag(X) wrt X failed for " + kern.name + " covariance function. Gradient values as follows:") + Kern_check_dKdiag_dX(kern, X=X).checkgrad(verbose=True) + pass_checks = False + assert(result) + return False + + return pass_checks + + + +class KernelGradientTestsContinuous(unittest.TestCase): + def setUp(self): + self.N, self.D = 10, 5 + self.X = np.random.randn(self.N,self.D) + self.X2 = np.random.randn(self.N+10,self.D) + + continuous_kerns = ['RBF', 'Linear'] + self.kernclasses = [getattr(GPy.kern, s) for s in continuous_kerns] + + def test_Matern32(self): + k = GPy.kern.Matern32(self.D) + k.randomize() + self.assertTrue(check_kernel_gradient_functions(k, X=self.X, X2=self.X2, verbose=verbose)) + + def test_Prod(self): + k = GPy.kern.Matern32(2, active_dims=[2,3]) * GPy.kern.RBF(2, active_dims=[0,4]) + GPy.kern.Linear(self.D) + k.randomize() + self.assertTrue(check_kernel_gradient_functions(k, X=self.X, X2=self.X2, verbose=verbose)) + + def test_Prod2(self): + k = (GPy.kern.RBF(2, active_dims=[0,4]) * GPy.kern.Linear(self.D)) + k.randomize() + self.assertTrue(check_kernel_gradient_functions(k, X=self.X, X2=self.X2, verbose=verbose)) + + def test_Prod3(self): + k = (GPy.kern.RBF(2, active_dims=[0,4]) * GPy.kern.Linear(self.D)) + k.randomize() + self.assertTrue(check_kernel_gradient_functions(k, X=self.X, X2=self.X2, verbose=verbose)) + + def test_Add(self): + k = GPy.kern.Matern32(2, active_dims=[2,3]) + GPy.kern.RBF(2, active_dims=[0,4]) + GPy.kern.Linear(self.D) + k += GPy.kern.Matern32(2, active_dims=[2,3]) + GPy.kern.RBF(2, active_dims=[0,4]) + GPy.kern.Linear(self.D) + k.randomize() + self.assertTrue(check_kernel_gradient_functions(k, X=self.X, X2=self.X2, verbose=verbose)) + + def test_Add_dims(self): + k = GPy.kern.Matern32(2, active_dims=[2,self.D]) + GPy.kern.RBF(2, active_dims=[0,4]) + GPy.kern.Linear(self.D) + k.randomize() + self.assertRaises(IndexError, k.K, self.X) + k = GPy.kern.Matern32(2, active_dims=[2,self.D-1]) + GPy.kern.RBF(2, active_dims=[0,4]) + GPy.kern.Linear(self.D) + k.randomize() + # assert it runs: + try: + k.K(self.X) + except AssertionError: + raise AssertionError, "k.K(X) should run on self.D-1 dimension" + + def test_Matern52(self): + k = GPy.kern.Matern52(self.D) + k.randomize() + self.assertTrue(check_kernel_gradient_functions(k, X=self.X, X2=self.X2, verbose=verbose)) + + def test_RBF(self): + k = GPy.kern.RBF(self.D) + k.randomize() + self.assertTrue(check_kernel_gradient_functions(k, X=self.X, X2=self.X2, verbose=verbose)) + + def test_Linear(self): + k = GPy.kern.Linear(self.D) + k.randomize() + self.assertTrue(check_kernel_gradient_functions(k, X=self.X, X2=self.X2, verbose=verbose)) + + def test_LinearFull(self): + k = GPy.kern.LinearFull(self.D, self.D-1) + k.randomize() + self.assertTrue(check_kernel_gradient_functions(k, X=self.X, X2=self.X2, verbose=verbose)) + +class KernelTestsMiscellaneous(unittest.TestCase): + def setUp(self): + N, D = 100, 10 + self.X = np.linspace(-np.pi, +np.pi, N)[:,None] * np.random.uniform(-10,10,D) + self.rbf = GPy.kern.RBF(2, active_dims=np.arange(0,4,2)) + self.linear = GPy.kern.Linear(2, active_dims=(3,9)) + self.matern = GPy.kern.Matern32(3, active_dims=np.array([1,7,9])) + self.sumkern = self.rbf + self.linear + self.sumkern += self.matern + self.sumkern.randomize() + + def test_which_parts(self): + self.assertTrue(np.allclose(self.sumkern.K(self.X, which_parts=[self.linear, self.matern]), self.linear.K(self.X)+self.matern.K(self.X))) + self.assertTrue(np.allclose(self.sumkern.K(self.X, which_parts=[self.linear, self.rbf]), self.linear.K(self.X)+self.rbf.K(self.X))) + self.assertTrue(np.allclose(self.sumkern.K(self.X, which_parts=self.sumkern.parts[0]), self.rbf.K(self.X))) + +class KernelTestsNonContinuous(unittest.TestCase): + def setUp(self): + N0 = 3 + N1 = 9 + N2 = 4 + N = N0+N1+N2 + self.D = 3 + self.X = np.random.randn(N, self.D+1) + indices = np.random.random_integers(0, 2, size=N) + self.X[indices==0, -1] = 0 + self.X[indices==1, -1] = 1 + self.X[indices==2, -1] = 2 + #self.X = self.X[self.X[:, -1].argsort(), :] + self.X2 = np.random.randn((N0+N1)*2, self.D+1) + self.X2[:(N0*2), -1] = 0 + self.X2[(N0*2):, -1] = 1 + + def test_IndependentOutputs(self): + k = GPy.kern.RBF(self.D, active_dims=range(self.D)) + kern = GPy.kern.IndependentOutputs(k, -1, 'ind_single') + self.assertTrue(check_kernel_gradient_functions(kern, X=self.X, X2=self.X2, verbose=verbose, fixed_X_dims=-1)) + k = [GPy.kern.RBF(1, active_dims=[1], name='rbf1'), GPy.kern.RBF(self.D, active_dims=range(self.D), name='rbf012'), GPy.kern.RBF(2, active_dims=[0,2], name='rbf02')] + kern = GPy.kern.IndependentOutputs(k, -1, name='ind_split') + self.assertTrue(check_kernel_gradient_functions(kern, X=self.X, X2=self.X2, verbose=verbose, fixed_X_dims=-1)) + + def test_Hierarchical(self): + k = [GPy.kern.RBF(2, active_dims=[0,2], name='rbf1'), GPy.kern.RBF(2, active_dims=[0,2], name='rbf2')] + kern = GPy.kern.IndependentOutputs(k, -1, name='ind_split') + self.assertTrue(check_kernel_gradient_functions(kern, X=self.X, X2=self.X2, verbose=verbose, fixed_X_dims=-1)) + + + def test_ODE_UY(self): + kern = GPy.kern.ODE_UY(2, active_dims=[0, self.D]) + X = self.X[self.X[:,-1]!=2] + X2 = self.X2[self.X2[:,-1]!=2] + self.assertTrue(check_kernel_gradient_functions(kern, X=X, X2=X2, verbose=verbose, fixed_X_dims=-1)) + +class Coregionalize_weave_test(unittest.TestCase): + """ + Make sure that the coregionalize kernel work with and without weave enabled + """ + def setUp(self): + self.k = GPy.kern.Coregionalize(1, output_dim=12) + self.N1, self.N2 = 100, 200 + self.X = np.random.randint(0,12,(self.N1,1)) + self.X2 = np.random.randint(0,12,(self.N2,1)) + + def test_sym(self): + dL_dK = np.random.randn(self.N1, self.N1) + GPy.util.config.config.set('weave', 'working', 'True') + K_weave = self.k.K(self.X) + self.k.update_gradients_full(dL_dK, self.X) + grads_weave = self.k.gradient.copy() + + GPy.util.config.config.set('weave', 'working', 'False') + K_numpy = self.k.K(self.X) + self.k.update_gradients_full(dL_dK, self.X) + grads_numpy = self.k.gradient.copy() + + self.assertTrue(np.allclose(K_numpy, K_weave)) + self.assertTrue(np.allclose(grads_numpy, grads_weave)) + + def test_nonsym(self): + dL_dK = np.random.randn(self.N1, self.N2) + GPy.util.config.config.set('weave', 'working', 'True') + K_weave = self.k.K(self.X, self.X2) + self.k.update_gradients_full(dL_dK, self.X, self.X2) + grads_weave = self.k.gradient.copy() + + GPy.util.config.config.set('weave', 'working', 'False') + K_numpy = self.k.K(self.X, self.X2) + self.k.update_gradients_full(dL_dK, self.X, self.X2) + grads_numpy = self.k.gradient.copy() + + self.assertTrue(np.allclose(K_numpy, K_weave)) + self.assertTrue(np.allclose(grads_numpy, grads_weave)) + + #reset the weave state for any other tests + GPy.util.config.config.set('weave', 'working', 'False') - # def test_coregionalization(self): - # X1 = np.random.rand(50,1)*8 - # X2 = np.random.rand(30,1)*5 - # index = np.vstack((np.zeros_like(X1),np.ones_like(X2))) - # X = np.hstack((np.vstack((X1,X2)),index)) - # Y1 = np.sin(X1) + np.random.randn(*X1.shape)*0.05 - # Y2 = np.sin(X2) + np.random.randn(*X2.shape)*0.05 + 2. - # Y = np.vstack((Y1,Y2)) - # k1 = GPy.kern.rbf(1) + GPy.kern.bias(1) - # k2 = GPy.kern.coregionalize(2,1) - # kern = k1**k2 - # self.assertTrue(GPy.kern.kern_test(kern, verbose=verbose)) if __name__ == "__main__": print "Running unit tests, please be (very) patient..." unittest.main() +# np.random.seed(0) +# N0 = 3 +# N1 = 9 +# N2 = 4 +# N = N0+N1+N2 +# D = 3 +# X = np.random.randn(N, D+1) +# indices = np.random.random_integers(0, 2, size=N) +# X[indices==0, -1] = 0 +# X[indices==1, -1] = 1 +# X[indices==2, -1] = 2 +# #X = X[X[:, -1].argsort(), :] +# X2 = np.random.randn((N0+N1)*2, D+1) +# X2[:(N0*2), -1] = 0 +# X2[(N0*2):, -1] = 1 +# k = [GPy.kern.RBF(1, active_dims=[1], name='rbf1'), GPy.kern.RBF(D, name='rbf012'), GPy.kern.RBF(2, active_dims=[0,2], name='rbf02')] +# kern = GPy.kern.IndependentOutputs(k, -1, name='ind_split') +# assert(check_kernel_gradient_functions(kern, X=X, X2=X2, verbose=verbose, fixed_X_dims=-1)) +# k = GPy.kern.RBF(D) +# kern = GPy.kern.IndependentOutputs(k, -1, 'ind_single') +# assert(check_kernel_gradient_functions(kern, X=X, X2=X2, verbose=verbose, fixed_X_dims=-1)) diff --git a/GPy/testing/likelihood_tests.py b/GPy/testing/likelihood_tests.py index d14c9a41..95929098 100644 --- a/GPy/testing/likelihood_tests.py +++ b/GPy/testing/likelihood_tests.py @@ -1,14 +1,18 @@ +# Copyright (c) 2014, Alan Saul +# Licensed under the BSD 3-clause license (see LICENSE.txt) import numpy as np import unittest import GPy from GPy.models import GradientChecker import functools import inspect -from GPy.likelihoods.noise_models import gp_transformations +from GPy.likelihoods import link_functions +from GPy.core.parameterization import Param from functools import partial #np.random.seed(300) -np.random.seed(7) +#np.random.seed(7) +#np.seterr(divide='raise') def dparam_partial(inst_func, *args): """ If we have a instance method that needs to be called but that doesn't @@ -22,12 +26,14 @@ def dparam_partial(inst_func, *args): the f or Y that are being used in the function whilst we tweak the param """ - def param_func(param, inst_func, args): - inst_func.im_self._set_params(param) + def param_func(param_val, param_name, inst_func, args): + #inst_func.im_self._set_params(param) + #inst_func.im_self.add_parameter(Param(param_name, param_val)) + inst_func.im_self[param_name] = param_val return inst_func(*args) return functools.partial(param_func, inst_func=inst_func, args=args) -def dparam_checkgrad(func, dfunc, params, args, constraints=None, randomize=False, verbose=False): +def dparam_checkgrad(func, dfunc, params, params_names, args, constraints=None, randomize=False, verbose=False): """ checkgrad expects a f: R^N -> R^1 and df: R^N -> R^N However if we are holding other parameters fixed and moving something else @@ -38,33 +44,40 @@ def dparam_checkgrad(func, dfunc, params, args, constraints=None, randomize=Fals The number of parameters and N is the number of data Need to take a slice out from f and a slice out of df """ - #print "\n{} likelihood: {} vs {}".format(func.im_self.__class__.__name__, - #func.__name__, dfunc.__name__) + print "\n{} likelihood: {} vs {}".format(func.im_self.__class__.__name__, + func.__name__, dfunc.__name__) partial_f = dparam_partial(func, *args) partial_df = dparam_partial(dfunc, *args) gradchecking = True - for param in params: - fnum = np.atleast_1d(partial_f(param)).shape[0] - dfnum = np.atleast_1d(partial_df(param)).shape[0] + zipped_params = zip(params, params_names) + for param_ind, (param_val, param_name) in enumerate(zipped_params): + #Check one parameter at a time, make sure it is 2d (as some gradients only return arrays) then strip out the parameter + fnum = np.atleast_2d(partial_f(param_val, param_name))[:, param_ind].shape[0] + dfnum = np.atleast_2d(partial_df(param_val, param_name))[:, param_ind].shape[0] for fixed_val in range(dfnum): #dlik and dlik_dvar gives back 1 value for each f_ind = min(fnum, fixed_val+1) - 1 print "fnum: {} dfnum: {} f_ind: {} fixed_val: {}".format(fnum, dfnum, f_ind, fixed_val) #Make grad checker with this param moving, note that set_params is NOT being called #The parameter is being set directly with __setattr__ - grad = GradientChecker(lambda x: np.atleast_1d(partial_f(x))[f_ind], - lambda x : np.atleast_1d(partial_df(x))[fixed_val], - param, 'p') - #This is not general for more than one param... + #Check only the parameter and function value we wish to check at a time + grad = GradientChecker(lambda p_val: np.atleast_2d(partial_f(p_val, param_name))[f_ind, param_ind], + lambda p_val: np.atleast_2d(partial_df(p_val, param_name))[fixed_val, param_ind], + param_val, [param_name]) + if constraints is not None: - for constraint in constraints: - constraint('p', grad) + for constrain_param, constraint in constraints: + if grad.grep_param_names(constrain_param): + constraint(constrain_param, grad) + else: + print "parameter didn't exist" + print constrain_param, " ", constraint if randomize: grad.randomize() if verbose: print grad grad.checkgrad(verbose=1) - if not grad.checkgrad(): + if not grad.checkgrad(verbose=True): gradchecking = False return gradchecking @@ -76,7 +89,7 @@ class TestNoiseModels(object): Generic model checker """ def setUp(self): - self.N = 5 + self.N = 15 self.D = 3 self.X = np.random.rand(self.N, self.D)*10 @@ -94,30 +107,33 @@ class TestNoiseModels(object): self.var = np.random.rand(1) #Make a bigger step as lower bound can be quite curved - self.step = 1e-3 + self.step = 1e-4 def tearDown(self): self.Y = None self.f = None self.X = None - def test_noise_models(self): + def test_scale2_models(self): self.setUp() #################################################### # Constraint wrappers so we can just list them off # #################################################### + def constrain_fixed(regex, model): + model[regex].constrain_fixed() + def constrain_negative(regex, model): - model.constrain_negative(regex) + model[regex].constrain_negative() def constrain_positive(regex, model): - model.constrain_positive(regex) + model[regex].constrain_positive() def constrain_bounded(regex, model, lower, upper): """ Used like: partial(constrain_bounded, lower=0, upper=1) """ - model.constrain_bounded(regex, lower, upper) + model[regex].constrain_bounded(lower, upper) """ Dictionary where we nest models we would like to check @@ -134,71 +150,81 @@ class TestNoiseModels(object): } """ noise_models = {"Student_t_default": { - "model": GPy.likelihoods.student_t(deg_free=5, sigma2=self.var), + "model": GPy.likelihoods.StudentT(deg_free=5, sigma2=self.var), "grad_params": { - "names": ["t_noise"], + "names": [".*t_scale2"], "vals": [self.var], - "constraints": [constrain_positive] + "constraints": [(".*t_scale2", constrain_positive), (".*deg_free", constrain_fixed)] + #"constraints": [("t_scale2", constrain_positive), ("deg_free", partial(constrain_fixed, value=5))] }, "laplace": True }, "Student_t_1_var": { - "model": GPy.likelihoods.student_t(deg_free=5, sigma2=self.var), + "model": GPy.likelihoods.StudentT(deg_free=5, sigma2=self.var), "grad_params": { - "names": ["t_noise"], + "names": [".*t_scale2"], "vals": [1.0], - "constraints": [constrain_positive] + "constraints": [(".*t_scale2", constrain_positive), (".*deg_free", constrain_fixed)] + }, + "laplace": True + }, + "Student_t_small_deg_free": { + "model": GPy.likelihoods.StudentT(deg_free=1.5, sigma2=self.var), + "grad_params": { + "names": [".*t_scale2"], + "vals": [self.var], + "constraints": [(".*t_scale2", constrain_positive), (".*deg_free", constrain_fixed)] }, "laplace": True }, "Student_t_small_var": { - "model": GPy.likelihoods.student_t(deg_free=5, sigma2=self.var), + "model": GPy.likelihoods.StudentT(deg_free=5, sigma2=self.var), "grad_params": { - "names": ["t_noise"], - "vals": [0.01], - "constraints": [constrain_positive] + "names": [".*t_scale2"], + "vals": [0.001], + "constraints": [(".*t_scale2", constrain_positive), (".*deg_free", constrain_fixed)] }, "laplace": True }, "Student_t_large_var": { - "model": GPy.likelihoods.student_t(deg_free=5, sigma2=self.var), + "model": GPy.likelihoods.StudentT(deg_free=5, sigma2=self.var), "grad_params": { - "names": ["t_noise"], + "names": [".*t_scale2"], "vals": [10.0], - "constraints": [constrain_positive] + "constraints": [(".*t_scale2", constrain_positive), (".*deg_free", constrain_fixed)] }, "laplace": True }, "Student_t_approx_gauss": { - "model": GPy.likelihoods.student_t(deg_free=1000, sigma2=self.var), + "model": GPy.likelihoods.StudentT(deg_free=1000, sigma2=self.var), "grad_params": { - "names": ["t_noise"], + "names": [".*t_scale2"], "vals": [self.var], - "constraints": [constrain_positive] + "constraints": [(".*t_scale2", constrain_positive), (".*deg_free", constrain_fixed)] }, "laplace": True }, "Student_t_log": { - "model": GPy.likelihoods.student_t(gp_link=gp_transformations.Log(), deg_free=5, sigma2=self.var), + "model": GPy.likelihoods.StudentT(gp_link=link_functions.Log(), deg_free=5, sigma2=self.var), "grad_params": { - "names": ["t_noise"], + "names": [".*t_scale2"], "vals": [self.var], - "constraints": [constrain_positive] + "constraints": [(".*t_scale2", constrain_positive), (".*deg_free", constrain_fixed)] }, "laplace": True }, "Gaussian_default": { - "model": GPy.likelihoods.gaussian(variance=self.var, D=self.D, N=self.N), + "model": GPy.likelihoods.Gaussian(variance=self.var), "grad_params": { - "names": ["noise_model_variance"], + "names": [".*variance"], "vals": [self.var], - "constraints": [constrain_positive] + "constraints": [(".*variance", constrain_positive)] }, "laplace": True, - "ep": True + "ep": False # FIXME: Should be True when we have it working again }, #"Gaussian_log": { - #"model": GPy.likelihoods.gaussian(gp_link=gp_transformations.Log(), variance=self.var, D=self.D, N=self.N), + #"model": GPy.likelihoods.gaussian(gp_link=link_functions.Log(), variance=self.var, D=self.D, N=self.N), #"grad_params": { #"names": ["noise_model_variance"], #"vals": [self.var], @@ -207,7 +233,7 @@ class TestNoiseModels(object): #"laplace": True #}, #"Gaussian_probit": { - #"model": GPy.likelihoods.gaussian(gp_link=gp_transformations.Probit(), variance=self.var, D=self.D, N=self.N), + #"model": GPy.likelihoods.gaussian(gp_link=link_functions.Probit(), variance=self.var, D=self.D, N=self.N), #"grad_params": { #"names": ["noise_model_variance"], #"vals": [self.var], @@ -216,7 +242,7 @@ class TestNoiseModels(object): #"laplace": True #}, #"Gaussian_log_ex": { - #"model": GPy.likelihoods.gaussian(gp_link=gp_transformations.Log_ex_1(), variance=self.var, D=self.D, N=self.N), + #"model": GPy.likelihoods.gaussian(gp_link=link_functions.Log_ex_1(), variance=self.var, D=self.D, N=self.N), #"grad_params": { #"names": ["noise_model_variance"], #"vals": [self.var], @@ -225,31 +251,31 @@ class TestNoiseModels(object): #"laplace": True #}, "Bernoulli_default": { - "model": GPy.likelihoods.bernoulli(), + "model": GPy.likelihoods.Bernoulli(), "link_f_constraints": [partial(constrain_bounded, lower=0, upper=1)], "laplace": True, "Y": self.binary_Y, - "ep": True + "ep": False # FIXME: Should be True when we have it working again }, "Exponential_default": { - "model": GPy.likelihoods.exponential(), + "model": GPy.likelihoods.Exponential(), "link_f_constraints": [constrain_positive], "Y": self.positive_Y, "laplace": True, }, "Poisson_default": { - "model": GPy.likelihoods.poisson(), + "model": GPy.likelihoods.Poisson(), "link_f_constraints": [constrain_positive], "Y": self.integer_Y, "laplace": True, "ep": False #Should work though... - }, - "Gamma_default": { - "model": GPy.likelihoods.gamma(), - "link_f_constraints": [constrain_positive], - "Y": self.positive_Y, - "laplace": True - } + }#, + #GAMMA needs some work!"Gamma_default": { + #"model": GPy.likelihoods.Gamma(), + #"link_f_constraints": [constrain_positive], + #"Y": self.positive_Y, + #"laplace": True + #} } for name, attributes in noise_models.iteritems(): @@ -286,8 +312,8 @@ class TestNoiseModels(object): else: ep = False - if len(param_vals) > 1: - raise NotImplementedError("Cannot support multiple params in likelihood yet!") + #if len(param_vals) > 1: + #raise NotImplementedError("Cannot support multiple params in likelihood yet!") #Required by all #Normal derivatives @@ -302,13 +328,13 @@ class TestNoiseModels(object): yield self.t_d3logpdf_df3, model, Y, f yield self.t_d3logpdf_dlink3, model, Y, f, link_f_constraints #Params - yield self.t_dlogpdf_dparams, model, Y, f, param_vals, param_constraints - yield self.t_dlogpdf_df_dparams, model, Y, f, param_vals, param_constraints - yield self.t_d2logpdf2_df2_dparams, model, Y, f, param_vals, param_constraints + yield self.t_dlogpdf_dparams, model, Y, f, param_vals, param_names, param_constraints + yield self.t_dlogpdf_df_dparams, model, Y, f, param_vals, param_names, param_constraints + yield self.t_d2logpdf2_df2_dparams, model, Y, f, param_vals, param_names, param_constraints #Link params - yield self.t_dlogpdf_link_dparams, model, Y, f, param_vals, param_constraints - yield self.t_dlogpdf_dlink_dparams, model, Y, f, param_vals, param_constraints - yield self.t_d2logpdf2_dlink2_dparams, model, Y, f, param_vals, param_constraints + yield self.t_dlogpdf_link_dparams, model, Y, f, param_vals, param_names, param_constraints + yield self.t_dlogpdf_dlink_dparams, model, Y, f, param_vals, param_names, param_constraints + yield self.t_d2logpdf2_dlink2_dparams, model, Y, f, param_vals, param_names, param_constraints #laplace likelihood gradcheck yield self.t_laplace_fit_rbf_white, model, self.X, Y, f, self.step, param_vals, param_names, param_constraints @@ -326,10 +352,10 @@ class TestNoiseModels(object): def t_logpdf(self, model, Y, f): print "\n{}".format(inspect.stack()[0][3]) print model - print model._get_params() + #print model._get_params() np.testing.assert_almost_equal( - model.pdf(f.copy(), Y.copy()), - np.exp(model.logpdf(f.copy(), Y.copy())) + model.pdf(f.copy(), Y.copy()).prod(), + np.exp(model.logpdf(f.copy(), Y.copy()).sum()) ) @with_setup(setUp, tearDown) @@ -340,9 +366,8 @@ class TestNoiseModels(object): dlogpdf_df = functools.partial(model.dlogpdf_df, y=Y) grad = GradientChecker(logpdf, dlogpdf_df, f.copy(), 'g') grad.randomize() - grad.checkgrad(verbose=1) print model - assert grad.checkgrad() + assert grad.checkgrad(verbose=1) @with_setup(setUp, tearDown) def t_d2logpdf_df2(self, model, Y, f): @@ -351,9 +376,8 @@ class TestNoiseModels(object): d2logpdf_df2 = functools.partial(model.d2logpdf_df2, y=Y) grad = GradientChecker(dlogpdf_df, d2logpdf_df2, f.copy(), 'g') grad.randomize() - grad.checkgrad(verbose=1) print model - assert grad.checkgrad() + assert grad.checkgrad(verbose=1) @with_setup(setUp, tearDown) def t_d3logpdf_df3(self, model, Y, f): @@ -362,41 +386,40 @@ class TestNoiseModels(object): d3logpdf_df3 = functools.partial(model.d3logpdf_df3, y=Y) grad = GradientChecker(d2logpdf_df2, d3logpdf_df3, f.copy(), 'g') grad.randomize() - grad.checkgrad(verbose=1) print model - assert grad.checkgrad() + assert grad.checkgrad(verbose=1) ############## # df_dparams # ############## @with_setup(setUp, tearDown) - def t_dlogpdf_dparams(self, model, Y, f, params, param_constraints): + def t_dlogpdf_dparams(self, model, Y, f, params, params_names, param_constraints): print "\n{}".format(inspect.stack()[0][3]) print model assert ( dparam_checkgrad(model.logpdf, model.dlogpdf_dtheta, - params, args=(f, Y), constraints=param_constraints, - randomize=True, verbose=True) + params, params_names, args=(f, Y), constraints=param_constraints, + randomize=False, verbose=True) ) @with_setup(setUp, tearDown) - def t_dlogpdf_df_dparams(self, model, Y, f, params, param_constraints): + def t_dlogpdf_df_dparams(self, model, Y, f, params, params_names, param_constraints): print "\n{}".format(inspect.stack()[0][3]) print model assert ( dparam_checkgrad(model.dlogpdf_df, model.dlogpdf_df_dtheta, - params, args=(f, Y), constraints=param_constraints, - randomize=True, verbose=True) + params, params_names, args=(f, Y), constraints=param_constraints, + randomize=False, verbose=True) ) @with_setup(setUp, tearDown) - def t_d2logpdf2_df2_dparams(self, model, Y, f, params, param_constraints): + def t_d2logpdf2_df2_dparams(self, model, Y, f, params, params_names, param_constraints): print "\n{}".format(inspect.stack()[0][3]) print model assert ( dparam_checkgrad(model.d2logpdf_df2, model.d2logpdf_df2_dtheta, - params, args=(f, Y), constraints=param_constraints, - randomize=True, verbose=True) + params, params_names, args=(f, Y), constraints=param_constraints, + randomize=False, verbose=True) ) ################ @@ -415,8 +438,8 @@ class TestNoiseModels(object): grad.randomize() print grad - grad.checkgrad(verbose=1) - assert grad.checkgrad() + print model + assert grad.checkgrad(verbose=1) @with_setup(setUp, tearDown) def t_d2logpdf_dlink2(self, model, Y, f, link_f_constraints): @@ -430,9 +453,9 @@ class TestNoiseModels(object): constraint('g', grad) grad.randomize() - grad.checkgrad(verbose=1) print grad - assert grad.checkgrad() + print model + assert grad.checkgrad(verbose=1) @with_setup(setUp, tearDown) def t_d3logpdf_dlink3(self, model, Y, f, link_f_constraints): @@ -446,40 +469,40 @@ class TestNoiseModels(object): constraint('g', grad) grad.randomize() - grad.checkgrad(verbose=1) print grad - assert grad.checkgrad() + print model + assert grad.checkgrad(verbose=1) ################# # dlink_dparams # ################# @with_setup(setUp, tearDown) - def t_dlogpdf_link_dparams(self, model, Y, f, params, param_constraints): + def t_dlogpdf_link_dparams(self, model, Y, f, params, param_names, param_constraints): print "\n{}".format(inspect.stack()[0][3]) print model assert ( dparam_checkgrad(model.logpdf_link, model.dlogpdf_link_dtheta, - params, args=(f, Y), constraints=param_constraints, + params, param_names, args=(f, Y), constraints=param_constraints, randomize=False, verbose=True) ) @with_setup(setUp, tearDown) - def t_dlogpdf_dlink_dparams(self, model, Y, f, params, param_constraints): + def t_dlogpdf_dlink_dparams(self, model, Y, f, params, param_names, param_constraints): print "\n{}".format(inspect.stack()[0][3]) print model assert ( dparam_checkgrad(model.dlogpdf_dlink, model.dlogpdf_dlink_dtheta, - params, args=(f, Y), constraints=param_constraints, + params, param_names, args=(f, Y), constraints=param_constraints, randomize=False, verbose=True) ) @with_setup(setUp, tearDown) - def t_d2logpdf2_dlink2_dparams(self, model, Y, f, params, param_constraints): + def t_d2logpdf2_dlink2_dparams(self, model, Y, f, params, param_names, param_constraints): print "\n{}".format(inspect.stack()[0][3]) print model assert ( dparam_checkgrad(model.d2logpdf_dlink2, model.d2logpdf_dlink2_dtheta, - params, args=(f, Y), constraints=param_constraints, + params, param_names, args=(f, Y), constraints=param_constraints, randomize=False, verbose=True) ) @@ -492,28 +515,31 @@ class TestNoiseModels(object): #Normalize Y = Y/Y.max() white_var = 1e-6 - kernel = GPy.kern.rbf(X.shape[1]) + GPy.kern.white(X.shape[1]) - laplace_likelihood = GPy.likelihoods.Laplace(Y.copy(), model) - m = GPy.models.GPRegression(X.copy(), Y.copy(), kernel, likelihood=laplace_likelihood) - m.ensure_default_constraints() - m.constrain_fixed('white', white_var) + kernel = GPy.kern.RBF(X.shape[1]) + GPy.kern.White(X.shape[1]) + laplace_likelihood = GPy.inference.latent_function_inference.Laplace() + m = GPy.core.GP(X.copy(), Y.copy(), kernel, likelihood=model, inference_method=laplace_likelihood) + m['.*white'].constrain_fixed(white_var) - for param_num in range(len(param_names)): - name = param_names[param_num] - m[name] = param_vals[param_num] - constraints[param_num](name, m) + #Set constraints + for constrain_param, constraint in constraints: + constraint(constrain_param, m) print m m.randomize() + + #Set params + for param_num in range(len(param_names)): + name = param_names[param_num] + m[name] = param_vals[param_num] + #m.optimize(max_iters=8) print m - m.checkgrad(verbose=1, step=step) #if not m.checkgrad(step=step): #m.checkgrad(verbose=1, step=step) - #import ipdb; ipdb.set_trace() #NOTE this test appears to be stochastic for some likelihoods (student t?) # appears to all be working in test mode right now... - assert m.checkgrad(step=step) + #if isinstance(model, GPy.likelihoods.StudentT): + assert m.checkgrad(verbose=1, step=step) ########### # EP test # @@ -524,11 +550,10 @@ class TestNoiseModels(object): #Normalize Y = Y/Y.max() white_var = 1e-6 - kernel = GPy.kern.rbf(X.shape[1]) + GPy.kern.white(X.shape[1]) - ep_likelihood = GPy.likelihoods.EP(Y.copy(), model) - m = GPy.models.GPRegression(X.copy(), Y.copy(), kernel, likelihood=ep_likelihood) - m.ensure_default_constraints() - m.constrain_fixed('white', white_var) + kernel = GPy.kern.RBF(X.shape[1]) + GPy.kern.White(X.shape[1]) + ep_inf = GPy.inference.latent_function_inference.EP() + m = GPy.core.GP(X.copy(), Y.copy(), kernel=kernel, likelihood=model, inference_method=ep_inf) + m['.*white'].constrain_fixed(white_var) for param_num in range(len(param_names)): name = param_names[param_num] @@ -536,9 +561,8 @@ class TestNoiseModels(object): constraints[param_num](name, m) m.randomize() - m.checkgrad(verbose=1, step=step) print m - assert m.checkgrad(step=step) + assert m.checkgrad(verbose=1, step=step) class LaplaceTests(unittest.TestCase): @@ -559,8 +583,9 @@ class LaplaceTests(unittest.TestCase): self.var = 0.2 self.var = np.random.rand(1) - self.stu_t = GPy.likelihoods.student_t(deg_free=5, sigma2=self.var) - self.gauss = GPy.likelihoods.gaussian(gp_transformations.Log(), variance=self.var, D=self.D, N=self.N) + self.stu_t = GPy.likelihoods.StudentT(deg_free=5, sigma2=self.var) + #TODO: gaussians with on Identity link. self.gauss = GPy.likelihoods.Gaussian(gp_link=link_functions.Log(), variance=self.var) + self.gauss = GPy.likelihoods.Gaussian(variance=self.var) #Make a bigger step as lower bound can be quite curved self.step = 1e-6 @@ -575,7 +600,6 @@ class LaplaceTests(unittest.TestCase): def test_gaussian_d2logpdf_df2_2(self): print "\n{}".format(inspect.stack()[0][3]) self.Y = None - self.gauss = None self.N = 2 self.D = 1 @@ -584,14 +608,13 @@ class LaplaceTests(unittest.TestCase): noise = np.random.randn(*self.X.shape)*self.real_std self.Y = np.sin(self.X*2*np.pi) + noise self.f = np.random.rand(self.N, 1) - self.gauss = GPy.likelihoods.gaussian(variance=self.var, D=self.D, N=self.N) dlogpdf_df = functools.partial(self.gauss.dlogpdf_df, y=self.Y) d2logpdf_df2 = functools.partial(self.gauss.d2logpdf_df2, y=self.Y) grad = GradientChecker(dlogpdf_df, d2logpdf_df2, self.f.copy(), 'g') grad.randomize() - grad.checkgrad(verbose=1) - self.assertTrue(grad.checkgrad()) + + self.assertTrue(grad.checkgrad(verbose=1)) def test_laplace_log_likelihood(self): debug = False @@ -604,24 +627,24 @@ class LaplaceTests(unittest.TestCase): Y = Y/Y.max() #Yc = Y.copy() #Yc[75:80] += 1 - kernel1 = GPy.kern.rbf(X.shape[1]) + GPy.kern.white(X.shape[1]) - kernel2 = kernel1.copy() + kernel1 = GPy.kern.RBF(X.shape[1]) + GPy.kern.White(X.shape[1]) + #FIXME: Make sure you can copy kernels when params is fixed + #kernel2 = kernel1.copy() + kernel2 = GPy.kern.RBF(X.shape[1]) + GPy.kern.White(X.shape[1]) - m1 = GPy.models.GPRegression(X, Y.copy(), kernel=kernel1) - m1.constrain_fixed('white', 1e-6) - m1['noise'] = initial_var_guess - m1.constrain_bounded('noise', 1e-4, 10) - m1.constrain_bounded('rbf', 1e-4, 10) - m1.ensure_default_constraints() + gauss_distr1 = GPy.likelihoods.Gaussian(variance=initial_var_guess) + exact_inf = GPy.inference.latent_function_inference.ExactGaussianInference() + m1 = GPy.core.GP(X, Y.copy(), kernel=kernel1, likelihood=gauss_distr1, inference_method=exact_inf) + m1['.*white'].constrain_fixed(1e-6) + m1['.*rbf.variance'] = initial_var_guess + m1['.*rbf.variance'].constrain_bounded(1e-4, 10) m1.randomize() - gauss_distr = GPy.likelihoods.gaussian(variance=initial_var_guess, D=1, N=Y.shape[0]) - laplace_likelihood = GPy.likelihoods.Laplace(Y.copy(), gauss_distr) - m2 = GPy.models.GPRegression(X, Y.copy(), kernel=kernel2, likelihood=laplace_likelihood) - m2.ensure_default_constraints() - m2.constrain_fixed('white', 1e-6) - m2.constrain_bounded('rbf', 1e-4, 10) - m2.constrain_bounded('noise', 1e-4, 10) + gauss_distr2 = GPy.likelihoods.Gaussian(variance=initial_var_guess) + laplace_inf = GPy.inference.latent_function_inference.Laplace() + m2 = GPy.core.GP(X, Y.copy(), kernel=kernel2, likelihood=gauss_distr2, inference_method=laplace_inf) + m2['.*white'].constrain_fixed(1e-6) + m2['.*rbf.variance'].constrain_bounded(1e-4, 10) m2.randomize() if debug: @@ -636,11 +659,11 @@ class LaplaceTests(unittest.TestCase): print m1 print m2 - m2._set_params(m1._get_params()) + m2[:] = m1[:] #Predict for training points to get posterior mean and variance - post_mean, post_var, _, _ = m1.predict(X) - post_mean_approx, post_var_approx, _, _ = m2.predict(X) + post_mean, post_var = m1.predict(X) + post_mean_approx, post_var_approx, = m2.predict(X) if debug: import pylab as pb @@ -667,19 +690,20 @@ class LaplaceTests(unittest.TestCase): #Check Y's are the same - np.testing.assert_almost_equal(Y, m2.likelihood.Y, decimal=5) + np.testing.assert_almost_equal(m1.Y, m2.Y, decimal=5) #Check marginals are the same np.testing.assert_almost_equal(m1.log_likelihood(), m2.log_likelihood(), decimal=2) #Check marginals are the same with random m1.randomize() - m2._set_params(m1._get_params()) + m2[:] = m1[:] + np.testing.assert_almost_equal(m1.log_likelihood(), m2.log_likelihood(), decimal=2) #Check they are checkgradding #m1.checkgrad(verbose=1) #m2.checkgrad(verbose=1) - self.assertTrue(m1.checkgrad()) - self.assertTrue(m2.checkgrad()) + self.assertTrue(m1.checkgrad(verbose=True)) + self.assertTrue(m2.checkgrad(verbose=True)) if __name__ == "__main__": print "Running unit tests" diff --git a/GPy/testing/model_tests.py b/GPy/testing/model_tests.py new file mode 100644 index 00000000..521baeb3 --- /dev/null +++ b/GPy/testing/model_tests.py @@ -0,0 +1,509 @@ +# Copyright (c) 2012, GPy authors (see AUTHORS.txt). +# Licensed under the BSD 3-clause license (see LICENSE.txt) + + +import unittest +import numpy as np +import GPy + +class MiscTests(unittest.TestCase): + def setUp(self): + self.N = 20 + self.N_new = 50 + self.D = 1 + self.X = np.random.uniform(-3., 3., (self.N, 1)) + self.Y = np.sin(self.X) + np.random.randn(self.N, self.D) * 0.05 + self.X_new = np.random.uniform(-3., 3., (self.N_new, 1)) + + def test_raw_predict(self): + k = GPy.kern.RBF(1) + m = GPy.models.GPRegression(self.X, self.Y, kernel=k) + m.randomize() + m.likelihood.variance = .5 + Kinv = np.linalg.pinv(k.K(self.X) + np.eye(self.N) * m.likelihood.variance) + K_hat = k.K(self.X_new) - k.K(self.X_new, self.X).dot(Kinv).dot(k.K(self.X, self.X_new)) + mu_hat = k.K(self.X_new, self.X).dot(Kinv).dot(m.Y_normalized) + + mu, covar = m._raw_predict(self.X_new, full_cov=True) + self.assertEquals(mu.shape, (self.N_new, self.D)) + self.assertEquals(covar.shape, (self.N_new, self.N_new)) + np.testing.assert_almost_equal(K_hat, covar) + np.testing.assert_almost_equal(mu_hat, mu) + + mu, var = m._raw_predict(self.X_new) + self.assertEquals(mu.shape, (self.N_new, self.D)) + self.assertEquals(var.shape, (self.N_new, 1)) + np.testing.assert_almost_equal(np.diag(K_hat)[:, None], var) + np.testing.assert_almost_equal(mu_hat, mu) + + def test_sparse_raw_predict(self): + k = GPy.kern.RBF(1) + m = GPy.models.SparseGPRegression(self.X, self.Y, kernel=k) + m.randomize() + Z = m.Z[:] + X = self.X[:] + + # Not easy to check if woodbury_inv is correct in itself as it requires a large derivation and expression + Kinv = m.posterior.woodbury_inv + K_hat = k.K(self.X_new) - k.K(self.X_new, Z).dot(Kinv).dot(k.K(Z, self.X_new)) + + mu, covar = m._raw_predict(self.X_new, full_cov=True) + self.assertEquals(mu.shape, (self.N_new, self.D)) + self.assertEquals(covar.shape, (self.N_new, self.N_new)) + np.testing.assert_almost_equal(K_hat, covar) + # np.testing.assert_almost_equal(mu_hat, mu) + + mu, var = m._raw_predict(self.X_new) + self.assertEquals(mu.shape, (self.N_new, self.D)) + self.assertEquals(var.shape, (self.N_new, 1)) + np.testing.assert_almost_equal(np.diag(K_hat)[:, None], var) + # np.testing.assert_almost_equal(mu_hat, mu) + + def test_likelihood_replicate(self): + m = GPy.models.GPRegression(self.X, self.Y) + m2 = GPy.models.GPRegression(self.X, self.Y) + np.testing.assert_equal(m.log_likelihood(), m2.log_likelihood()) + m.randomize() + m2[:] = m[''].values() + np.testing.assert_almost_equal(m.log_likelihood(), m2.log_likelihood()) + m.randomize() + m2[''] = m[:] + np.testing.assert_almost_equal(m.log_likelihood(), m2.log_likelihood()) + m.randomize() + m2[:] = m[:] + np.testing.assert_almost_equal(m.log_likelihood(), m2.log_likelihood()) + m.randomize() + m2[''] = m[''] + np.testing.assert_almost_equal(m.log_likelihood(), m2.log_likelihood()) + + m.kern.lengthscale.randomize() + m2[:] = m[:] + np.testing.assert_almost_equal(m.log_likelihood(), m2.log_likelihood()) + + m.Gaussian_noise.randomize() + m2[:] = m[:] + np.testing.assert_almost_equal(m.log_likelihood(), m2.log_likelihood()) + + m['.*var'] = 2 + m2['.*var'] = m['.*var'] + np.testing.assert_almost_equal(m.log_likelihood(), m2.log_likelihood()) + + + def test_likelihood_set(self): + m = GPy.models.GPRegression(self.X, self.Y) + m2 = GPy.models.GPRegression(self.X, self.Y) + np.testing.assert_equal(m.log_likelihood(), m2.log_likelihood()) + + m.kern.lengthscale.randomize() + m2.kern.lengthscale = m.kern.lengthscale + np.testing.assert_equal(m.log_likelihood(), m2.log_likelihood()) + + m.kern.lengthscale.randomize() + m2['.*lengthscale'] = m.kern.lengthscale + np.testing.assert_equal(m.log_likelihood(), m2.log_likelihood()) + + m.kern.lengthscale.randomize() + m2['.*lengthscale'] = m.kern['.*lengthscale'] + np.testing.assert_equal(m.log_likelihood(), m2.log_likelihood()) + + m.kern.lengthscale.randomize() + m2.kern.lengthscale = m.kern['.*lengthscale'] + np.testing.assert_equal(m.log_likelihood(), m2.log_likelihood()) + + def test_missing_data(self): + from GPy import kern + from GPy.models.bayesian_gplvm_minibatch import BayesianGPLVMMiniBatch + from GPy.examples.dimensionality_reduction import _simulate_matern + + D1, D2, D3, N, num_inducing, Q = 13, 5, 8, 400, 3, 4 + _, _, Ylist = _simulate_matern(D1, D2, D3, N, num_inducing, False) + Y = Ylist[0] + + inan = np.random.binomial(1, .9, size=Y.shape).astype(bool) # 80% missing data + Ymissing = Y.copy() + Ymissing[inan] = np.nan + + k = kern.Linear(Q, ARD=True) + kern.White(Q, np.exp(-2)) # + kern.bias(Q) + m = BayesianGPLVMMiniBatch(Ymissing, Q, init="random", num_inducing=num_inducing, + kernel=k, missing_data=True) + assert(m.checkgrad()) + + k = kern.RBF(Q, ARD=True) + kern.White(Q, np.exp(-2)) # + kern.bias(Q) + m = BayesianGPLVMMiniBatch(Ymissing, Q, init="random", num_inducing=num_inducing, + kernel=k, missing_data=True) + assert(m.checkgrad()) + + def test_likelihood_replicate_kern(self): + m = GPy.models.GPRegression(self.X, self.Y) + m2 = GPy.models.GPRegression(self.X, self.Y) + np.testing.assert_equal(m.log_likelihood(), m2.log_likelihood()) + m.kern.randomize() + m2.kern[''] = m.kern[:] + np.testing.assert_almost_equal(m.log_likelihood(), m2.log_likelihood()) + m.kern.randomize() + m2.kern[:] = m.kern[:] + np.testing.assert_almost_equal(m.log_likelihood(), m2.log_likelihood()) + m.kern.randomize() + m2.kern[''] = m.kern[''] + np.testing.assert_almost_equal(m.log_likelihood(), m2.log_likelihood()) + m.kern.randomize() + m2.kern[:] = m.kern[''].values() + np.testing.assert_almost_equal(m.log_likelihood(), m2.log_likelihood()) + + def test_big_model(self): + m = GPy.examples.dimensionality_reduction.mrd_simulation(optimize=0, plot=0, plot_sim=0) + m.X.fix() + print m + m.unfix() + m.checkgrad() + print m + m.fix() + print m + m.inducing_inputs.unfix() + print m + m.checkgrad() + m.unfix() + m.checkgrad() + m.checkgrad() + print m + + def test_model_set_params(self): + m = GPy.models.GPRegression(self.X, self.Y) + lengthscale = np.random.uniform() + m.kern.lengthscale = lengthscale + np.testing.assert_equal(m.kern.lengthscale, lengthscale) + m.kern.lengthscale *= 1 + m['.*var'] -= .1 + np.testing.assert_equal(m.kern.lengthscale, lengthscale) + m.optimize() + print m + + def test_model_optimize(self): + X = np.random.uniform(-3., 3., (20, 1)) + Y = np.sin(X) + np.random.randn(20, 1) * 0.05 + m = GPy.models.GPRegression(X, Y) + m.optimize() + print m + +class GradientTests(np.testing.TestCase): + def setUp(self): + ###################################### + # # 1 dimensional example + + # sample inputs and outputs + self.X1D = np.random.uniform(-3., 3., (20, 1)) + self.Y1D = np.sin(self.X1D) + np.random.randn(20, 1) * 0.05 + + ###################################### + # # 2 dimensional example + + # sample inputs and outputs + self.X2D = np.random.uniform(-3., 3., (40, 2)) + self.Y2D = np.sin(self.X2D[:, 0:1]) * np.sin(self.X2D[:, 1:2]) + np.random.randn(40, 1) * 0.05 + + def check_model(self, kern, model_type='GPRegression', dimension=1, uncertain_inputs=False): + # Get the correct gradients + if dimension == 1: + X = self.X1D + Y = self.Y1D + else: + X = self.X2D + Y = self.Y2D + # Get model type (GPRegression, SparseGPRegression, etc) + model_fit = getattr(GPy.models, model_type) + + # noise = GPy.kern.White(dimension) + kern = kern # + noise + if uncertain_inputs: + m = model_fit(X, Y, kernel=kern, X_variance=np.random.rand(X.shape[0], X.shape[1])) + else: + m = model_fit(X, Y, kernel=kern) + m.randomize() + # contrain all parameters to be positive + self.assertTrue(m.checkgrad()) + + def test_GPRegression_rbf_1d(self): + ''' Testing the GP regression with rbf kernel with white kernel on 1d data ''' + rbf = GPy.kern.RBF(1) + self.check_model(rbf, model_type='GPRegression', dimension=1) + + def test_GPRegression_rbf_2D(self): + ''' Testing the GP regression with rbf kernel on 2d data ''' + rbf = GPy.kern.RBF(2) + self.check_model(rbf, model_type='GPRegression', dimension=2) + + def test_GPRegression_rbf_ARD_2D(self): + ''' Testing the GP regression with rbf kernel on 2d data ''' + k = GPy.kern.RBF(2, ARD=True) + self.check_model(k, model_type='GPRegression', dimension=2) + + def test_GPRegression_mlp_1d(self): + ''' Testing the GP regression with mlp kernel with white kernel on 1d data ''' + mlp = GPy.kern.MLP(1) + self.check_model(mlp, model_type='GPRegression', dimension=1) + + # TODO: + # def test_GPRegression_poly_1d(self): + # ''' Testing the GP regression with polynomial kernel with white kernel on 1d data ''' + # mlp = GPy.kern.Poly(1, degree=5) + # self.check_model(mlp, model_type='GPRegression', dimension=1) + + def test_GPRegression_matern52_1D(self): + ''' Testing the GP regression with matern52 kernel on 1d data ''' + matern52 = GPy.kern.Matern52(1) + self.check_model(matern52, model_type='GPRegression', dimension=1) + + def test_GPRegression_matern52_2D(self): + ''' Testing the GP regression with matern52 kernel on 2d data ''' + matern52 = GPy.kern.Matern52(2) + self.check_model(matern52, model_type='GPRegression', dimension=2) + + def test_GPRegression_matern52_ARD_2D(self): + ''' Testing the GP regression with matern52 kernel on 2d data ''' + matern52 = GPy.kern.Matern52(2, ARD=True) + self.check_model(matern52, model_type='GPRegression', dimension=2) + + def test_GPRegression_matern32_1D(self): + ''' Testing the GP regression with matern32 kernel on 1d data ''' + matern32 = GPy.kern.Matern32(1) + self.check_model(matern32, model_type='GPRegression', dimension=1) + + def test_GPRegression_matern32_2D(self): + ''' Testing the GP regression with matern32 kernel on 2d data ''' + matern32 = GPy.kern.Matern32(2) + self.check_model(matern32, model_type='GPRegression', dimension=2) + + def test_GPRegression_matern32_ARD_2D(self): + ''' Testing the GP regression with matern32 kernel on 2d data ''' + matern32 = GPy.kern.Matern32(2, ARD=True) + self.check_model(matern32, model_type='GPRegression', dimension=2) + + def test_GPRegression_exponential_1D(self): + ''' Testing the GP regression with exponential kernel on 1d data ''' + exponential = GPy.kern.Exponential(1) + self.check_model(exponential, model_type='GPRegression', dimension=1) + + def test_GPRegression_exponential_2D(self): + ''' Testing the GP regression with exponential kernel on 2d data ''' + exponential = GPy.kern.Exponential(2) + self.check_model(exponential, model_type='GPRegression', dimension=2) + + def test_GPRegression_exponential_ARD_2D(self): + ''' Testing the GP regression with exponential kernel on 2d data ''' + exponential = GPy.kern.Exponential(2, ARD=True) + self.check_model(exponential, model_type='GPRegression', dimension=2) + + def test_GPRegression_bias_kern_1D(self): + ''' Testing the GP regression with bias kernel on 1d data ''' + bias = GPy.kern.Bias(1) + self.check_model(bias, model_type='GPRegression', dimension=1) + + def test_GPRegression_bias_kern_2D(self): + ''' Testing the GP regression with bias kernel on 2d data ''' + bias = GPy.kern.Bias(2) + self.check_model(bias, model_type='GPRegression', dimension=2) + + def test_GPRegression_linear_kern_1D_ARD(self): + ''' Testing the GP regression with linear kernel on 1d data ''' + linear = GPy.kern.Linear(1, ARD=True) + self.check_model(linear, model_type='GPRegression', dimension=1) + + def test_GPRegression_linear_kern_2D_ARD(self): + ''' Testing the GP regression with linear kernel on 2d data ''' + linear = GPy.kern.Linear(2, ARD=True) + self.check_model(linear, model_type='GPRegression', dimension=2) + + def test_GPRegression_linear_kern_1D(self): + ''' Testing the GP regression with linear kernel on 1d data ''' + linear = GPy.kern.Linear(1) + self.check_model(linear, model_type='GPRegression', dimension=1) + + def test_GPRegression_linear_kern_2D(self): + ''' Testing the GP regression with linear kernel on 2d data ''' + linear = GPy.kern.Linear(2) + self.check_model(linear, model_type='GPRegression', dimension=2) + + def test_SparseGPRegression_rbf_white_kern_1d(self): + ''' Testing the sparse GP regression with rbf kernel with white kernel on 1d data ''' + rbf = GPy.kern.RBF(1) + self.check_model(rbf, model_type='SparseGPRegression', dimension=1) + + def test_SparseGPRegression_rbf_white_kern_2D(self): + ''' Testing the sparse GP regression with rbf kernel on 2d data ''' + rbf = GPy.kern.RBF(2) + self.check_model(rbf, model_type='SparseGPRegression', dimension=2) + + def test_SparseGPRegression_rbf_linear_white_kern_1D(self): + ''' Testing the sparse GP regression with rbf kernel on 2d data ''' + rbflin = GPy.kern.RBF(1) + GPy.kern.Linear(1) + self.check_model(rbflin, model_type='SparseGPRegression', dimension=1) + + def test_SparseGPRegression_rbf_linear_white_kern_2D(self): + ''' Testing the sparse GP regression with rbf kernel on 2d data ''' + rbflin = GPy.kern.RBF(2) + GPy.kern.Linear(2) + self.check_model(rbflin, model_type='SparseGPRegression', dimension=2) + + # @unittest.expectedFailure + def test_SparseGPRegression_rbf_linear_white_kern_2D_uncertain_inputs(self): + ''' Testing the sparse GP regression with rbf, linear kernel on 2d data with uncertain inputs''' + rbflin = GPy.kern.RBF(2) + GPy.kern.Linear(2) + raise unittest.SkipTest("This is not implemented yet!") + self.check_model(rbflin, model_type='SparseGPRegression', dimension=2, uncertain_inputs=1) + + # @unittest.expectedFailure + def test_SparseGPRegression_rbf_linear_white_kern_1D_uncertain_inputs(self): + ''' Testing the sparse GP regression with rbf, linear kernel on 1d data with uncertain inputs''' + rbflin = GPy.kern.RBF(1) + GPy.kern.Linear(1) + raise unittest.SkipTest("This is not implemented yet!") + self.check_model(rbflin, model_type='SparseGPRegression', dimension=1, uncertain_inputs=1) + + def test_GPLVM_rbf_bias_white_kern_2D(self): + """ Testing GPLVM with rbf + bias kernel """ + N, input_dim, D = 50, 1, 2 + X = np.random.rand(N, input_dim) + k = GPy.kern.RBF(input_dim, 0.5, 0.9 * np.ones((1,))) + GPy.kern.Bias(input_dim, 0.1) + GPy.kern.White(input_dim, 0.05) + K = k.K(X) + Y = np.random.multivariate_normal(np.zeros(N), K, input_dim).T + m = GPy.models.GPLVM(Y, input_dim, kernel=k) + self.assertTrue(m.checkgrad()) + + def test_GPLVM_rbf_linear_white_kern_2D(self): + """ Testing GPLVM with rbf + bias kernel """ + N, input_dim, D = 50, 1, 2 + X = np.random.rand(N, input_dim) + k = GPy.kern.Linear(input_dim) + GPy.kern.Bias(input_dim, 0.1) + GPy.kern.White(input_dim, 0.05) + K = k.K(X) + Y = np.random.multivariate_normal(np.zeros(N), K, input_dim).T + m = GPy.models.GPLVM(Y, input_dim, init='PCA', kernel=k) + self.assertTrue(m.checkgrad()) + + def test_GP_EP_probit(self): + N = 20 + X = np.hstack([np.random.normal(5, 2, N / 2), np.random.normal(10, 2, N / 2)])[:, None] + Y = np.hstack([np.ones(N / 2), np.zeros(N / 2)])[:, None] + kernel = GPy.kern.RBF(1) + m = GPy.models.GPClassification(X, Y, kernel=kernel) + self.assertTrue(m.checkgrad()) + + def test_sparse_EP_DTC_probit(self): + N = 20 + X = np.hstack([np.random.normal(5, 2, N / 2), np.random.normal(10, 2, N / 2)])[:, None] + Y = np.hstack([np.ones(N / 2), np.zeros(N / 2)])[:, None] + Z = np.linspace(0, 15, 4)[:, None] + kernel = GPy.kern.RBF(1) + m = GPy.models.SparseGPClassification(X, Y, kernel=kernel, Z=Z) + # distribution = GPy.likelihoods.likelihood_functions.Bernoulli() + # likelihood = GPy.likelihoods.EP(Y, distribution) + # m = GPy.core.SparseGP(X, likelihood, kernel, Z) + # m.ensure_default_constraints() + self.assertTrue(m.checkgrad()) + + @unittest.expectedFailure + def test_generalized_FITC(self): + N = 20 + X = np.hstack([np.random.rand(N / 2) + 1, np.random.rand(N / 2) - 1])[:, None] + k = GPy.kern.RBF(1) + GPy.kern.White(1) + Y = np.hstack([np.ones(N / 2), np.zeros(N / 2)])[:, None] + m = GPy.models.FITCClassification(X, Y, kernel=k) + m.update_likelihood_approximation() + self.assertTrue(m.checkgrad()) + + @unittest.expectedFailure + def test_multioutput_regression_1D(self): + X1 = np.random.rand(50, 1) * 8 + X2 = np.random.rand(30, 1) * 5 + X = np.vstack((X1, X2)) + Y1 = np.sin(X1) + np.random.randn(*X1.shape) * 0.05 + Y2 = -np.sin(X2) + np.random.randn(*X2.shape) * 0.05 + Y = np.vstack((Y1, Y2)) + + k1 = GPy.kern.RBF(1) + m = GPy.models.GPMultioutputRegression(X_list=[X1, X2], Y_list=[Y1, Y2], kernel_list=[k1]) + import ipdb;ipdb.set_trace() + m.constrain_fixed('.*rbf_var', 1.) + self.assertTrue(m.checkgrad()) + + @unittest.expectedFailure + def test_multioutput_sparse_regression_1D(self): + X1 = np.random.rand(500, 1) * 8 + X2 = np.random.rand(300, 1) * 5 + X = np.vstack((X1, X2)) + Y1 = np.sin(X1) + np.random.randn(*X1.shape) * 0.05 + Y2 = -np.sin(X2) + np.random.randn(*X2.shape) * 0.05 + Y = np.vstack((Y1, Y2)) + + k1 = GPy.kern.RBF(1) + m = GPy.models.SparseGPMultioutputRegression(X_list=[X1, X2], Y_list=[Y1, Y2], kernel_list=[k1]) + m.constrain_fixed('.*rbf_var', 1.) + self.assertTrue(m.checkgrad()) + + def test_gp_heteroscedastic_regression(self): + num_obs = 25 + X = np.random.randint(0, 140, num_obs) + X = X[:, None] + Y = 25. + np.sin(X / 20.) * 2. + np.random.rand(num_obs)[:, None] + kern = GPy.kern.Bias(1) + GPy.kern.RBF(1) + m = GPy.models.GPHeteroscedasticRegression(X, Y, kern) + self.assertTrue(m.checkgrad()) + + def test_sparse_gp_heteroscedastic_regression(self): + num_obs = 25 + X = np.random.randint(0, 140, num_obs) + X = X[:, None] + Y = 25. + np.sin(X / 20.) * 2. + np.random.rand(num_obs)[:, None] + kern = GPy.kern.Bias(1) + GPy.kern.RBF(1) + Y_metadata = {'output_index':np.arange(num_obs)[:,None]} + noise_terms = np.unique(Y_metadata['output_index'].flatten()) + likelihoods_list = [GPy.likelihoods.Gaussian(name="Gaussian_noise_%s" %j) for j in noise_terms] + likelihood = GPy.likelihoods.MixedNoise(likelihoods_list=likelihoods_list) + m = GPy.core.SparseGP(X, Y, X[np.random.choice(num_obs, 10)], + kern, likelihood, + GPy.inference.latent_function_inference.VarDTC(), + Y_metadata=Y_metadata) + self.assertTrue(m.checkgrad()) + + def test_gp_kronecker_gaussian(self): + N1, N2 = 30, 20 + X1 = np.random.randn(N1, 1) + X2 = np.random.randn(N2, 1) + X1.sort(0); X2.sort(0) + k1 = GPy.kern.RBF(1) # + GPy.kern.White(1) + k2 = GPy.kern.RBF(1) # + GPy.kern.White(1) + Y = np.random.randn(N1, N2) + Y = Y - Y.mean(0) + Y = Y / Y.std(0) + m = GPy.models.GPKroneckerGaussianRegression(X1, X2, Y, k1, k2) + + # build the model the dumb way + assert (N1 * N2 < 1000), "too much data for standard GPs!" + yy, xx = np.meshgrid(X2, X1) + Xgrid = np.vstack((xx.flatten(order='F'), yy.flatten(order='F'))).T + kg = GPy.kern.RBF(1, active_dims=[0]) * GPy.kern.RBF(1, active_dims=[1]) + mm = GPy.models.GPRegression(Xgrid, Y.reshape(-1, 1, order='F'), kernel=kg) + + m.randomize() + mm[:] = m[:] + assert np.allclose(m.log_likelihood(), mm.log_likelihood()) + assert np.allclose(m.gradient, mm.gradient) + X1test = np.random.randn(100, 1) + X2test = np.random.randn(100, 1) + mean1, var1 = m.predict(X1test, X2test) + yy, xx = np.meshgrid(X2test, X1test) + Xgrid = np.vstack((xx.flatten(order='F'), yy.flatten(order='F'))).T + mean2, var2 = mm.predict(Xgrid) + assert np.allclose(mean1, mean2) + assert np.allclose(var1, var2) + + def test_gp_VGPC(self): + num_obs = 25 + X = np.random.randint(0, 140, num_obs) + X = X[:, None] + Y = 25. + np.sin(X / 20.) * 2. + np.random.rand(num_obs)[:, None] + kern = GPy.kern.Bias(1) + GPy.kern.RBF(1) + m = GPy.models.GPVariationalGaussianApproximation(X, Y, kern) + self.assertTrue(m.checkgrad()) + + +if __name__ == "__main__": + print "Running unit tests, please be (very) patient..." + unittest.main() diff --git a/GPy/testing/mpi_tests.py b/GPy/testing/mpi_tests.py new file mode 100644 index 00000000..5c489032 --- /dev/null +++ b/GPy/testing/mpi_tests.py @@ -0,0 +1,92 @@ +# Copyright (c) 2013-2014, Zhenwen Dai +# Licensed under the BSD 3-clause license (see LICENSE.txt) + +import unittest +import numpy as np +import GPy + +try: + from mpi4py import MPI + import subprocess + + class MPITests(unittest.TestCase): + + def test_BayesianGPLVM_MPI(self): + code = """ +import numpy as np +import GPy +from mpi4py import MPI +np.random.seed(123456) +comm = MPI.COMM_WORLD +N = 100 +x = np.linspace(-6., 6., N) +y = np.sin(x) + np.random.randn(N) * 0.05 +comm.Bcast(y) +data = np.vstack([x,y]) +infr = GPy.inference.latent_function_inference.VarDTC_minibatch(mpi_comm=comm) +m = GPy.models.BayesianGPLVM(data.T,1,mpi_comm=comm) +m.optimize(max_iters=10) +if comm.rank==0: + print float(m.objective_function()) + m.inference_method.mpi_comm=None + m.mpi_comm=None + m._trigger_params_changed() + print float(m.objective_function()) + """ + with open('mpi_test__.py','w') as f: + f.write(code) + f.close() + p = subprocess.Popen('mpirun -n 4 python mpi_test__.py',stdout=subprocess.PIPE,shell=True) + (stdout, stderr) = p.communicate() + L1 = float(stdout.splitlines()[-2]) + L2 = float(stdout.splitlines()[-1]) + self.assertTrue(np.allclose(L1,L2)) + import os + os.remove('mpi_test__.py') + + def test_SparseGPRegression_MPI(self): + code = """ +import numpy as np +import GPy +from mpi4py import MPI +np.random.seed(123456) +comm = MPI.COMM_WORLD +N = 100 +x = np.linspace(-6., 6., N) +y = np.sin(x) + np.random.randn(N) * 0.05 +comm.Bcast(y) +data = np.vstack([x,y]) +#infr = GPy.inference.latent_function_inference.VarDTC_minibatch(mpi_comm=comm) +m = GPy.models.SparseGPRegression(data[:1].T,data[1:2].T,mpi_comm=comm) +m.optimize(max_iters=10) +if comm.rank==0: + print float(m.objective_function()) + m.inference_method.mpi_comm=None + m.mpi_comm=None + m._trigger_params_changed() + print float(m.objective_function()) + """ + with open('mpi_test__.py','w') as f: + f.write(code) + f.close() + p = subprocess.Popen('mpirun -n 4 python mpi_test__.py',stdout=subprocess.PIPE,shell=True) + (stdout, stderr) = p.communicate() + L1 = float(stdout.splitlines()[-2]) + L2 = float(stdout.splitlines()[-1]) + self.assertTrue(np.allclose(L1,L2)) + import os + os.remove('mpi_test__.py') + + +except: + pass + + + +if __name__ == "__main__": + print "Running unit tests, please be (very) patient..." + try: + import mpi4py + unittest.main() + except: + pass diff --git a/GPy/testing/mrd_tests.py b/GPy/testing/mrd_tests.py deleted file mode 100644 index 40fcb86a..00000000 --- a/GPy/testing/mrd_tests.py +++ /dev/null @@ -1,32 +0,0 @@ -# Copyright (c) 2013, Max Zwiessele -# Licensed under the BSD 3-clause license (see LICENSE.txt) -''' -Created on 10 Apr 2013 - -@author: maxz -''' - -import unittest -import numpy as np -import GPy - -class MRDTests(unittest.TestCase): - - def test_gradients(self): - num_m = 3 - N, num_inducing, input_dim, D = 20, 8, 6, 20 - X = np.random.rand(N, input_dim) - - k = GPy.kern.linear(input_dim) + GPy.kern.bias(input_dim) + GPy.kern.white(input_dim) - K = k.K(X) - - Ylist = [np.random.multivariate_normal(np.zeros(N), K, input_dim).T for _ in range(num_m)] - likelihood_list = [GPy.likelihoods.Gaussian(Y) for Y in Ylist] - - m = GPy.models.MRD(likelihood_list, input_dim=input_dim, kernels=k, num_inducing=num_inducing) - - self.assertTrue(m.checkgrad()) - -if __name__ == "__main__": - print "Running unit tests, please be (very) patient..." - unittest.main() diff --git a/GPy/testing/observable_tests.py b/GPy/testing/observable_tests.py new file mode 100644 index 00000000..84059d98 --- /dev/null +++ b/GPy/testing/observable_tests.py @@ -0,0 +1,132 @@ +# Copyright (c) 2014, Max Zwiessele +# Licensed under the BSD 3-clause license (see LICENSE.txt) +import unittest +from GPy.core.parameterization.parameterized import Parameterized +from GPy.core.parameterization.param import Param +import numpy + +# One trigger in init +_trigger_start = -1 + +class ParamTestParent(Parameterized): + parent_changed_count = _trigger_start + def parameters_changed(self): + self.parent_changed_count += 1 + +class ParameterizedTest(Parameterized): + # One trigger after initialization + params_changed_count = _trigger_start + def parameters_changed(self): + self.params_changed_count += 1 + +class Test(unittest.TestCase): + + def setUp(self): + self.parent = ParamTestParent('test parent') + self.par = ParameterizedTest('test model') + self.par2 = ParameterizedTest('test model 2') + self.p = Param('test parameter', numpy.random.normal(1,2,(10,3))) + + self.par.link_parameter(self.p) + self.par.link_parameter(Param('test1', numpy.random.normal(0,1,(1,)))) + self.par.link_parameter(Param('test2', numpy.random.normal(0,1,(1,)))) + + self.par2.link_parameter(Param('par2 test1', numpy.random.normal(0,1,(1,)))) + self.par2.link_parameter(Param('par2 test2', numpy.random.normal(0,1,(1,)))) + + self.parent.link_parameter(self.par) + self.parent.link_parameter(self.par2) + + self._observer_triggered = None + self._trigger_count = 0 + self._first = None + self._second = None + + def _trigger(self, me, which): + self._observer_triggered = which + self._trigger_count += 1 + if self._first is not None: + self._second = self._trigger + else: + self._first = self._trigger + + def _trigger_priority(self, me, which): + if self._first is not None: + self._second = self._trigger_priority + else: + self._first = self._trigger_priority + + def test_observable(self): + self.par.add_observer(self, self._trigger, -1) + self.assertEqual(self.par.params_changed_count, 0, 'no params changed yet') + self.assertEqual(self.par.params_changed_count, self.parent.parent_changed_count, 'parent should be triggered as often as param') + + self.p[0,1] = 3 # trigger observers + self.assertIs(self._observer_triggered, self.p, 'observer should have triggered') + self.assertEqual(self._trigger_count, 1, 'observer should have triggered once') + self.assertEqual(self.par.params_changed_count, 1, 'params changed once') + self.assertEqual(self.par.params_changed_count, self.parent.parent_changed_count, 'parent should be triggered as often as param') + + self.par.remove_observer(self) + self.p[0,1] = 4 + self.assertIs(self._observer_triggered, self.p, 'observer should not have triggered') + self.assertEqual(self._trigger_count, 1, 'observer should have triggered once') + self.assertEqual(self.par.params_changed_count, 2, 'params changed second') + self.assertEqual(self.par.params_changed_count, self.parent.parent_changed_count, 'parent should be triggered as often as param') + + self.par.add_observer(self, self._trigger, -1) + self.p[0,1] = 4 + self.assertIs(self._observer_triggered, self.p, 'observer should have triggered') + self.assertEqual(self._trigger_count, 2, 'observer should have triggered once') + self.assertEqual(self.par.params_changed_count, 3, 'params changed second') + self.assertEqual(self.par.params_changed_count, self.parent.parent_changed_count, 'parent should be triggered as often as param') + + self.par.remove_observer(self, self._trigger) + self.p[0,1] = 3 + self.assertIs(self._observer_triggered, self.p, 'observer should not have triggered') + self.assertEqual(self._trigger_count, 2, 'observer should have triggered once') + self.assertEqual(self.par.params_changed_count, 4, 'params changed second') + self.assertEqual(self.par.params_changed_count, self.parent.parent_changed_count, 'parent should be triggered as often as param') + + def test_set_params(self): + self.assertEqual(self.par.params_changed_count, 0, 'no params changed yet') + self.par.param_array[:] = 1 + self.par._trigger_params_changed() + self.assertEqual(self.par.params_changed_count, 1, 'now params changed') + self.assertEqual(self.parent.parent_changed_count, self.par.params_changed_count) + + self.par.param_array[:] = 2 + self.par._trigger_params_changed() + self.assertEqual(self.par.params_changed_count, 2, 'now params changed') + self.assertEqual(self.parent.parent_changed_count, self.par.params_changed_count) + + + def test_priority_notify(self): + self.assertEqual(self.par.params_changed_count, 0) + self.par.notify_observers(0, None) + self.assertEqual(self.par.params_changed_count, 1) + self.assertEqual(self.parent.parent_changed_count, self.par.params_changed_count) + + self.par.notify_observers(0, -numpy.inf) + self.assertEqual(self.par.params_changed_count, 2) + self.assertEqual(self.parent.parent_changed_count, 1) + + def test_priority(self): + self.par.add_observer(self, self._trigger, -1) + self.par.add_observer(self, self._trigger_priority, 0) + self.par.notify_observers(0) + self.assertEqual(self._first, self._trigger_priority, 'priority should be first') + self.assertEqual(self._second, self._trigger, 'priority should be first') + + self.par.remove_observer(self) + self._first = self._second = None + + self.par.add_observer(self, self._trigger, 1) + self.par.add_observer(self, self._trigger_priority, 0) + self.par.notify_observers(0) + self.assertEqual(self._first, self._trigger, 'priority should be second') + self.assertEqual(self._second, self._trigger_priority, 'priority should be second') + +if __name__ == "__main__": + #import sys;sys.argv = ['', 'Test.testName'] + unittest.main() diff --git a/GPy/testing/parameterized_tests.py b/GPy/testing/parameterized_tests.py new file mode 100644 index 00000000..7c4f4ce2 --- /dev/null +++ b/GPy/testing/parameterized_tests.py @@ -0,0 +1,257 @@ +''' +Created on Feb 13, 2014 + +@author: maxzwiessele +''' +import unittest +import GPy +import numpy as np +from GPy.core.parameterization.parameter_core import HierarchyError +from GPy.core.parameterization.observable_array import ObsAr +from GPy.core.parameterization.transformations import NegativeLogexp, Logistic +from GPy.core.parameterization.parameterized import Parameterized +from GPy.core.parameterization.param import Param +from GPy.core.parameterization.index_operations import ParameterIndexOperations + +class ArrayCoreTest(unittest.TestCase): + def setUp(self): + self.X = np.random.normal(1,1, size=(100,10)) + self.obsX = ObsAr(self.X) + + def test_init(self): + X = ObsAr(self.X) + X2 = ObsAr(X) + self.assertIs(X, X2, "no new Observable array, when Observable is given") + + def test_slice(self): + t1 = self.X[2:78] + t2 = self.obsX[2:78] + self.assertListEqual(t1.tolist(), t2.tolist(), "Slicing should be the exact same, as in ndarray") + +class ParameterizedTest(unittest.TestCase): + + def setUp(self): + self.rbf = GPy.kern.RBF(20) + self.white = GPy.kern.White(1) + from GPy.core.parameterization import Param + from GPy.core.parameterization.transformations import Logistic + self.param = Param('param', np.random.uniform(0,1,(10,5)), Logistic(0, 1)) + + self.test1 = GPy.core.Parameterized("test model") + self.test1.param = self.param + self.test1.kern = self.rbf+self.white + self.test1.link_parameter(self.test1.kern) + self.test1.link_parameter(self.param, 0) + + # print self.test1: + #============================================================================= + # test_model. | Value | Constraint | Prior | Tied to + # param | (25L, 2L) | {0.0,1.0} | | + # add.rbf.variance | 1.0 | 0.0,1.0 +ve | | + # add.rbf.lengthscale | 1.0 | 0.0,1.0 +ve | | + # add.white.variance | 1.0 | 0.0,1.0 +ve | | + #============================================================================= + + x = np.linspace(-2,6,4)[:,None] + y = np.sin(x) + self.testmodel = GPy.models.GPRegression(x,y) + # print self.testmodel: + #============================================================================= + # GP_regression. | Value | Constraint | Prior | Tied to + # rbf.variance | 1.0 | +ve | | + # rbf.lengthscale | 1.0 | +ve | | + # Gaussian_noise.variance | 1.0 | +ve | | + #============================================================================= + + def test_add_parameter(self): + self.assertEquals(self.rbf._parent_index_, 0) + self.assertEquals(self.white._parent_index_, 1) + self.assertEquals(self.param._parent_index_, 0) + pass + + def test_fixes(self): + self.white.fix(warning=False) + self.test1.unlink_parameter(self.param) + self.assertTrue(self.test1._has_fixes()) + from GPy.core.parameterization.transformations import FIXED, UNFIXED + self.assertListEqual(self.test1._fixes_.tolist(),[UNFIXED,UNFIXED,FIXED]) + self.test1.kern.link_parameter(self.white, 0) + self.assertListEqual(self.test1._fixes_.tolist(),[FIXED,UNFIXED,UNFIXED]) + self.test1.kern.rbf.fix() + self.assertListEqual(self.test1._fixes_.tolist(),[FIXED]*3) + self.test1.fix() + self.assertTrue(self.test1.is_fixed) + self.assertListEqual(self.test1._fixes_.tolist(),[FIXED]*self.test1.size) + + def test_remove_parameter(self): + from GPy.core.parameterization.transformations import FIXED, UNFIXED, __fixed__, Logexp + self.white.fix() + self.test1.kern.unlink_parameter(self.white) + self.assertIs(self.test1._fixes_,None) + + self.assertIsInstance(self.white.constraints, ParameterIndexOperations) + self.assertListEqual(self.white._fixes_.tolist(), [FIXED]) + self.assertIs(self.test1.constraints, self.rbf.constraints._param_index_ops) + self.assertIs(self.test1.constraints, self.param.constraints._param_index_ops) + + self.test1.link_parameter(self.white, 0) + self.assertIs(self.test1.constraints, self.white.constraints._param_index_ops) + self.assertIs(self.test1.constraints, self.rbf.constraints._param_index_ops) + self.assertIs(self.test1.constraints, self.param.constraints._param_index_ops) + self.assertListEqual(self.test1.constraints[__fixed__].tolist(), [0]) + self.assertIs(self.white._fixes_,None) + self.assertListEqual(self.test1._fixes_.tolist(),[FIXED] + [UNFIXED] * 52) + + self.test1.unlink_parameter(self.white) + self.assertIs(self.test1._fixes_,None) + self.assertListEqual(self.white._fixes_.tolist(), [FIXED]) + self.assertIs(self.test1.constraints, self.rbf.constraints._param_index_ops) + self.assertIs(self.test1.constraints, self.param.constraints._param_index_ops) + self.assertListEqual(self.test1.constraints[Logexp()].tolist(), range(self.param.size, self.param.size+self.rbf.size)) + + def test_remove_parameter_param_array_grad_array(self): + val = self.test1.kern.param_array.copy() + self.test1.kern.unlink_parameter(self.white) + self.assertListEqual(self.test1.kern.param_array.tolist(), val[:2].tolist()) + + def test_add_parameter_already_in_hirarchy(self): + self.assertRaises(HierarchyError, self.test1.link_parameter, self.white.parameters[0]) + + def test_default_constraints(self): + self.assertIs(self.rbf.variance.constraints._param_index_ops, self.rbf.constraints._param_index_ops) + self.assertIs(self.test1.constraints, self.rbf.constraints._param_index_ops) + self.assertListEqual(self.rbf.constraints.indices()[0].tolist(), range(2)) + from GPy.core.parameterization.transformations import Logexp + kern = self.test1.kern + self.test1.unlink_parameter(kern) + self.assertListEqual(kern.constraints[Logexp()].tolist(), range(3)) + + def test_constraints(self): + self.rbf.constrain(GPy.transformations.Square(), False) + self.assertListEqual(self.test1.constraints[GPy.transformations.Square()].tolist(), range(self.param.size, self.param.size+self.rbf.size)) + self.assertListEqual(self.test1.constraints[GPy.transformations.Logexp()].tolist(), [self.param.size+self.rbf.size]) + + self.test1.kern.unlink_parameter(self.rbf) + self.assertListEqual(self.test1.constraints[GPy.transformations.Square()].tolist(), []) + + def test_constraints_link_unlink(self): + self.test1.unlink_parameter(self.test1.kern) + self.test1.kern.rbf.unlink_parameter(self.test1.kern.rbf.lengthscale) + self.test1.kern.rbf.link_parameter(self.test1.kern.rbf.lengthscale) + self.test1.kern.rbf.unlink_parameter(self.test1.kern.rbf.lengthscale) + self.test1.link_parameter(self.test1.kern) + + def test_constraints_views(self): + self.assertEqual(self.white.constraints._offset, self.param.size+self.rbf.size) + self.assertEqual(self.rbf.constraints._offset, self.param.size) + self.assertEqual(self.param.constraints._offset, 0) + + def test_fixing_randomize(self): + self.white.fix(warning=True) + val = float(self.white.variance) + self.test1.randomize() + self.assertEqual(val, self.white.variance) + + def test_randomize(self): + ps = self.test1.param.view(np.ndarray).copy() + self.test1.param[2:5].fix() + self.test1.param.randomize() + self.assertFalse(np.all(ps==self.test1.param),str(ps)+str(self.test1.param)) + + def test_fixing_randomize_parameter_handling(self): + self.rbf.fix(warning=True) + val = float(self.rbf.variance) + self.test1.kern.randomize() + self.assertEqual(val, self.rbf.variance) + + def test_updates(self): + val = float(self.testmodel.log_likelihood()) + self.testmodel.update_model(False) + self.testmodel.kern.randomize() + self.testmodel.likelihood.randomize() + self.assertEqual(val, self.testmodel.log_likelihood()) + self.testmodel.update_model(True) + self.assertNotEqual(val, self.testmodel.log_likelihood()) + + def test_fixing_optimize(self): + self.testmodel.kern.lengthscale.fix() + val = float(self.testmodel.kern.lengthscale) + self.testmodel.randomize() + self.assertEqual(val, self.testmodel.kern.lengthscale) + + def test_add_parameter_in_hierarchy(self): + self.test1.kern.rbf.link_parameter(Param("NEW", np.random.rand(2), NegativeLogexp()), 1) + self.assertListEqual(self.test1.constraints[NegativeLogexp()].tolist(), range(self.param.size+1, self.param.size+1 + 2)) + self.assertListEqual(self.test1.constraints[GPy.transformations.Logistic(0,1)].tolist(), range(self.param.size)) + self.assertListEqual(self.test1.constraints[GPy.transformations.Logexp(0,1)].tolist(), np.r_[50, 53:55].tolist()) + + def test_regular_expression_misc(self): + self.testmodel.kern.lengthscale.fix() + val = float(self.testmodel.kern.lengthscale) + self.testmodel.randomize() + self.assertEqual(val, self.testmodel.kern.lengthscale) + + variances = self.testmodel['.*var'].values() + self.testmodel['.*var'].fix() + self.testmodel.randomize() + np.testing.assert_equal(variances, self.testmodel['.*var'].values()) + + def test_fix_unfix(self): + fixed = self.testmodel.kern.lengthscale.fix() + self.assertListEqual(fixed.tolist(), [0]) + unfixed = self.testmodel.kern.lengthscale.unfix() + self.testmodel.kern.lengthscale.constrain_positive() + self.assertListEqual(unfixed.tolist(), [0]) + + fixed = self.testmodel.kern.fix() + self.assertListEqual(fixed.tolist(), [0,1]) + unfixed = self.testmodel.kern.unfix() + self.assertListEqual(unfixed.tolist(), [0,1]) + + def test_constraints_in_init(self): + class Test(Parameterized): + def __init__(self, name=None, parameters=[], *a, **kw): + super(Test, self).__init__(name=name) + self.x = Param('x', np.random.uniform(0,1,(3,4))) + self.x[0].constrain_bounded(0,1) + self.link_parameter(self.x) + self.x[1].fix() + t = Test() + c = {Logistic(0,1): np.array([0, 1, 2, 3]), 'fixed': np.array([4, 5, 6, 7])} + np.testing.assert_equal(t.x.constraints[Logistic(0,1)], c[Logistic(0,1)]) + np.testing.assert_equal(t.x.constraints['fixed'], c['fixed']) + + def test_parameter_modify_in_init(self): + class TestLikelihood(Parameterized): + def __init__(self, param1 = 2., param2 = 3.): + super(TestLikelihood, self).__init__("TestLike") + self.p1 = Param('param1', param1) + self.p2 = Param('param2', param2) + + self.link_parameter(self.p1) + self.link_parameter(self.p2) + + self.p1.fix() + self.p1.unfix() + self.p2.constrain_negative() + self.p1.fix() + self.p2.constrain_positive() + self.p2.fix() + self.p2.constrain_positive() + + m = TestLikelihood() + print m + val = m.p1.values.copy() + self.assert_(m.p1.is_fixed) + self.assert_(m.constraints[GPy.constraints.Logexp()].tolist(), [1]) + m.randomize() + self.assertEqual(m.p1, val) + + def test_printing(self): + print self.test1 + print self.param + print self.test1[''] + +if __name__ == "__main__": + #import sys;sys.argv = ['', 'Test.test_add_parameter'] + unittest.main() diff --git a/GPy/testing/pickle_tests.py b/GPy/testing/pickle_tests.py new file mode 100644 index 00000000..d6d6f923 --- /dev/null +++ b/GPy/testing/pickle_tests.py @@ -0,0 +1,220 @@ +''' +Created on 13 Mar 2014 + +@author: maxz +''' +import unittest, itertools +#import cPickle as pickle +import pickle +import numpy as np +from GPy.core.parameterization.index_operations import ParameterIndexOperations,\ + ParameterIndexOperationsView +import tempfile +from GPy.core.parameterization.param import Param +from GPy.core.parameterization.observable_array import ObsAr +from GPy.core.parameterization.priors import Gaussian +from GPy.kern._src.rbf import RBF +from GPy.kern._src.linear import Linear +from GPy.kern._src.static import Bias, White +from GPy.examples.dimensionality_reduction import mrd_simulation +from GPy.core.parameterization.variational import NormalPosterior +from GPy.models.gp_regression import GPRegression + +def toy_model(): + X = np.linspace(0,1,50)[:, None] + Y = np.sin(X) + m = GPRegression(X=X, Y=Y) + return m + +class ListDictTestCase(unittest.TestCase): + def assertListDictEquals(self, d1, d2, msg=None): + for k,v in d1.iteritems(): + self.assertListEqual(list(v), list(d2[k]), msg) + def assertArrayListEquals(self, l1, l2): + for a1, a2 in itertools.izip(l1,l2): + np.testing.assert_array_equal(a1, a2) + +class Test(ListDictTestCase): + def test_parameter_index_operations(self): + pio = ParameterIndexOperations(dict(test1=np.array([4,3,1,6,4]), test2=np.r_[2:130])) + piov = ParameterIndexOperationsView(pio, 20, 250) + self.assertListDictEquals(dict(piov.items()), dict(piov.copy().iteritems())) + self.assertListDictEquals(dict(pio.iteritems()), dict(pio.copy().items())) + + self.assertArrayListEquals(pio.copy().indices(), pio.indices()) + self.assertArrayListEquals(piov.copy().indices(), piov.indices()) + + with tempfile.TemporaryFile('w+b') as f: + pickle.dump(pio, f) + f.seek(0) + pio2 = pickle.load(f) + self.assertListDictEquals(pio._properties, pio2._properties) + + with tempfile.TemporaryFile('w+b') as f: + pickle.dump(piov, f) + f.seek(0) + pio2 = pickle.load(f) + self.assertListDictEquals(dict(piov.items()), dict(pio2.iteritems())) + + def test_param(self): + param = Param('test', np.arange(4*2).reshape(4,2)) + param[0].constrain_positive() + param[1].fix() + param[2].set_prior(Gaussian(0,1)) + pcopy = param.copy() + self.assertListEqual(param.tolist(), pcopy.tolist()) + self.assertListEqual(str(param).split('\n'), str(pcopy).split('\n')) + self.assertIsNot(param, pcopy) + with tempfile.TemporaryFile('w+b') as f: + pickle.dump(param, f) + f.seek(0) + pcopy = pickle.load(f) + self.assertListEqual(param.tolist(), pcopy.tolist()) + self.assertSequenceEqual(str(param), str(pcopy)) + + def test_observable_array(self): + obs = ObsAr(np.arange(4*2).reshape(4,2)) + pcopy = obs.copy() + self.assertListEqual(obs.tolist(), pcopy.tolist()) + with tempfile.TemporaryFile('w+b') as f: + pickle.dump(obs, f) + f.seek(0) + pcopy = pickle.load(f) + self.assertListEqual(obs.tolist(), pcopy.tolist()) + self.assertSequenceEqual(str(obs), str(pcopy)) + + def test_parameterized(self): + par = RBF(1, active_dims=[1]) + Linear(2, active_dims=[0,2]) + Bias(3) + White(3) + par.gradient = 10 + par.randomize() + pcopy = par.copy() + self.assertIsInstance(pcopy.constraints, ParameterIndexOperations) + self.assertIsInstance(pcopy.rbf.constraints, ParameterIndexOperationsView) + self.assertIs(pcopy.constraints, pcopy.rbf.constraints._param_index_ops) + self.assertIs(pcopy.constraints, pcopy.rbf.lengthscale.constraints._param_index_ops) + self.assertIs(pcopy.constraints, pcopy.linear.constraints._param_index_ops) + self.assertListEqual(par.param_array.tolist(), pcopy.param_array.tolist()) + pcopy.gradient = 10 # gradient does not get copied anymore + self.assertListEqual(par.gradient_full.tolist(), pcopy.gradient_full.tolist()) + self.assertSequenceEqual(str(par), str(pcopy)) + self.assertIsNot(par.param_array, pcopy.param_array) + self.assertIsNot(par.gradient_full, pcopy.gradient_full) + with tempfile.TemporaryFile('w+b') as f: + par.pickle(f) + f.seek(0) + pcopy = pickle.load(f) + self.assertListEqual(par.param_array.tolist(), pcopy.param_array.tolist()) + pcopy.gradient = 10 + np.testing.assert_allclose(par.linear.gradient_full, pcopy.linear.gradient_full) + np.testing.assert_allclose(pcopy.linear.gradient_full, 10) + self.assertSequenceEqual(str(par), str(pcopy)) + + def test_model(self): + par = toy_model() + pcopy = par.copy() + self.assertListEqual(par.param_array.tolist(), pcopy.param_array.tolist()) + np.testing.assert_allclose(par.gradient_full, pcopy.gradient_full) + self.assertSequenceEqual(str(par), str(pcopy)) + self.assertIsNot(par.param_array, pcopy.param_array) + self.assertIsNot(par.gradient_full, pcopy.gradient_full) + self.assertTrue(pcopy.checkgrad()) + self.assert_(np.any(pcopy.gradient!=0.0)) + with tempfile.TemporaryFile('w+b') as f: + par.pickle(f) + f.seek(0) + pcopy = pickle.load(f) + self.assertListEqual(par.param_array.tolist(), pcopy.param_array.tolist()) + np.testing.assert_allclose(par.gradient_full, pcopy.gradient_full) + self.assertSequenceEqual(str(par), str(pcopy)) + self.assert_(pcopy.checkgrad()) + + def test_modelrecreation(self): + par = toy_model() + pcopy = GPRegression(par.X.copy(), par.Y.copy(), kernel=par.kern.copy()) + np.testing.assert_allclose(par.param_array, pcopy.param_array) + np.testing.assert_allclose(par.gradient_full, pcopy.gradient_full) + self.assertSequenceEqual(str(par), str(pcopy)) + self.assertIsNot(par.param_array, pcopy.param_array) + self.assertIsNot(par.gradient_full, pcopy.gradient_full) + self.assertTrue(pcopy.checkgrad()) + self.assert_(np.any(pcopy.gradient!=0.0)) + pcopy.optimize('bfgs') + par.optimize('bfgs') + np.testing.assert_allclose(pcopy.param_array, par.param_array, atol=1e-6) + par.randomize() + with tempfile.TemporaryFile('w+b') as f: + par.pickle(f) + f.seek(0) + pcopy = pickle.load(f) + np.testing.assert_allclose(par.param_array, pcopy.param_array) + np.testing.assert_allclose(par.gradient_full, pcopy.gradient_full, atol=1e-6) + self.assertSequenceEqual(str(par), str(pcopy)) + self.assert_(pcopy.checkgrad()) + + def test_posterior(self): + X = np.random.randn(3,5) + Xv = np.random.rand(*X.shape) + par = NormalPosterior(X,Xv) + par.gradient = 10 + pcopy = par.copy() + pcopy.gradient = 10 + self.assertListEqual(par.param_array.tolist(), pcopy.param_array.tolist()) + self.assertListEqual(par.gradient_full.tolist(), pcopy.gradient_full.tolist()) + self.assertSequenceEqual(str(par), str(pcopy)) + self.assertIsNot(par.param_array, pcopy.param_array) + self.assertIsNot(par.gradient_full, pcopy.gradient_full) + with tempfile.TemporaryFile('w+b') as f: + par.pickle(f) + f.seek(0) + pcopy = pickle.load(f) + self.assertListEqual(par.param_array.tolist(), pcopy.param_array.tolist()) + pcopy.gradient = 10 + np.testing.assert_allclose(par.gradient_full, pcopy.gradient_full) + np.testing.assert_allclose(pcopy.mean.gradient_full, 10) + self.assertSequenceEqual(str(par), str(pcopy)) + + def test_model_concat(self): + par = mrd_simulation(optimize=0, plot=0, plot_sim=0) + par.randomize() + pcopy = par.copy() + self.assertListEqual(par.param_array.tolist(), pcopy.param_array.tolist()) + self.assertListEqual(par.gradient_full.tolist(), pcopy.gradient_full.tolist()) + self.assertSequenceEqual(str(par), str(pcopy)) + self.assertIsNot(par.param_array, pcopy.param_array) + self.assertIsNot(par.gradient_full, pcopy.gradient_full) + self.assertTrue(par.checkgrad()) + self.assertTrue(pcopy.checkgrad()) + self.assert_(np.any(pcopy.gradient!=0.0)) + with tempfile.TemporaryFile('w+b') as f: + par.pickle(f) + f.seek(0) + pcopy = pickle.load(f) + self.assertListEqual(par.param_array.tolist(), pcopy.param_array.tolist()) + np.testing.assert_allclose(par.gradient_full, pcopy.gradient_full) + self.assertSequenceEqual(str(par), str(pcopy)) + self.assert_(pcopy.checkgrad()) + + def _callback(self, what, which): + what.count += 1 + + @unittest.skip + def test_add_observer(self): + par = toy_model() + par.name = "original" + par.count = 0 + par.add_observer(self, self._callback, 1) + pcopy = GPRegression(par.X.copy(), par.Y.copy(), kernel=par.kern.copy()) + self.assertNotIn(par.observers[0], pcopy.observers) + pcopy = par.copy() + pcopy.name = "copy" + self.assertTrue(par.checkgrad()) + self.assertTrue(pcopy.checkgrad()) + self.assertTrue(pcopy.kern.checkgrad()) + import ipdb;ipdb.set_trace() + self.assertIn(par.observers[0], pcopy.observers) + self.assertEqual(par.count, 3) + self.assertEqual(pcopy.count, 6) # 3 of each call to checkgrad + +if __name__ == "__main__": + #import sys;sys.argv = ['', 'Test.test_parameter_index_operations'] + unittest.main() diff --git a/GPy/testing/prior_tests.py b/GPy/testing/prior_tests.py index c16057db..6a61fbb5 100644 --- a/GPy/testing/prior_tests.py +++ b/GPy/testing/prior_tests.py @@ -15,7 +15,7 @@ class PriorTests(unittest.TestCase): X, y = X[:, None], y[:, None] m = GPy.models.GPRegression(X, y) lognormal = GPy.priors.LogGaussian(1, 2) - m.set_prior('rbf', lognormal) + m.rbf.set_prior(lognormal) m.randomize() self.assertTrue(m.checkgrad()) @@ -28,7 +28,7 @@ class PriorTests(unittest.TestCase): X, y = X[:, None], y[:, None] m = GPy.models.GPRegression(X, y) Gamma = GPy.priors.Gamma(1, 1) - m.set_prior('rbf', Gamma) + m.rbf.set_prior(Gamma) m.randomize() self.assertTrue(m.checkgrad()) @@ -41,16 +41,72 @@ class PriorTests(unittest.TestCase): X, y = X[:, None], y[:, None] m = GPy.models.GPRegression(X, y) gaussian = GPy.priors.Gaussian(1, 1) - success = False - # setting a Gaussian prior on non-negative parameters # should raise an assertionerror. - try: - m.set_prior('rbf', gaussian) - except AssertionError: - success = True + self.assertRaises(AssertionError, m.rbf.set_prior, gaussian) + + def test_set_prior(self): + xmin, xmax = 1, 2.5*np.pi + b, C, SNR = 1, 0, 0.1 + X = np.linspace(xmin, xmax, 500) + y = b*X + C + 1*np.sin(X) + y += 0.05*np.random.randn(len(X)) + X, y = X[:, None], y[:, None] + m = GPy.models.GPRegression(X, y) + + gaussian = GPy.priors.Gaussian(1, 1) + #m.rbf.set_prior(gaussian) + # setting a Gaussian prior on non-negative parameters + # should raise an assertionerror. + self.assertRaises(AssertionError, m.rbf.set_prior, gaussian) + + def test_set_gaussian_for_reals(self): + xmin, xmax = 1, 2.5*np.pi + b, C, SNR = 1, 0, 0.1 + X = np.linspace(xmin, xmax, 500) + y = b*X + C + 1*np.sin(X) + y += 0.05*np.random.randn(len(X)) + X, y = X[:, None], y[:, None] + m = GPy.models.SparseGPRegression(X, y) + + gaussian = GPy.priors.Gaussian(1, 1) + m.Z.set_prior(gaussian) + # setting a Gaussian prior on non-negative parameters + # should raise an assertionerror. + #self.assertRaises(AssertionError, m.Z.set_prior, gaussian) + + + + def test_fixed_domain_check(self): + xmin, xmax = 1, 2.5*np.pi + b, C, SNR = 1, 0, 0.1 + X = np.linspace(xmin, xmax, 500) + y = b*X + C + 1*np.sin(X) + y += 0.05*np.random.randn(len(X)) + X, y = X[:, None], y[:, None] + m = GPy.models.GPRegression(X, y) + + m.rbf.fix() + gaussian = GPy.priors.Gaussian(1, 1) + # setting a Gaussian prior on non-negative parameters + # should raise an assertionerror. + self.assertRaises(AssertionError, m.rbf.set_prior, gaussian) + + def test_fixed_domain_check1(self): + xmin, xmax = 1, 2.5*np.pi + b, C, SNR = 1, 0, 0.1 + X = np.linspace(xmin, xmax, 500) + y = b*X + C + 1*np.sin(X) + y += 0.05*np.random.randn(len(X)) + X, y = X[:, None], y[:, None] + m = GPy.models.GPRegression(X, y) + + m.kern.lengthscale.fix() + gaussian = GPy.priors.Gaussian(1, 1) + # setting a Gaussian prior on non-negative parameters + # should raise an assertionerror. + self.assertRaises(AssertionError, m.rbf.set_prior, gaussian) - self.assertTrue(success) if __name__ == "__main__": diff --git a/GPy/testing/unit_tests.py b/GPy/testing/unit_tests.py deleted file mode 100644 index 9269a4c4..00000000 --- a/GPy/testing/unit_tests.py +++ /dev/null @@ -1,260 +0,0 @@ -# Copyright (c) 2012, GPy authors (see AUTHORS.txt). -# Licensed under the BSD 3-clause license (see LICENSE.txt) - - -import unittest -import numpy as np -import GPy - -class GradientTests(unittest.TestCase): - def setUp(self): - ###################################### - # # 1 dimensional example - - # sample inputs and outputs - self.X1D = np.random.uniform(-3., 3., (20, 1)) - self.Y1D = np.sin(self.X1D) + np.random.randn(20, 1) * 0.05 - - ###################################### - # # 2 dimensional example - - # sample inputs and outputs - self.X2D = np.random.uniform(-3., 3., (40, 2)) - self.Y2D = np.sin(self.X2D[:, 0:1]) * np.sin(self.X2D[:, 1:2]) + np.random.randn(40, 1) * 0.05 - - def check_model(self, kern, model_type='GPRegression', dimension=1, uncertain_inputs=False): - # Get the correct gradients - if dimension == 1: - X = self.X1D - Y = self.Y1D - else: - X = self.X2D - Y = self.Y2D - # Get model type (GPRegression, SparseGPRegression, etc) - model_fit = getattr(GPy.models, model_type) - - # noise = GPy.kern.white(dimension) - kern = kern # + noise - if uncertain_inputs: - m = model_fit(X, Y, kernel=kern, X_variance=np.random.rand(X.shape[0], X.shape[1])) - else: - m = model_fit(X, Y, kernel=kern) - m.randomize() - # contrain all parameters to be positive - self.assertTrue(m.checkgrad()) - - def test_GPRegression_rbf_1d(self): - ''' Testing the GP regression with rbf kernel with white kernel on 1d data ''' - rbf = GPy.kern.rbf(1) - self.check_model(rbf, model_type='GPRegression', dimension=1) - - def test_GPRegression_rbf_2D(self): - ''' Testing the GP regression with rbf kernel on 2d data ''' - rbf = GPy.kern.rbf(2) - self.check_model(rbf, model_type='GPRegression', dimension=2) - - def test_GPRegression_rbf_ARD_2D(self): - ''' Testing the GP regression with rbf kernel on 2d data ''' - k = GPy.kern.rbf(2, ARD=True) - self.check_model(k, model_type='GPRegression', dimension=2) - - def test_GPRegression_mlp_1d(self): - ''' Testing the GP regression with mlp kernel with white kernel on 1d data ''' - mlp = GPy.kern.mlp(1) - self.check_model(mlp, model_type='GPRegression', dimension=1) - - def test_GPRegression_poly_1d(self): - ''' Testing the GP regression with polynomial kernel with white kernel on 1d data ''' - mlp = GPy.kern.poly(1, degree=5) - self.check_model(mlp, model_type='GPRegression', dimension=1) - - def test_GPRegression_matern52_1D(self): - ''' Testing the GP regression with matern52 kernel on 1d data ''' - matern52 = GPy.kern.Matern52(1) - self.check_model(matern52, model_type='GPRegression', dimension=1) - - def test_GPRegression_matern52_2D(self): - ''' Testing the GP regression with matern52 kernel on 2d data ''' - matern52 = GPy.kern.Matern52(2) - self.check_model(matern52, model_type='GPRegression', dimension=2) - - def test_GPRegression_matern52_ARD_2D(self): - ''' Testing the GP regression with matern52 kernel on 2d data ''' - matern52 = GPy.kern.Matern52(2, ARD=True) - self.check_model(matern52, model_type='GPRegression', dimension=2) - - def test_GPRegression_matern32_1D(self): - ''' Testing the GP regression with matern32 kernel on 1d data ''' - matern32 = GPy.kern.Matern32(1) - self.check_model(matern32, model_type='GPRegression', dimension=1) - - def test_GPRegression_matern32_2D(self): - ''' Testing the GP regression with matern32 kernel on 2d data ''' - matern32 = GPy.kern.Matern32(2) - self.check_model(matern32, model_type='GPRegression', dimension=2) - - def test_GPRegression_matern32_ARD_2D(self): - ''' Testing the GP regression with matern32 kernel on 2d data ''' - matern32 = GPy.kern.Matern32(2, ARD=True) - self.check_model(matern32, model_type='GPRegression', dimension=2) - - def test_GPRegression_exponential_1D(self): - ''' Testing the GP regression with exponential kernel on 1d data ''' - exponential = GPy.kern.exponential(1) - self.check_model(exponential, model_type='GPRegression', dimension=1) - - def test_GPRegression_exponential_2D(self): - ''' Testing the GP regression with exponential kernel on 2d data ''' - exponential = GPy.kern.exponential(2) - self.check_model(exponential, model_type='GPRegression', dimension=2) - - def test_GPRegression_exponential_ARD_2D(self): - ''' Testing the GP regression with exponential kernel on 2d data ''' - exponential = GPy.kern.exponential(2, ARD=True) - self.check_model(exponential, model_type='GPRegression', dimension=2) - - def test_GPRegression_bias_kern_1D(self): - ''' Testing the GP regression with bias kernel on 1d data ''' - bias = GPy.kern.bias(1) - self.check_model(bias, model_type='GPRegression', dimension=1) - - def test_GPRegression_bias_kern_2D(self): - ''' Testing the GP regression with bias kernel on 2d data ''' - bias = GPy.kern.bias(2) - self.check_model(bias, model_type='GPRegression', dimension=2) - - def test_GPRegression_linear_kern_1D_ARD(self): - ''' Testing the GP regression with linear kernel on 1d data ''' - linear = GPy.kern.linear(1, ARD=True) - self.check_model(linear, model_type='GPRegression', dimension=1) - - def test_GPRegression_linear_kern_2D_ARD(self): - ''' Testing the GP regression with linear kernel on 2d data ''' - linear = GPy.kern.linear(2, ARD=True) - self.check_model(linear, model_type='GPRegression', dimension=2) - - def test_GPRegression_linear_kern_1D(self): - ''' Testing the GP regression with linear kernel on 1d data ''' - linear = GPy.kern.linear(1) - self.check_model(linear, model_type='GPRegression', dimension=1) - - def test_GPRegression_linear_kern_2D(self): - ''' Testing the GP regression with linear kernel on 2d data ''' - linear = GPy.kern.linear(2) - self.check_model(linear, model_type='GPRegression', dimension=2) - - def test_SparseGPRegression_rbf_white_kern_1d(self): - ''' Testing the sparse GP regression with rbf kernel with white kernel on 1d data ''' - rbf = GPy.kern.rbf(1) - self.check_model(rbf, model_type='SparseGPRegression', dimension=1) - - def test_SparseGPRegression_rbf_white_kern_2D(self): - ''' Testing the sparse GP regression with rbf kernel on 2d data ''' - rbf = GPy.kern.rbf(2) - self.check_model(rbf, model_type='SparseGPRegression', dimension=2) - - def test_SparseGPRegression_rbf_linear_white_kern_1D(self): - ''' Testing the sparse GP regression with rbf kernel on 2d data ''' - rbflin = GPy.kern.rbf(1) + GPy.kern.linear(1) - self.check_model(rbflin, model_type='SparseGPRegression', dimension=1) - - def test_SparseGPRegression_rbf_linear_white_kern_2D(self): - ''' Testing the sparse GP regression with rbf kernel on 2d data ''' - rbflin = GPy.kern.rbf(2) + GPy.kern.linear(2) - self.check_model(rbflin, model_type='SparseGPRegression', dimension=2) - - #@unittest.expectedFailure - def test_SparseGPRegression_rbf_linear_white_kern_2D_uncertain_inputs(self): - ''' Testing the sparse GP regression with rbf, linear kernel on 2d data with uncertain inputs''' - rbflin = GPy.kern.rbf(2) + GPy.kern.linear(2) - raise unittest.SkipTest("This is not implemented yet!") - self.check_model(rbflin, model_type='SparseGPRegression', dimension=2, uncertain_inputs=1) - - #@unittest.expectedFailure - def test_SparseGPRegression_rbf_linear_white_kern_1D_uncertain_inputs(self): - ''' Testing the sparse GP regression with rbf, linear kernel on 1d data with uncertain inputs''' - rbflin = GPy.kern.rbf(1) + GPy.kern.linear(1) - raise unittest.SkipTest("This is not implemented yet!") - self.check_model(rbflin, model_type='SparseGPRegression', dimension=1, uncertain_inputs=1) - - def test_GPLVM_rbf_bias_white_kern_2D(self): - """ Testing GPLVM with rbf + bias kernel """ - N, input_dim, D = 50, 1, 2 - X = np.random.rand(N, input_dim) - k = GPy.kern.rbf(input_dim, 0.5, 0.9 * np.ones((1,))) + GPy.kern.bias(input_dim, 0.1) + GPy.kern.white(input_dim, 0.05) - K = k.K(X) - Y = np.random.multivariate_normal(np.zeros(N), K, input_dim).T - m = GPy.models.GPLVM(Y, input_dim, kernel=k) - self.assertTrue(m.checkgrad()) - - def test_GPLVM_rbf_linear_white_kern_2D(self): - """ Testing GPLVM with rbf + bias kernel """ - N, input_dim, D = 50, 1, 2 - X = np.random.rand(N, input_dim) - k = GPy.kern.linear(input_dim) + GPy.kern.bias(input_dim, 0.1) + GPy.kern.white(input_dim, 0.05) - K = k.K(X) - Y = np.random.multivariate_normal(np.zeros(N), K, input_dim).T - m = GPy.models.GPLVM(Y, input_dim, init='PCA', kernel=k) - self.assertTrue(m.checkgrad()) - - def test_GP_EP_probit(self): - N = 20 - X = np.hstack([np.random.normal(5, 2, N / 2), np.random.normal(10, 2, N / 2)])[:, None] - Y = np.hstack([np.ones(N / 2), np.zeros(N / 2)])[:, None] - kernel = GPy.kern.rbf(1) - m = GPy.models.GPClassification(X,Y,kernel=kernel) - m.update_likelihood_approximation() - self.assertTrue(m.checkgrad()) - - def test_sparse_EP_DTC_probit(self): - N = 20 - X = np.hstack([np.random.normal(5, 2, N / 2), np.random.normal(10, 2, N / 2)])[:, None] - Y = np.hstack([np.ones(N / 2), np.zeros(N / 2)])[:, None] - Z = np.linspace(0, 15, 4)[:, None] - kernel = GPy.kern.rbf(1) - m = GPy.models.SparseGPClassification(X,Y,kernel=kernel,Z=Z) - #distribution = GPy.likelihoods.likelihood_functions.Bernoulli() - #likelihood = GPy.likelihoods.EP(Y, distribution) - #m = GPy.core.SparseGP(X, likelihood, kernel, Z) - #m.ensure_default_constraints() - m.update_likelihood_approximation() - self.assertTrue(m.checkgrad()) - - def test_generalized_FITC(self): - N = 20 - X = np.hstack([np.random.rand(N / 2) + 1, np.random.rand(N / 2) - 1])[:, None] - k = GPy.kern.rbf(1) + GPy.kern.white(1) - Y = np.hstack([np.ones(N/2),np.zeros(N/2)])[:,None] - m = GPy.models.FITCClassification(X, Y, kernel = k) - m.update_likelihood_approximation() - self.assertTrue(m.checkgrad()) - - def multioutput_regression_1D(self): - X1 = np.random.rand(50, 1) * 8 - X2 = np.random.rand(30, 1) * 5 - X = np.vstack((X1, X2)) - Y1 = np.sin(X1) + np.random.randn(*X1.shape) * 0.05 - Y2 = -np.sin(X2) + np.random.randn(*X2.shape) * 0.05 - Y = np.vstack((Y1, Y2)) - - k1 = GPy.kern.rbf(1) - m = GPy.models.GPMultioutputRegression(X_list=[X1,X2],Y_list=[Y1,Y2],kernel_list=[k1]) - m.constrain_fixed('.*rbf_var', 1.) - self.assertTrue(m.checkgrad()) - - def multioutput_sparse_regression_1D(self): - X1 = np.random.rand(500, 1) * 8 - X2 = np.random.rand(300, 1) * 5 - X = np.vstack((X1, X2)) - Y1 = np.sin(X1) + np.random.randn(*X1.shape) * 0.05 - Y2 = -np.sin(X2) + np.random.randn(*X2.shape) * 0.05 - Y = np.vstack((Y1, Y2)) - - k1 = GPy.kern.rbf(1) - m = GPy.models.SparseGPMultioutputRegression(X_list=[X1,X2],Y_list=[Y1,Y2],kernel_list=[k1]) - m.constrain_fixed('.*rbf_var', 1.) - self.assertTrue(m.checkgrad()) - -if __name__ == "__main__": - print "Running unit tests, please be (very) patient..." - unittest.main() diff --git a/GPy/util/__init__.py b/GPy/util/__init__.py index 2d2b6e17..c3edfc48 100644 --- a/GPy/util/__init__.py +++ b/GPy/util/__init__.py @@ -4,25 +4,16 @@ import linalg import misc -import plot import squashers -import Tango import warping_functions import datasets import mocap -import visualize import decorators import classification -import latent_space_visualizations +import subarray_and_sorting +import caching +import diag +import initialization +import multioutput +import linalg_gpu -try: - import sympy - _sympy_available = True - del sympy -except ImportError as e: - _sympy_available = False - -if _sympy_available: - import symbolic - -import netpbmfile diff --git a/GPy/util/block_matrices.py b/GPy/util/block_matrices.py index 8fd5f89d..95920868 100644 --- a/GPy/util/block_matrices.py +++ b/GPy/util/block_matrices.py @@ -1,3 +1,5 @@ +# Copyright (c) 2012, GPy authors (see AUTHORS.txt). +# Licensed under the BSD 3-clause license (see LICENSE.txt) import numpy as np def get_blocks(A, blocksizes): diff --git a/GPy/util/caching.py b/GPy/util/caching.py new file mode 100644 index 00000000..16adc320 --- /dev/null +++ b/GPy/util/caching.py @@ -0,0 +1,195 @@ +# Copyright (c) 2012, GPy authors (see AUTHORS.txt). +# Licensed under the BSD 3-clause license (see LICENSE.txt) +from ..core.parameterization.observable import Observable +import collections, weakref + +class Cacher(object): + def __init__(self, operation, limit=5, ignore_args=(), force_kwargs=()): + """ + Parameters: + *********** + :param callable operation: function to cache + :param int limit: depth of cacher + :param [int] ignore_args: list of indices, pointing at arguments to ignore in *args of operation(*args). This includes self! + :param [str] force_kwargs: list of kwarg names (strings). If a kwarg with that name is given, the cacher will force recompute and wont cache anything. + :param int verbose: verbosity level. 0: no print outs, 1: casual print outs, 2: debug level print outs + """ + self.limit = int(limit) + self.ignore_args = ignore_args + self.force_kwargs = force_kwargs + self.operation = operation + self.order = collections.deque() + self.cached_inputs = {} # point from cache_ids to a list of [ind_ids], which where used in cache cache_id + + #======================================================================= + # point from each ind_id to [ref(obj), cache_ids] + # 0: a weak reference to the object itself + # 1: the cache_ids in which this ind_id is used (len will be how many times we have seen this ind_id) + self.cached_input_ids = {} + #======================================================================= + + self.cached_outputs = {} # point from cache_ids to outputs + self.inputs_changed = {} # point from cache_ids to bools + + def id(self, obj): + """returns the self.id of an object, to be used in caching individual self.ids""" + return hex(id(obj)) + + def combine_inputs(self, args, kw, ignore_args): + "Combines the args and kw in a unique way, such that ordering of kwargs does not lead to recompute" + inputs= args + tuple(c[1] for c in sorted(kw.items(), key=lambda x: x[0])) + # REMOVE the ignored arguments from input and PREVENT it from being checked!!! + return [a for i,a in enumerate(inputs) if i not in ignore_args] + + def prepare_cache_id(self, combined_args_kw): + "get the cacheid (conc. string of argument self.ids in order)" + cache_id = "".join(self.id(a) for a in combined_args_kw) + return cache_id + + def ensure_cache_length(self, cache_id): + "Ensures the cache is within its limits and has one place free" + if len(self.order) == self.limit: + # we have reached the limit, so lets release one element + cache_id = self.order.popleft() + combined_args_kw = self.cached_inputs[cache_id] + for ind in combined_args_kw: + if ind is not None: + ind_id = self.id(ind) + tmp = self.cached_input_ids.get(ind_id, None) + if tmp is not None: + ref, cache_ids = tmp + if len(cache_ids) == 1 and ref() is not None: + ref().remove_observer(self, self.on_cache_changed) + del self.cached_input_ids[ind_id] + else: + cache_ids.remove(cache_id) + self.cached_input_ids[ind_id] = [ref, cache_ids] + del self.cached_outputs[cache_id] + del self.inputs_changed[cache_id] + del self.cached_inputs[cache_id] + + def add_to_cache(self, cache_id, inputs, output): + """This adds cache_id to the cache, with inputs and output""" + self.inputs_changed[cache_id] = False + self.cached_outputs[cache_id] = output + self.order.append(cache_id) + self.cached_inputs[cache_id] = inputs + for a in inputs: + if a is not None: + ind_id = self.id(a) + v = self.cached_input_ids.get(ind_id, [weakref.ref(a), []]) + v[1].append(cache_id) + if len(v[1]) == 1: + a.add_observer(self, self.on_cache_changed) + self.cached_input_ids[ind_id] = v + + def __call__(self, *args, **kw): + """ + A wrapper function for self.operation, + """ + #======================================================================= + # !WARNING CACHE OFFSWITCH! + # return self.operation(*args, **kw) + #======================================================================= + + # 1: Check whether we have forced recompute arguments: + if len(self.force_kwargs) != 0: + for k in self.force_kwargs: + if k in kw and kw[k] is not None: + return self.operation(*args, **kw) + + # 2: prepare_cache_id and get the unique self.id string for this call + inputs = self.combine_inputs(args, kw, self.ignore_args) + cache_id = self.prepare_cache_id(inputs) + # 2: if anything is not cachable, we will just return the operation, without caching + if reduce(lambda a, b: a or (not (isinstance(b, Observable) or b is None)), inputs, False): + #print 'WARNING: '+self.operation.__name__ + ' not cacheable!' + #print [not (isinstance(b, Observable)) for b in inputs] + return self.operation(*args, **kw) + # 3&4: check whether this cache_id has been cached, then has it changed? + try: + if(self.inputs_changed[cache_id]): + # 4: This happens, when elements have changed for this cache self.id + self.inputs_changed[cache_id] = False + self.cached_outputs[cache_id] = self.operation(*args, **kw) + except KeyError: + # 3: This is when we never saw this chache_id: + self.ensure_cache_length(cache_id) + self.add_to_cache(cache_id, inputs, self.operation(*args, **kw)) + except: + self.reset() + raise + # 5: We have seen this cache_id and it is cached: + return self.cached_outputs[cache_id] + + def on_cache_changed(self, direct, which=None): + """ + A callback funtion, which sets local flags when the elements of some cached inputs change + + this function gets 'hooked up' to the inputs when we cache them, and upon their elements being changed we update here. + """ + for what in [direct, which]: + if what is not None: + ind_id = self.id(what) + _, cache_ids = self.cached_input_ids.get(ind_id, [None, []]) + for cache_id in cache_ids: + self.inputs_changed[cache_id] = True + + def reset(self): + """ + Totally reset the cache + """ + [a().remove_observer(self, self.on_cache_changed) if (a() is not None) else None for [a, _] in self.cached_input_ids.values()] + self.cached_input_ids = {} + self.cached_outputs = {} + self.inputs_changed = {} + + def __deepcopy__(self, memo=None): + return Cacher(self.operation, self.limit, self.ignore_args, self.force_kwargs) + + def __getstate__(self, memo=None): + raise NotImplementedError, "Trying to pickle Cacher object with function {}, pickling functions not possible.".format(str(self.operation)) + + def __setstate__(self, memo=None): + raise NotImplementedError, "Trying to pickle Cacher object with function {}, pickling functions not possible.".format(str(self.operation)) + + @property + def __name__(self): + return self.operation.__name__ + +from functools import partial, update_wrapper + +class Cacher_wrap(object): + def __init__(self, f, limit, ignore_args, force_kwargs): + self.limit = limit + self.ignore_args = ignore_args + self.force_kwargs = force_kwargs + self.f = f + update_wrapper(self, self.f) + def __get__(self, obj, objtype=None): + return partial(self, obj) + def __call__(self, *args, **kwargs): + obj = args[0] + # import ipdb;ipdb.set_trace() + try: + caches = obj.__cachers + except AttributeError: + caches = obj.__cachers = {} + try: + cacher = caches[self.f] + except KeyError: + cacher = caches[self.f] = Cacher(self.f, self.limit, self.ignore_args, self.force_kwargs) + return cacher(*args, **kwargs) + +class Cache_this(object): + """ + A decorator which can be applied to bound methods in order to cache them + """ + def __init__(self, limit=5, ignore_args=(), force_kwargs=()): + self.limit = limit + self.ignore_args = ignore_args + self.force_args = force_kwargs + def __call__(self, f): + newf = Cacher_wrap(f, self.limit, self.ignore_args, self.force_args) + update_wrapper(newf, f) + return newf diff --git a/GPy/util/classification.py b/GPy/util/classification.py index 41701949..c0859793 100644 --- a/GPy/util/classification.py +++ b/GPy/util/classification.py @@ -1,3 +1,5 @@ +# Copyright (c) 2012, GPy authors (see AUTHORS.txt). +# Licensed under the BSD 3-clause license (see LICENSE.txt) import numpy as np def conf_matrix(p,labels,names=['1','0'],threshold=.5,show=True): diff --git a/GPy/util/config.py b/GPy/util/config.py index b0789fe0..6dad46c8 100644 --- a/GPy/util/config.py +++ b/GPy/util/config.py @@ -5,18 +5,19 @@ import ConfigParser import os config = ConfigParser.ConfigParser() -home = os.getenv('HOME') or os.getenv('USERPROFILE') -user_file = os.path.join(home,'.gpy_config.cfg') -default_file = os.path.abspath(os.path.join(os.path.dirname( __file__ ), '..', 'gpy_config.cfg')) -# print user_file, os.path.isfile(user_file) -# print default_file, os.path.isfile(default_file) +# This is the default configuration file that always needs to be present. +default_file = os.path.abspath(os.path.join(os.path.dirname( __file__ ), '..', 'defaults.cfg')) -# 1. check if the user has a ~/.gpy_config.cfg -if os.path.isfile(user_file): - config.read(user_file) -elif os.path.isfile(default_file): - # 2. if not, use the default one - config.read(default_file) -else: - #3. panic - raise ValueError, "no configuration file found" +# These files are optional +# This specifies configurations that are typically specific to the machine (it is found alongside the GPy installation). +local_file = os.path.abspath(os.path.join(os.path.dirname( __file__ ), '..', 'installation.cfg')) + +# This specifies configurations specific to the user (it is found in the user home directory) +home = os.getenv('HOME') or os.getenv('USERPROFILE') +user_file = os.path.join(home,'.gpy_user.cfg') + +# Read in the given files. +config.readfp(open(default_file)) +config.read([local_file, user_file]) +if not config: + raise ValueError, "No configuration file found at either " + user_file + " or " + local_file + " or " + default_file + "." diff --git a/GPy/util/data_resources.json b/GPy/util/data_resources.json index 845d56be..1ed735c3 100644 --- a/GPy/util/data_resources.json +++ b/GPy/util/data_resources.json @@ -1 +1,605 @@ -{"rogers_girolami_data": {"files": [["firstcoursemldata.tar.gz"]], "license": null, "citation": "A First Course in Machine Learning. Simon Rogers and Mark Girolami: Chapman & Hall/CRC, ISBN-13: 978-1439824146", "details": "Data from the textbook 'A First Course in Machine Learning'. Available from http://www.dcs.gla.ac.uk/~srogers/firstcourseml/.", "urls": ["https://www.dropbox.com/sh/7p6tu1t29idgliq/_XqlH_3nt9/"], "suffices": [["?dl=1"]], "size": 21949154}, "ankur_pose_data": {"files": [["ankurDataPoseSilhouette.mat"]], "citation": "3D Human Pose from Silhouettes by Relevance Vector Regression (In CVPR'04). A. Agarwal and B. Triggs.", "license": null, "urls": ["http://staffwww.dcs.shef.ac.uk/people/N.Lawrence/dataset_mirror/ankur_pose_data/"], "details": "Artificially generated data of silhouettes given poses. Note that the data does not display a left/right ambiguity because across the entire data set one of the arms sticks out more the the other, disambiguating the pose as to which way the individual is facing."}, "osu_accad": {"files": [["swagger1TXT.ZIP", "handspring1TXT.ZIP", "quickwalkTXT.ZIP", "run1TXT.ZIP", "sprintTXT.ZIP", "dogwalkTXT.ZIP", "camper_04TXT.ZIP", "dance_KB3_TXT.ZIP", "per20_TXT.ZIP", "perTWO07_TXT.ZIP", "perTWO13_TXT.ZIP", "perTWO14_TXT.ZIP", "perTWO15_TXT.ZIP", "perTWO16_TXT.ZIP"], ["connections.txt"]], "license": "Data is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License (http://creativecommons.org/licenses/by-nc-sa/3.0/).", "citation": "The Open Motion Data Project by The Ohio State University Advanced Computing Center for the Arts and Design, http://accad.osu.edu/research/mocap/mocap_data.htm.", "details": "Motion capture data of different motions from the Open Motion Data Project at Ohio State University.", "urls": ["http://accad.osu.edu/research/mocap/data/", "http://staffwww.dcs.shef.ac.uk/people/N.Lawrence/dataset_mirror/stick/"], "size": 15922790}, "isomap_face_data": {"files": [["face_data.mat"]], "license": null, "citation": "A Global Geometric Framework for Nonlinear Dimensionality Reduction, J. B. Tenenbaum, V. de Silva and J. C. Langford, Science 290 (5500): 2319-2323, 22 December 2000", "details": "Face data made available by Tenenbaum, de Silva and Langford to demonstrate isomap, available from http://isomap.stanford.edu/datasets.html.", "urls": ["http://staffwww.dcs.shef.ac.uk/people/N.Lawrence/dataset_mirror/isomap_face_data/"], "size": 24229368}, "boston_housing": {"files": [["Index", "housing.data", "housing.names"]], "license": null, "citation": "Harrison, D. and Rubinfeld, D.L. 'Hedonic prices and the demand for clean air', J. Environ. Economics & Management, vol.5, 81-102, 1978.", "details": "The Boston Housing data relates house values in Boston to a range of input variables.", "urls": ["http://archive.ics.uci.edu/ml/machine-learning-databases/housing/"], "size": 51276}, "cmu_mocap_full": {"files": [["allasfamc.zip"]], "license": "From http://mocap.cs.cmu.edu. This data is free for use in research projects. You may include this data in commercially-sold products, but you may not resell this data directly, even in converted form. If you publish results obtained using this data, we would appreciate it if you would send the citation to your published paper to jkh+mocap@cs.cmu.edu, and also would add this text to your acknowledgments section: The data used in this project was obtained from mocap.cs.cmu.edu. The database was created with funding from NSF EIA-0196217.", "citation": "Please include this in your acknowledgements: The data used in this project was obtained from mocap.cs.cmu.edu.'\n 'The database was created with funding from NSF EIA-0196217.", "details": "CMU Motion Capture data base. Captured by a Vicon motion capture system consisting of 12 infrared MX-40 cameras, each of which is capable of recording at 120 Hz with images of 4 megapixel resolution. Motions are captured in a working volume of approximately 3m x 8m. The capture subject wears 41 markers and a stylish black garment.", "urls": ["http://mocap.cs.cmu.edu"], "size": null}, "brendan_faces": {"files": [["frey_rawface.mat"]], "license": null, "citation": "Frey, B. J., Colmenarez, A and Huang, T. S. Mixtures of Local Linear Subspaces for Face Recognition. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition 1998, 32-37, June 1998. Computer Society Press, Los Alamitos, CA.", "details": "A video of Brendan Frey's face popularized as a benchmark for visualization by the Locally Linear Embedding.", "urls": ["http://www.cs.nyu.edu/~roweis/data/"], "size": 1100584}, "olympic_marathon_men": {"files": [["olympicMarathonTimes.csv"]], "license": null, "citation": null, "details": "Olympic mens' marathon gold medal winning times from 1896 to 2012. Time given in pace (minutes per kilometer). Data is originally downloaded and collated from Wikipedia, we are not responsible for errors in the data", "urls": ["http://staffwww.dcs.shef.ac.uk/people/N.Lawrence/dataset_mirror/olympic_marathon_men/"], "size": 584}, "pumadyn-32nm": {"files": [["pumadyn-32nm.tar.gz"]], "license": "Data is made available by the Delve system at the University of Toronto", "citation": "Created by Zoubin Ghahramani using the Matlab Robotics Toolbox of Peter Corke. Corke, P. I. (1996). A Robotics Toolbox for MATLAB. IEEE Robotics and Automation Magazine, 3 (1): 24-32.", "details": "Pumadyn non linear 32 input data set with moderate noise. See http://www.cs.utoronto.ca/~delve/data/pumadyn/desc.html for details.", "urls": ["ftp://ftp.cs.toronto.edu/pub/neuron/delve/data/tarfiles/pumadyn-family/"], "size": 5861646}, "ripley_prnn_data": {"files": [["Cushings.dat", "README", "crabs.dat", "fglass.dat", "fglass.grp", "pima.te", "pima.tr", "pima.tr2", "synth.te", "synth.tr", "viruses.dat", "virus3.dat"]], "license": null, "citation": "Pattern Recognition and Neural Networks by B.D. Ripley (1996) Cambridge University Press ISBN 0 521 46986 7", "details": "Data sets from Brian Ripley's Pattern Recognition and Neural Networks", "urls": ["http://www.stats.ox.ac.uk/pub/PRNN/"], "size": 93565}, "three_phase_oil_flow": {"files": [["DataTrnLbls.txt", "DataTrn.txt", "DataTst.txt", "DataTstLbls.txt", "DataVdn.txt", "DataVdnLbls.txt"]], "license": null, "citation": "Bishop, C. M. and G. D. James (1993). Analysis of multiphase flows using dual-energy gamma densitometry and neural networks. Nuclear Instruments and Methods in Physics Research A327, 580-593", "details": "The three phase oil data used initially for demonstrating the Generative Topographic mapping.", "urls": ["http://staffwww.dcs.shef.ac.uk/people/N.Lawrence/dataset_mirror/three_phase_oil_flow/"], "size": 712796}, "robot_wireless": {"files": [["uw-floor.txt"]], "license": null, "citation": "WiFi-SLAM using Gaussian Process Latent Variable Models by Brian Ferris, Dieter Fox and Neil Lawrence in IJCAI'07 Proceedings pages 2480-2485. Data used in A Unifying Probabilistic Perspective for Spectral Dimensionality Reduction: Insights and New Models by Neil D. Lawrence, JMLR 13 pg 1609--1638, 2012.", "details": "Data created by Brian Ferris and Dieter Fox. 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F. Brun and T. Yoshida.", "details": "Provides 2066 creep rupture test results of steels (mainly of two kinds of steels: 2.25Cr and 9-12 wt% Cr ferritic steels). See http://www.msm.cam.ac.uk/map/data/materials/creeprupt-b.html.", "urls": ["http://www.msm.cam.ac.uk/map/data/tar/"], "size": 602797}, "hapmap3": {"files": [["hapmap3_r2_b36_fwd.consensus.qc.poly.map.bz2", "hapmap3_r2_b36_fwd.consensus.qc.poly.ped.bz2", "relationships_w_pops_121708.txt"]], "license": "International HapMap Project Public Access License (http://hapmap.ncbi.nlm.nih.gov/cgi-perl/registration#licence)", "citation": "Gibbs, Richard A., et al. \"The international HapMap project.\" Nature 426.6968 (2003): 789-796.", "details": "HapMap Project: Single Nucleotide Polymorphism sequenced in all human populations. 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", "urls": ["http://staffwww.dcs.shef.ac.uk/people/N.Lawrence/dataset_mirror/olivetti_faces/", "http://www.cs.nyu.edu/~roweis/data/"], "size": 8561331}, "della_gatta": {"files": [["DellaGattadata.mat"]], "license": null, "citation": "Direct targets of the TRP63 transcription factor revealed by a combination of gene expression profiling and reverse engineering. Giusy Della Gatta, Mukesh Bansal, Alberto Ambesi-Impiombato, Dario Antonini, Caterina Missero, and Diego di Bernardo, Genome Research 2008", "details": "The full gene expression data set from della Gatta et al (http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2413161/) processed by RMA.", "urls": ["http://staffwww.dcs.shef.ac.uk/people/N.Lawrence/dataset_mirror/della_gatta/"], "size": 3729650}, "epomeo_gpx": {"files": [["endomondo_1.gpx", "endomondo_2.gpx", "garmin_watch_via_endomondo.gpx", "viewranger_phone.gpx", "viewranger_tablet.gpx"]], "license": null, "citation": "", "details": "Five different GPS traces of the same run up Mount Epomeo in Ischia. 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Note that the data does not display a left/right ambiguity because across the entire data set one of the arms sticks out more the the other, disambiguating the pose as to which way the individual is facing.", + "files": [ + [ + "ankurDataPoseSilhouette.mat" + ] + ], + "license": null, + "size": 1, + "urls": [ + "http://staffwww.dcs.shef.ac.uk/people/N.Lawrence/dataset_mirror/ankur_pose_data/" + ] + }, + "boston_housing": { + "citation": "Harrison, D. and Rubinfeld, D.L. 'Hedonic prices and the demand for clean air', J. Environ. Economics & Management, vol.5, 81-102, 1978.", + "details": "The Boston Housing data relates house values in Boston to a range of input variables.", + "files": [ + [ + "Index", + "housing.data", + "housing.names" + ] + ], + "license": null, + "size": 51276, + "urls": [ + "http://archive.ics.uci.edu/ml/machine-learning-databases/housing/" + ] + }, + "boxjenkins_airline": { + "citation": "Box & Jenkins (1976), in file: data/airpass, Description: International airline passengers: monthly totals in thousands. Jan 49 \\u2013 Dec 60", + "details": "International airline passengers, monthly totals from January 1949 to December 1960.", + "files": [ + [ + "boxjenkins_airline.csv" + ] + ], + "license": "You may copy and redistribute the data. You may make derivative works from the data. You may use the data for commercial purposes. You may not sublicence the data when redistributing it. You may not redistribute the data under a different license. Source attribution on any use of this data: Must refer source.", + "size": 46779, + "urls": [ + "http://staffwww.dcs.shef.ac.uk/people/N.Lawrence/dataset_mirror/boxjenkins_airline/" + ] + }, + "brendan_faces": { + "citation": "Frey, B. J., Colmenarez, A and Huang, T. S. Mixtures of Local Linear Subspaces for Face Recognition. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition 1998, 32-37, June 1998. Computer Society Press, Los Alamitos, CA.", + "details": "A video of Brendan Frey's face popularized as a benchmark for visualization by the Locally Linear Embedding.", + "files": [ + [ + "frey_rawface.mat" + ] + ], + "license": null, + "size": 1100584, + "urls": [ + "http://www.cs.nyu.edu/~roweis/data/" + ] + }, + "cifar-10": { + "citation": "Learning Multiple Layers of Features from Tiny Images, Alex Krizhevsky, 2009, Tech report available here: http://www.cs.toronto.edu/~kriz/learning-features-2009-TR.pdf", + "details": "The CIFAR-10 and CIFAR-100 are labeled subsets of the 80 million tiny images dataset. They were collected by Alex Krizhevsky, Vinod Nair, and Geoffrey Hinton. Details are available on this webpage: http://www.cs.toronto.edu/~kriz/cifar.html. The CIFAR-10 dataset consists of 60000 32x32 colour images in 10 classes, with 6000 images per class. There are 50000 training images and 10000 test images.", + "files": [ + [ + "cifar-10-python.tar.gz" + ] + ], + "license": null, + "size": 0, + "urls": [ + "http://www.cs.toronto.edu/~kriz/" + ] + }, + "cmu_mocap_full": { + "citation": "Please include this in your acknowledgements: The data used in this project was obtained from mocap.cs.cmu.edu.\\nThe database was created with funding from NSF EIA-0196217.", + "details": "CMU Motion Capture data base. Captured by a Vicon motion capture system consisting of 12 infrared MX-40 cameras, each of which is capable of recording at 120 Hz with images of 4 megapixel resolution. Motions are captured in a working volume of approximately 3m x 8m. The capture subject wears 41 markers and a stylish black garment.", + "files": [ + [ + "allasfamc.zip" + ] + ], + "license": "From http://mocap.cs.cmu.edu. This data is free for use in research projects. You may include this data in commercially-sold products, but you may not resell this data directly, even in converted form. If you publish results obtained using this data, we would appreciate it if you would send the citation to your published paper to jkh+mocap@cs.cmu.edu, and also would add this text to your acknowledgments section: The data used in this project was obtained from mocap.cs.cmu.edu. The database was created with funding from NSF EIA-0196217.", + "size": null, + "urls": [ + "http://mocap.cs.cmu.edu/subjects" + ] + }, + "creep_rupture": { + "citation": "Materials Algorithms Project Data Library: MAP_DATA_CREEP_RUPTURE. F. Brun and T. Yoshida.", + "details": "Provides 2066 creep rupture test results of steels (mainly of two kinds of steels: 2.25Cr and 9-12 wt% Cr ferritic steels). See http://www.msm.cam.ac.uk/map/data/materials/creeprupt-b.html.", + "files": [ + [ + "creeprupt.tar" + ] + ], + "license": null, + "size": 602797, + "urls": [ + "http://www.msm.cam.ac.uk/map/data/tar/" + ] + }, + "decampos_characters": { + "citation": "T. de Campos, B. R. Babu, and M. Varma. Character recognition in natural images. VISAPP 2009.", + "details": "Examples of hand written digits taken from the de Campos et al paper on Character Recognition in Natural Images.", + "files": [ + [ + "characters.npy", + "digits.npy" + ] + ], + "license": null, + "size": 2031872, + "urls": [ + "http://staffwww.dcs.shef.ac.uk/people/N.Lawrence/dataset_mirror/decampos_digits/" + ] + }, + "della_gatta": { + "citation": "Direct targets of the TRP63 transcription factor revealed by a combination of gene expression profiling and reverse engineering. Giusy Della Gatta, Mukesh Bansal, Alberto Ambesi-Impiombato, Dario Antonini, Caterina Missero, and Diego di Bernardo, Genome Research 2008", + "details": "The full gene expression data set from della Gatta et al (http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2413161/) processed by RMA.", + "files": [ + [ + "DellaGattadata.mat" + ] + ], + "license": null, + "size": 3729650, + "urls": [ + "http://staffwww.dcs.shef.ac.uk/people/N.Lawrence/dataset_mirror/della_gatta/" + ] + }, + "drosophila_protein": { + "citation": "Becker K, Balsa-Canto E, Cicin-Sain D, Hoermann A, Janssens H, et al. (2013) Reverse-Engineering Post-Transcriptional Regulation of Gap Genes in Drosophila melanogaster. PLoS Comput Biol 9(10): e1003281. doi:10.1371/journal.pcbi.1003281", + "details": "Expression of the gap genes Krüppel, knirps, and giant in Drosophila melanogaster. Data includes quantitative datasets of gap gene mRNA and protein expression to solve and fit a model of post-transcriptional regulation, and establish its structural and practical identifiability", + "files": [ + [ + "becker_et_al.csv" + ] + ], + "license": null, + "size": 20258, + "urls": [ + "http://staffwww.dcs.shef.ac.uk/people/N.Lawrence/dataset_mirror/drosophila_protein/" + ] + }, + "spellman_yeast": { + "citation": "Paul T. Spellman, Gavin Sherlock, Michael Q. Zhang, Vishwanath R. Iyer, Kirk Anders, Michael B. Eisen, Patrick O. Brown, David Botstein, and Bruce Futcher 'Comprehensive Identification of Cell Cycle-regulated Genes of the Yeast Saccharomyces cerevisiae by Microarray Hybridization.' Molecular Biology of the Cell 9, 3273-3297", + "details": "Two colour spotted cDNA array data set of a series of experiments to identify which genes in Yeast are cell cycle regulated.", + "files": [ + [ + "combined.txt" + ] + ], + "license": null, + "size": 2510955, + "urls": [ + "http://genome-www.stanford.edu/cellcycle/data/rawdata/" + ] + }, + "lee_yeast_ChIP": { + "citation": "Tong Ihn Lee, Nicola J. Rinaldi, Francois Robert, Duncan T. Odom, Ziv Bar-Joseph, Georg K. Gerber, Nancy M. Hannett, Christopher T. Harbison, Craig M. Thompson, Itamar Simon, Julia Zeitlinger, Ezra G. Jennings, Heather L. Murray, D. Benjamin Gordon, Bing Ren, John J. Wyrick, Jean-Bosco Tagne, Thomas L. Volkert, Ernest Fraenkel, David K. Gifford, Richard A. Young 'Transcriptional Regulatory Networks in Saccharomyces cerevisiae' Science 298 (5594) pg 799--804. DOI: 10.1126/science.1075090", + "details": "Binding location analysis for 106 regulators in yeast. The data consists of p-values for binding of regulators to genes derived from ChIP-chip experiments.", + "files": [ + [ + "binding_by_gene.tsv" + ] + ], + "license": null, + "size": 1674161, + "urls": [ + "http://jura.wi.mit.edu/young_public/regulatory_network/" + ] + }, + "epomeo_gpx": { + "citation": "", + "details": "Five different GPS traces of the same run up Mount Epomeo in Ischia. The traces are from different sources. endomondo_1 and endomondo_2 are traces from the mobile phone app Endomondo, with a split in the middle. garmin_watch_via_endomondo is the trace from a Garmin watch, with a segment missing about 4 kilometers in. viewranger_phone and viewranger_tablet are traces from a phone and a tablet through the viewranger app. The viewranger_phone data comes from the same mobile phone as the Endomondo data (i.e. there are 3 GPS devices, but one device recorded two traces).", + "files": [ + [ + "endomondo_1.gpx", + "endomondo_2.gpx", + "garmin_watch_via_endomondo.gpx", + "viewranger_phone.gpx", + "viewranger_tablet.gpx" + ] + ], + "license": null, + "size": 2031872, + "urls": [ + "http://staffwww.dcs.shef.ac.uk/people/N.Lawrence/dataset_mirror/epomeo_gpx/" + ] + }, + "football_data": { + "citation": "", + "details": "Results of English football matches since 1993/94 season.", + "files": [ + [ + "E0.csv", + "E1.csv", + "E2.csv", + "E3.csv" + ] + ], + "license": null, + "size": 1, + "urls": [ + "http://www.football-data.co.uk/mmz4281/" + ] + }, + "fruitfly_tomancak": { + "citation": "", + "details": "", + "files": [ + [ + "tomancak_exprs.csv", + "tomancak_se.csv", + "tomancak_prctile5.csv", + "tomancak_prctile25.csv", + "tomancak_prctile50.csv", + "tomancak_prctile75.csv", + "tomancak_prctile95.csv" + ] + ], + "license": null, + "size": 59000000, + "urls": [ + "http://staffwww.dcs.shef.ac.uk/people/N.Lawrence/dataset_mirror/fruitfly_tomancak/" + ] + }, + "fruitfly_tomancak_cel_files": { + "citation": "'Systematic determination of patterns of gene expression during Drosophila embryogenesis' Pavel Tomancak, Amy Beaton, Richard Weiszmann, Elaine Kwan, ShengQiang Shu, Suzanna E Lewis, Stephen Richards, Michael Ashburner, Volker Hartenstein, Susan E Celniker, and Gerald M Rubin", + "details": "Gene expression results from blastoderm development in Drosophila Melanogaster.", + "files": [ + [ + "embryo_tc_4_1.CEL", + "embryo_tc_4_2.CEL", + "embryo_tc_4_3.CEL", + "embryo_tc_4_4.CEL", + "embryo_tc_4_5.CEL", + "embryo_tc_4_6.CEL", + "embryo_tc_4_7.CEL", + "embryo_tc_4_8.CEL", + "embryo_tc_4_9.CEL", + "embryo_tc_4_10.CEL", + "embryo_tc_4_11.CEL", + "embryo_tc_4_12.CEL", + "embryo_tc_6_1.CEL", + "embryo_tc_6_2.CEL", + "embryo_tc_6_3.CEL", + "embryo_tc_6_4.CEL", + "embryo_tc_6_5.CEL", + "embryo_tc_6_6.CEL", + "embryo_tc_6_7.CEL", + "embryo_tc_6_8.CEL", + "embryo_tc_6_9.CEL", + "embryo_tc_6_10.CEL", + "embryo_tc_6_11.CEL", + "embryo_tc_6_12.CEL", + "embryo_tc_8_1.CEL", + "embryo_tc_8_2.CEL", + "embryo_tc_8_3.CEL", + "embryo_tc_8_4.CEL", + "embryo_tc_8_5.CEL", + "embryo_tc_8_6.CEL", + "embryo_tc_8_7.CEL", + "embryo_tc_8_8.CEL", + "embryo_tc_8_9.CEL", + "embryo_tc_8_10.CEL", + "embryo_tc_8_11.CEL", + "embryo_tc_8_12.CEL", + "CG_AffyOligo_Gadfly3_01_13_03", + "embryo_tc_rma_release2.txt", + "embryo_tc_rma_release3.txt", + "na_affy_oligo.dros", + "README.TXT" + ] + ], + "license": null, + "size": 389000000, + "urls": [ + "ftp://ftp.fruitfly.org/pub/embryo_tc_array_data/" + ] + }, + "google_trends": { + "citation": "", + "details": "Google trends results.", + "files": [ + [ + + ] + ], + "license": null, + "size": 0, + "urls": [ + "http://www.google.com/trends/" + ] + }, + + "hapmap3": { + "citation": "Gibbs, Richard A., et al. 'The international HapMap project.' Nature 426.6968 (2003): 789-796.", + "details": "HapMap Project: Single Nucleotide Polymorphism sequenced in all human populations. \n The HapMap phase three SNP dataset - 1184 samples out of 11 populations.\n See http://www.nature.com/nature/journal/v426/n6968/abs/nature02168.html for details.\n\n SNP_matrix (A) encoding [see Paschou et all. 2007 (PCA-Correlated SNPs...)]:\n Let (B1,B2) be the alphabetically sorted bases, which occur in the j-th SNP, then\n\n / 1, iff SNPij==(B1,B1)\n Aij = | 0, iff SNPij==(B1,B2)\n \\\\ -1, iff SNPij==(B2,B2)\n\n The SNP data and the meta information (such as iid, sex and phenotype) are\n stored in the dataframe datadf, index is the Individual ID, \n with following columns for metainfo:\n\n * family_id -> Family ID\n * paternal_id -> Paternal ID\n * maternal_id -> Maternal ID\n * sex -> Sex (1=male; 2=female; other=unknown)\n * phenotype -> Phenotype (-9, or 0 for unknown)\n * population -> Population string (e.g. 'ASW' - 'YRI')\n * rest are SNP rs (ids)\n\n More information is given in infodf:\n\n * Chromosome:\n - autosomal chromosemes -> 1-22\n - X X chromosome -> 23\n - Y Y chromosome -> 24\n - XY Pseudo-autosomal region of X -> 25\n - MT Mitochondrial -> 26\n * Relative Positon (to Chromosome) [base pairs]\n\n ", + "files": [ + [ + "hapmap3_r2_b36_fwd.consensus.qc.poly.map.bz2", + "hapmap3_r2_b36_fwd.consensus.qc.poly.ped.bz2", + "relationships_w_pops_121708.txt" + ] + ], + "license": "International HapMap Project Public Access License (http://hapmap.ncbi.nlm.nih.gov/cgi-perl/registration#licence)", + "size": 3458246739, + "urls": [ + "http://hapmap.ncbi.nlm.nih.gov/downloads/genotypes/latest_phaseIII_ncbi_b36/plink_format/" + ] + }, + "isomap_face_data": { + "citation": "A Global Geometric Framework for Nonlinear Dimensionality Reduction, J. B. Tenenbaum, V. de Silva and J. C. Langford, Science 290 (5500): 2319-2323, 22 December 2000", + "details": "Face data made available by Tenenbaum, de Silva and Langford to demonstrate isomap, available from http://isomap.stanford.edu/datasets.html.", + "files": [ + [ + "face_data.mat" + ] + ], + "license": null, + "size": 24229368, + "urls": [ + "http://staffwww.dcs.shef.ac.uk/people/N.Lawrence/dataset_mirror/isomap_face_data/" + ] + }, + "mauna_loa": { + "citation": "Mauna Loa Data. Dr. Pieter Tans, NOAA/ESRL (www.esrl.noaa.gov/gmd/ccgg/trends/) and Dr. Ralph Keeling, Scripps Institution of Oceanography (scrippsco2.ucsd.edu/).", + "details": "The 'average' column contains the monthly mean CO2 mole fraction determined from daily averages. The mole fraction of CO2, expressed as parts per million (ppm) is the number of molecules of CO2 in every one million molecules of dried air (water vapor removed). If there are missing days concentrated either early or late in the month, the monthly mean is corrected to the middle of the month using the average seasonal cycle. Missing months are denoted by -99.99. The 'interpolated' column includes average values from the preceding column and interpolated values where data are missing. Interpolated values are computed in two steps. First, we compute for each month the average seasonal cycle in a 7-year window around each monthly value. In this way the seasonal cycle is allowed to change slowly over time. We then determine the 'trend' value for each month by removing the seasonal cycle; this result is shown in the 'trend' column. Trend values are linearly interpolated for missing months. The interpolated monthly mean is then the sum of the average seasonal cycle value and the trend value for the missing month.\n\nNOTE: In general, the data presented for the last year are subject to change, depending on recalibration of the reference gas mixtures used, and other quality control procedures. Occasionally, earlier years may also be changed for the same reasons. Usually these changes are minor.\n\nCO2 expressed as a mole fraction in dry air, micromol/mol, abbreviated as ppm \n\n (-99.99 missing data; -1 no data for daily means in month)", + "files": [ + [ + "co2_mm_mlo.txt" + ] + ], + "license": "-------------------------------------------------------------------- USE OF NOAA ESRL DATA\n\n These data are made freely available to the public and the scientific community in the belief that their wide dissemination will lead to greater understanding and new scientific insights. The availability of these data does not constitute publication of the data. NOAA relies on the ethics and integrity of the user to insure that ESRL receives fair credit for their work. If the data are obtained for potential use in a publication or presentation, ESRL should be informed at the outset of the nature of this work. If the ESRL data are essential to the work, or if an important result or conclusion depends on the ESRL data, co-authorship may be appropriate. This should be discussed at an early stage in the work. Manuscripts using the ESRL data should be sent to ESRL for review before they are submitted for publication so we can insure that the quality and limitations of the data are accurately represented.\n\n Contact: Pieter Tans (303 497 6678; pieter.tans@noaa.gov)\n\n RECIPROCITY Use of these data implies an agreement to reciprocate. Laboratories making similar measurements agree to make their own data available to the general public and to the scientific community in an equally complete and easily accessible form. Modelers are encouraged to make available to the community, upon request, their own tools used in the interpretation of the ESRL data, namely well documented model code, transport fields, and additional information necessary for other scientists to repeat the work and to run modified versions. Model availability includes collaborative support for new users of the models.\n --------------------------------------------------------------------\n\n See www.esrl.noaa.gov/gmd/ccgg/trends/ for additional details.", + "size": 46779, + "urls": [ + "ftp://aftp.cmdl.noaa.gov/products/trends/co2/" + ] + }, + "olivetti_faces": { + "citation": "Ferdinando Samaria and Andy Harter, Parameterisation of a Stochastic Model for Human Face Identification. Proceedings of 2nd IEEE Workshop on Applications of Computer Vision, Sarasota FL, December 1994", + "details": "Olivetti Research Labs Face data base, acquired between December 1992 and December 1994 in the Olivetti Research Lab, Cambridge (which later became AT&T Laboratories, Cambridge). When using these images please give credit to AT&T Laboratories, Cambridge. ", + "files": [ + [ + "att_faces.zip" + ], + [ + "olivettifaces.mat" + ] + ], + "license": null, + "size": 8561331, + "urls": [ + "http://staffwww.dcs.shef.ac.uk/people/N.Lawrence/dataset_mirror/olivetti_faces/", + "http://www.cs.nyu.edu/~roweis/data/" + ] + }, + "olivetti_glasses": { + "citation": "Information recorded in olivetti_faces entry. Should be used from there.", + "details": "Information recorded in olivetti_faces entry. Should be used from there.", + "files": [ + [ + "has_glasses.np" + ], + [ + "olivettifaces.mat" + ] + ], + "license": null, + "size": 4261047, + "urls": [ + "http://staffwww.dcs.shef.ac.uk/people/N.Lawrence/dataset_mirror/olivetti_faces/", + "http://www.cs.nyu.edu/~roweis/data/" + ] + }, + "olympic_marathon_men": { + "citation": null, + "details": "Olympic mens' marathon gold medal winning times from 1896 to 2012. Time given in pace (minutes per kilometer). Data is originally downloaded and collated from Wikipedia, we are not responsible for errors in the data", + "files": [ + [ + "olympicMarathonTimes.csv" + ] + ], + "license": null, + "size": 584, + "urls": [ + "http://staffwww.dcs.shef.ac.uk/people/N.Lawrence/dataset_mirror/olympic_marathon_men/" + ] + }, + "osu_accad": { + "citation": "The Open Motion Data Project by The Ohio State University Advanced Computing Center for the Arts and Design, http://accad.osu.edu/research/mocap/mocap_data.htm.", + "details": "Motion capture data of different motions from the Open Motion Data Project at Ohio State University.", + "files": [ + [ + "swagger1TXT.ZIP", + "handspring1TXT.ZIP", + "quickwalkTXT.ZIP", + "run1TXT.ZIP", + "sprintTXT.ZIP", + "dogwalkTXT.ZIP", + "camper_04TXT.ZIP", + "dance_KB3_TXT.ZIP", + "per20_TXT.ZIP", + "perTWO07_TXT.ZIP", + "perTWO13_TXT.ZIP", + "perTWO14_TXT.ZIP", + "perTWO15_TXT.ZIP", + "perTWO16_TXT.ZIP" + ], + [ + "connections.txt" + ] + ], + "license": "Data is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License (http://creativecommons.org/licenses/by-nc-sa/3.0/).", + "size": 15922790, + "urls": [ + "http://accad.osu.edu/research/mocap/data/", + "http://staffwww.dcs.shef.ac.uk/people/N.Lawrence/dataset_mirror/stick/" + ] + }, + "osu_run1": { + "citation": "The Open Motion Data Project by The Ohio State University Advanced Computing Center for the Arts and Design, http://accad.osu.edu/research/mocap/mocap_data.htm.", + "details": "Motion capture data of a stick man running from the Open Motion Data Project at Ohio State University.", + "files": [ + [ + "run1TXT.ZIP" + ], + [ + "connections.txt" + ] + ], + "license": "Data is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License (http://creativecommons.org/licenses/by-nc-sa/3.0/).", + "size": 338103, + "urls": [ + "http://accad.osu.edu/research/mocap/data/", + "http://staffwww.dcs.shef.ac.uk/people/N.Lawrence/dataset_mirror/stick/" + ] + }, + "pumadyn-32nm": { + "citation": "Created by Zoubin Ghahramani using the Matlab Robotics Toolbox of Peter Corke. Corke, P. I. (1996). A Robotics Toolbox for MATLAB. IEEE Robotics and Automation Magazine, 3 (1): 24-32.", + "details": "Pumadyn non linear 32 input data set with moderate noise. See http://www.cs.utoronto.ca/~delve/data/pumadyn/desc.html for details.", + "files": [ + [ + "pumadyn-32nm.tar.gz" + ] + ], + "license": "Data is made available by the Delve system at the University of Toronto", + "size": 5861646, + "urls": [ + "ftp://ftp.cs.toronto.edu/pub/neuron/delve/data/tarfiles/pumadyn-family/" + ] + }, + "ripley_prnn_data": { + "citation": "Pattern Recognition and Neural Networks by B.D. Ripley (1996) Cambridge University Press ISBN 0 521 46986 7", + "details": "Data sets from Brian Ripley's Pattern Recognition and Neural Networks", + "files": [ + [ + "Cushings.dat", + "README", + "crabs.dat", + "fglass.dat", + "fglass.grp", + "pima.te", + "pima.tr", + "pima.tr2", + "synth.te", + "synth.tr", + "viruses.dat", + "virus3.dat" + ] + ], + "license": null, + "size": 93565, + "urls": [ + "http://www.stats.ox.ac.uk/pub/PRNN/" + ] + }, + "robot_wireless": { + "citation": "WiFi-SLAM using Gaussian Process Latent Variable Models by Brian Ferris, Dieter Fox and Neil Lawrence in IJCAI'07 Proceedings pages 2480-2485. Data used in A Unifying Probabilistic Perspective for Spectral Dimensionality Reduction: Insights and New Models by Neil D. Lawrence, JMLR 13 pg 1609--1638, 2012.", + "details": "Data created by Brian Ferris and Dieter Fox. Consists of WiFi access point strengths taken during a circuit of the Paul Allen building at the University of Washington.", + "files": [ + [ + "uw-floor.txt" + ] + ], + "license": null, + "size": 284390, + "urls": [ + "http://staffwww.dcs.shef.ac.uk/people/N.Lawrence/dataset_mirror/robot_wireless/" + ] + }, + "rogers_girolami_data": { + "citation": "A First Course in Machine Learning. Simon Rogers and Mark Girolami: Chapman & Hall/CRC, ISBN-13: 978-1439824146", + "details": "Data from the textbook 'A First Course in Machine Learning'. Available from http://www.dcs.gla.ac.uk/~srogers/firstcourseml/.", + "files": [ + [ + "firstcoursemldata.tar.gz" + ] + ], + "license": null, + "size": 21949154, + "suffices": [ + [ + "?dl=1" + ] + ], + "urls": [ + "https://www.dropbox.com/sh/7p6tu1t29idgliq/_XqlH_3nt9/" + ] + }, + "singlecell": { + "citation": "Guoji Guo, Mikael Huss, Guo Qing Tong, Chaoyang Wang, Li Li Sun, Neil D. Clarke, Paul Robson, Resolution of Cell Fate Decisions Revealed by Single-Cell Gene Expression Analysis from Zygote to Blastocyst, Developmental Cell, Volume 18, Issue 4, 20 April 2010, Pages 675-685, ISSN 1534-5807, http://dx.doi.org/10.1016/j.devcel.2010.02.012. (http://www.sciencedirect.com/science/article/pii/S1534580710001103) Keywords: DEVBIO", + "details": "qPCR TaqMan array single cell experiment in mouse. The data is taken from the early stages of development when the Blastocyst is forming. At the 32 cell stage the data is already separated into the trophectoderm (TE) which goes onto form the placenta and the inner cellular mass (ICM). The ICM further differentiates into the epiblast (EPI)---which gives rise to the endoderm, mesoderm and ectoderm---and the primitive endoderm (PE) which develops into the amniotic sack. Guo et al selected 48 genes for expression measurement. They labelled the resulting cells and their labels are included as an aide to visualization.", + "files": [ + [ + "singlecell.csv" + ] + ], + "license": "ScienceDirect: http://www.elsevier.com/locate/termsandconditions?utm_source=sciencedirect&utm_medium=link&utm_campaign=terms", + "size": 233.1, + "urls": [ + "http://staffwww.dcs.shef.ac.uk/people/N.Lawrence/dataset_mirror/singlecell/" + ] + }, + "singlecell_islam": { + "citation": "Single-Cell RNA-Seq Reveals Dynamic, Random Monoallelic Gene Expression in Mammalian Cells Qiaolin Deng, Daniel Ramskoeld, Bjoern Reinius, and Rickard Sandberg Science 10 January 2014: 343 (6167), 193-196. [DOI:10.1126/science.1245316]", + "details" : "92 single cells (48 mouse ES cells, 44 mouse embryonic fibroblasts and 4 negative controls) were analyzed by single-cell tagged reverse transcription (STRT)", + "files" : [["GSE29087_L139_expression_tab.txt.gz"], ["GSE29087_family.soft.gz"]], + "license" : "Gene Expression Omnibus: http://www.ncbi.nlm.nih.gov/geo/info/disclaimer.html", + "size" : 1159449, + "urls" : ["ftp://ftp.ncbi.nlm.nih.gov/geo/series/GSE29nnn/GSE29087/suppl/", "ftp://ftp.ncbi.nlm.nih.gov/geo/series/GSE29nnn/GSE29087/soft/"] + }, + "singlecell_deng": { + "citation": "Deng Q, Ramsköld D, Reinius B, Sandberg R. Single-cell RNA-seq reveals dynamic, random monoallelic gene expression in mammalian cells. Science 2014 Jan 10;343(6167):193-6. PMID: 24408435", + "details" : "First generation mouse strain crosses were used to study monoallelic expression on the single cell level", + "files" : [["?acc=GSE45719&format=file"], ["GSE45719_series_matrix.txt.gz"]], + "license" : "Gene Expression Omnibus: http://www.ncbi.nlm.nih.gov/geo/info/disclaimer.html", + "size" : 1159449, + "save_names": [["GSE45719_Raw.tar"], [null]], + "urls" : ["http://www.ncbi.nlm.nih.gov/geo/download/", "ftp://ftp.ncbi.nlm.nih.gov/geo/series/GSE45nnn/GSE45719/matrix/"] + }, + "sod1_mouse": { + "citation": "Transcriptomic indices of fast and slow disease progression in two mouse models of amyotrophic lateral sclerosis' Nardo G1, Iennaco R, Fusi N, Heath PR, Marino M, Trolese MC, Ferraiuolo L, Lawrence N, Shaw PJ, Bendotti C Brain. 2013 Nov;136(Pt 11):3305-32. doi: 10.1093/brain/awt250. Epub 2013 Sep 24.", + "details": "Gene expression data from two separate strains of mice: C57 and 129Sv in wild type and SOD1 mutant strains.", + "files": [ + [ + "sod1_C57_129_exprs.csv", + "sod1_C57_129_se.csv" + ] + ], + "license": null, + "size": 0, + "urls": [ + "http://staffwww.dcs.shef.ac.uk/people/N.Lawrence/dataset_mirror/sod1_mouse/" + ] + }, + "swiss_roll": { + "citation": "A Global Geometric Framework for Nonlinear Dimensionality Reduction, J. B. Tenenbaum, V. de Silva and J. C. Langford, Science 290 (5500): 2319-2323, 22 December 2000", + "details": "Swiss roll data made available by Tenenbaum, de Silva and Langford to demonstrate isomap, available from http://isomap.stanford.edu/datasets.html.", + "files": [ + [ + "swiss_roll_data.mat" + ] + ], + "license": null, + "size": 800256, + "urls": [ + "http://isomap.stanford.edu/" + ] + }, + "three_phase_oil_flow": { + "citation": "Bishop, C. M. and G. D. James (1993). Analysis of multiphase flows using dual-energy gamma densitometry and neural networks. Nuclear Instruments and Methods in Physics Research A327, 580-593", + "details": "The three phase oil data used initially for demonstrating the Generative Topographic mapping.", + "files": [ + [ + "DataTrnLbls.txt", + "DataTrn.txt", + "DataTst.txt", + "DataTstLbls.txt", + "DataVdn.txt", + "DataVdnLbls.txt" + ] + ], + "license": null, + "size": 712796, + "urls": [ + "http://staffwww.dcs.shef.ac.uk/people/N.Lawrence/dataset_mirror/three_phase_oil_flow/" + ] + }, + "xw_pen": { + "citation": "Michael E. Tipping and Neil D. Lawrence. Variational inference for Student-t models: Robust Bayesian interpolation and generalised component analysis. Neurocomputing, 69:123--141, 2005", + "details": "Accelerometer pen data used for robust regression by Tipping and Lawrence.", + "files": [ + [ + "xw_pen_15.csv" + ] + ], + "license": null, + "size": 3410, + "urls": [ + "http://staffwww.dcs.shef.ac.uk/people/N.Lawrence/dataset_mirror/xw_pen/" + ] + } +} diff --git a/GPy/util/datasets.py b/GPy/util/datasets.py index a878c1d8..254639a6 100644 --- a/GPy/util/datasets.py +++ b/GPy/util/datasets.py @@ -1,4 +1,6 @@ +import csv import os +import copy import numpy as np import GPy import scipy.io @@ -7,6 +9,10 @@ import zipfile import tarfile import datetime import json +import re + +from config import * + ipython_available=True try: import IPython @@ -24,19 +30,28 @@ def reporthook(a,b,c): sys.stdout.flush() # Global variables -data_path = os.path.join(os.path.dirname(__file__), 'datasets') +data_path = os.path.expandvars(config.get('datasets', 'dir')) +#data_path = os.path.join(os.path.dirname(__file__), 'datasets') default_seed = 10000 -overide_manual_authorize=True +overide_manual_authorize=False neil_url = 'http://staffwww.dcs.shef.ac.uk/people/N.Lawrence/dataset_mirror/' # Read data resources from json file. # Don't do this when ReadTheDocs is scanning as it breaks things on_rtd = os.environ.get('READTHEDOCS', None) == 'True' #Checks if RTD is scanning + if not (on_rtd): path = os.path.join(os.path.dirname(__file__), 'data_resources.json') json_data=open(path).read() data_resources = json.loads(json_data) +if not (on_rtd): + path = os.path.join(os.path.dirname(__file__), 'football_teams.json') + json_data=open(path).read() + football_dict = json.loads(json_data) + + + def prompt_user(prompt): """Ask user for agreeing to data set licenses.""" # raw_input returns the empty string for "enter" @@ -67,20 +82,32 @@ def prompt_user(prompt): def data_available(dataset_name=None): """Check if the data set is available on the local machine already.""" - for file_list in data_resources[dataset_name]['files']: - for file in file_list: - if not os.path.exists(os.path.join(data_path, dataset_name, file)): + from itertools import izip_longest + dr = data_resources[dataset_name] + zip_urls = (dr['files'], ) + if dr.has_key('save_names'): zip_urls += (dr['save_names'], ) + else: zip_urls += ([],) + + for file_list, save_list in izip_longest(*zip_urls, fillvalue=[]): + for f, s in izip_longest(file_list, save_list, fillvalue=None): + if s is not None: f=s # If there is a save_name given, use that one + if not os.path.exists(os.path.join(data_path, dataset_name, f)): return False return True -def download_url(url, store_directory, save_name = None, messages = True, suffix=''): +def download_url(url, store_directory, save_name=None, messages=True, suffix=''): """Download a file from a url and save it to disk.""" i = url.rfind('/') file = url[i+1:] print file dir_name = os.path.join(data_path, store_directory) - save_name = os.path.join(dir_name, file) - print "Downloading ", url, "->", os.path.join(store_directory, file) + + if save_name is None: save_name = os.path.join(dir_name, file) + else: save_name = os.path.join(dir_name, save_name) + + if suffix is None: suffix='' + + print "Downloading ", url, "->", save_name if not os.path.exists(dir_name): os.makedirs(dir_name) try: @@ -95,7 +122,11 @@ def download_url(url, store_directory, save_name = None, messages = True, suffix raise ValueError('Tried url ' + url + suffix + ' and received server error ' + str(response.code)) with open(save_name, 'wb') as f: meta = response.info() - file_size = int(meta.getheaders("Content-Length")[0]) + content_length_str = meta.getheaders("Content-Length") + if content_length_str: + file_size = int(content_length_str[0]) + else: + file_size = None status = "" file_size_dl = 0 block_sz = 8192 @@ -107,9 +138,15 @@ def download_url(url, store_directory, save_name = None, messages = True, suffix file_size_dl += len(buff) f.write(buff) sys.stdout.write(" "*(len(status)) + "\r") - status = r"[{perc: <{ll}}] {dl:7.3f}/{full:.3f}MB".format(dl=file_size_dl/(1.*1e6), - full=file_size/(1.*1e6), ll=line_length, + if file_size: + status = r"[{perc: <{ll}}] {dl:7.3f}/{full:.3f}MB".format(dl=file_size_dl/(1048576.), + full=file_size/(1048576.), ll=line_length, perc="="*int(line_length*float(file_size_dl)/file_size)) + else: + status = r"[{perc: <{ll}}] {dl:7.3f}MB".format(dl=file_size_dl/(1048576.), + ll=line_length, + perc="."*int(line_length*float(file_size_dl/(10*1048576.)))) + sys.stdout.write(status) sys.stdout.flush() sys.stdout.write(" "*(len(status)) + "\r") @@ -153,19 +190,24 @@ def authorize_download(dataset_name=None): def download_data(dataset_name=None): """Check with the user that the are happy with terms and conditions for the data set, then download it.""" + import itertools dr = data_resources[dataset_name] if not authorize_download(dataset_name): raise Exception("Permission to download data set denied.") - if dr.has_key('suffices'): - for url, files, suffices in zip(dr['urls'], dr['files'], dr['suffices']): - for file, suffix in zip(files, suffices): - download_url(os.path.join(url,file), dataset_name, dataset_name, suffix=suffix) - else: - for url, files in zip(dr['urls'], dr['files']): - for file in files: - download_url(os.path.join(url,file), dataset_name, dataset_name) + zip_urls = (dr['urls'], dr['files']) + + if dr.has_key('save_names'): zip_urls += (dr['save_names'], ) + else: zip_urls += ([],) + + if dr.has_key('suffices'): zip_urls += (dr['suffices'], ) + else: zip_urls += ([],) + + for url, files, save_names, suffices in itertools.izip_longest(*zip_urls, fillvalue=[]): + for f, save_name, suffix in itertools.izip_longest(files, save_names, suffices, fillvalue=None): + download_url(os.path.join(url,f), dataset_name, save_name, suffix=suffix) + return True def data_details_return(data, data_set): @@ -214,7 +256,7 @@ def cmu_urls_files(subj_motions, messages = True): if not os.path.exists(cur_skel_file): # Current skel file doesn't exist. if not os.path.isdir(skel_dir): - os.mkdir(skel_dir) + os.makedirs(skel_dir) # Add skel file to list. url_required = True file_download.append(subjects[i] + '.asf') @@ -296,6 +338,202 @@ def della_gatta_TRP63_gene_expression(data_set='della_gatta', gene_number=None): +def football_data(season='1314', data_set='football_data'): + """Football data from English games since 1993. This downloads data from football-data.co.uk for the given season. """ + def league2num(string): + league_dict = {'E0':0, 'E1':1, 'E2': 2, 'E3': 3, 'EC':4} + return league_dict[string] + + def football2num(string): + if football_dict.has_key(string): + return football_dict[string] + else: + football_dict[string] = len(football_dict)+1 + return len(football_dict)+1 + + data_set_season = data_set + '_' + season + data_resources[data_set_season] = copy.deepcopy(data_resources[data_set]) + data_resources[data_set_season]['urls'][0]+=season + '/' + start_year = int(season[0:2]) + end_year = int(season[2:4]) + files = ['E0.csv', 'E1.csv', 'E2.csv', 'E3.csv'] + if start_year>4 and start_year < 93: + files += ['EC.csv'] + data_resources[data_set_season]['files'] = [files] + if not data_available(data_set_season): + download_data(data_set_season) + import pylab as pb + for file in reversed(files): + filename = os.path.join(data_path, data_set_season, file) + # rewrite files removing blank rows. + writename = os.path.join(data_path, data_set_season, 'temp.csv') + input = open(filename, 'rb') + output = open(writename, 'wb') + writer = csv.writer(output) + for row in csv.reader(input): + if any(field.strip() for field in row): + writer.writerow(row) + input.close() + output.close() + table = np.loadtxt(writename,skiprows=1, usecols=(0, 1, 2, 3, 4, 5), converters = {0: league2num, 1: pb.datestr2num, 2:football2num, 3:football2num}, delimiter=',') + X = table[:, :4] + Y = table[:, 4:] + return data_details_return({'X': X, 'Y': Y}, data_set) + +def sod1_mouse(data_set='sod1_mouse'): + if not data_available(data_set): + download_data(data_set) + from pandas import read_csv + dir_path = os.path.join(data_path, data_set) + filename = os.path.join(dir_path, 'sod1_C57_129_exprs.csv') + Y = read_csv(filename, header=0, index_col=0) + num_repeats=4 + num_time=4 + num_cond=4 + X = 1 + return data_details_return({'X': X, 'Y': Y}, data_set) + +def spellman_yeast(data_set='spellman_yeast'): + if not data_available(data_set): + download_data(data_set) + from pandas import read_csv + dir_path = os.path.join(data_path, data_set) + filename = os.path.join(dir_path, 'combined.txt') + Y = read_csv(filename, header=0, index_col=0, sep='\t') + return data_details_return({'Y': Y}, data_set) + +def spellman_yeast_cdc15(data_set='spellman_yeast'): + if not data_available(data_set): + download_data(data_set) + from pandas import read_csv + dir_path = os.path.join(data_path, data_set) + filename = os.path.join(dir_path, 'combined.txt') + Y = read_csv(filename, header=0, index_col=0, sep='\t') + t = np.asarray([10, 30, 50, 70, 80, 90, 100, 110, 120, 130, 140, 150, 170, 180, 190, 200, 210, 220, 230, 240, 250, 270, 290]) + times = ['cdc15_'+str(time) for time in t] + Y = Y[times].T + t = t[:, None] + return data_details_return({'Y' : Y, 't': t, 'info': 'Time series of synchronized yeast cells from the CDC-15 experiment of Spellman et al (1998).'}, data_set) + +def lee_yeast_ChIP(data_set='lee_yeast_ChIP'): + if not data_available(data_set): + download_data(data_set) + from pandas import read_csv + import zipfile + dir_path = os.path.join(data_path, data_set) + filename = os.path.join(dir_path, 'binding_by_gene.tsv') + S = read_csv(filename, header=1, index_col=0, sep='\t') + transcription_factors = [col for col in S.columns if col[:7] != 'Unnamed'] + annotations = S[['Unnamed: 1', 'Unnamed: 2', 'Unnamed: 3']] + S = S[transcription_factors] + return data_details_return({'annotations' : annotations, 'Y' : S, 'transcription_factors': transcription_factors}, data_set) + + + +def fruitfly_tomancak(data_set='fruitfly_tomancak', gene_number=None): + if not data_available(data_set): + download_data(data_set) + from pandas import read_csv + dir_path = os.path.join(data_path, data_set) + filename = os.path.join(dir_path, 'tomancak_exprs.csv') + Y = read_csv(filename, header=0, index_col=0).T + num_repeats = 3 + num_time = 12 + xt = np.linspace(0, num_time-1, num_time) + xr = np.linspace(0, num_repeats-1, num_repeats) + xtime, xrepeat = np.meshgrid(xt, xr) + X = np.vstack((xtime.flatten(), xrepeat.flatten())).T + return data_details_return({'X': X, 'Y': Y, 'gene_number' : gene_number}, data_set) + +def drosophila_protein(data_set='drosophila_protein'): + if not data_available(data_set): + download_data(data_set) + from pandas import read_csv + dir_path = os.path.join(data_path, data_set) + filename = os.path.join(dir_path, 'becker_et_al.csv') + Y = read_csv(filename, header=0) + return data_details_return({'Y': Y}, data_set) + +def drosophila_knirps(data_set='drosophila_protein'): + if not data_available(data_set): + download_data(data_set) + from pandas import read_csv + dir_path = os.path.join(data_path, data_set) + filename = os.path.join(dir_path, 'becker_et_al.csv') + # in the csv file we have facts_kni and ext_kni. We treat facts_kni as protein and ext_kni as mRNA + df = read_csv(filename, header=0) + t = df['t'][:,None] + x = df['x'][:,None] + + g = df['expression1'][:,None] + p = df['expression2'][:,None] + + leng = x.shape[0] + + T = np.vstack([t,t]) + S = np.vstack([x,x]) + inx = np.zeros(leng*2)[:,None] + + inx[leng*2/2:leng*2]=1 + X = np.hstack([T,S,inx]) + Y = np.vstack([g,p]) + return data_details_return({'Y': Y, 'X': X}, data_set) + +# This will be for downloading google trends data. +def google_trends(query_terms=['big data', 'machine learning', 'data science'], data_set='google_trends', refresh_data=False): + """Data downloaded from Google trends for given query terms. Warning, if you use this function multiple times in a row you get blocked due to terms of service violations. The function will cache the result of your query, if you wish to refresh an old query set refresh_data to True. The function is inspired by this notebook: http://nbviewer.ipython.org/github/sahuguet/notebooks/blob/master/GoogleTrends%20meet%20Notebook.ipynb""" + query_terms.sort() + import pandas + + # Create directory name for data + dir_path = os.path.join(data_path,'google_trends') + if not os.path.isdir(dir_path): + os.makedirs(dir_path) + dir_name = '-'.join(query_terms) + dir_name = dir_name.replace(' ', '_') + dir_path = os.path.join(dir_path,dir_name) + file = 'data.csv' + file_name = os.path.join(dir_path,file) + if not os.path.exists(file_name) or refresh_data: + print "Accessing Google trends to acquire the data. Note that repeated accesses will result in a block due to a google terms of service violation. Failure at this point may be due to such blocks." + # quote the query terms. + quoted_terms = [] + for term in query_terms: + quoted_terms.append(urllib2.quote(term)) + print "Query terms: ", ', '.join(query_terms) + + print "Fetching query:" + query = 'http://www.google.com/trends/fetchComponent?q=%s&cid=TIMESERIES_GRAPH_0&export=3' % ",".join(quoted_terms) + + data = urllib2.urlopen(query).read() + print "Done." + # In the notebook they did some data cleaning: remove Javascript header+footer, and translate new Date(....,..,..) into YYYY-MM-DD. + header = """// Data table response\ngoogle.visualization.Query.setResponse(""" + data = data[len(header):-2] + data = re.sub('new Date\((\d+),(\d+),(\d+)\)', (lambda m: '"%s-%02d-%02d"' % (m.group(1).strip(), 1+int(m.group(2)), int(m.group(3)))), data) + timeseries = json.loads(data) + columns = [k['label'] for k in timeseries['table']['cols']] + rows = map(lambda x: [k['v'] for k in x['c']], timeseries['table']['rows']) + df = pandas.DataFrame(rows, columns=columns) + if not os.path.isdir(dir_path): + os.makedirs(dir_path) + + df.to_csv(file_name) + else: + print "Reading cached data for google trends. To refresh the cache set 'refresh_data=True' when calling this function." + print "Query terms: ", ', '.join(query_terms) + + df = pandas.read_csv(file_name, parse_dates=[0]) + + columns = df.columns + terms = len(query_terms) + import datetime + X = np.asarray([(row, i) for i in range(terms) for row in df.index]) + Y = np.asarray([[df.ix[row][query_terms[i]]] for i in range(terms) for row in df.index ]) + output_info = columns[1:] + + return data_details_return({'data frame' : df, 'X': X, 'Y': Y, 'query_terms': output_info, 'info': "Data downloaded from google trends with query terms: " + ', '.join(output_info) + '.'}, data_set) + # The data sets def oil(data_set='three_phase_oil_flow'): """The three phase oil data from Bishop and James (1993).""" @@ -415,6 +653,18 @@ def silhouette(data_set='ankur_pose_data'): Ytest = mat_data['Z_test'] return data_details_return({'X': X, 'Y': Y, 'Xtest': Xtest, 'Ytest': Ytest}, data_set) +def decampos_digits(data_set='decampos_characters', which_digits=[0,1,2,3,4,5,6,7,8,9]): + if not data_available(data_set): + download_data(data_set) + path = os.path.join(data_path, data_set) + digits = np.load(os.path.join(path, 'digits.npy')) + digits = digits[which_digits,:,:,:] + num_classes, num_samples, height, width = digits.shape + Y = digits.reshape((digits.shape[0]*digits.shape[1],digits.shape[2]*digits.shape[3])) + lbls = np.array([[l]*num_samples for l in which_digits]).reshape(Y.shape[0], 1) + str_lbls = np.array([[str(l)]*num_samples for l in which_digits]) + return data_details_return({'Y': Y, 'lbls': lbls, 'str_lbls' : str_lbls, 'info': 'Digits data set from the de Campos characters data'}, data_set) + def ripley_synth(data_set='ripley_prnn_data'): if not data_available(data_set): download_data(data_set) @@ -424,7 +674,52 @@ def ripley_synth(data_set='ripley_prnn_data'): test = np.genfromtxt(os.path.join(data_path, data_set, 'synth.te'), skip_header=1) Xtest = test[:, 0:2] ytest = test[:, 2:3] - return data_details_return({'X': X, 'y': y, 'Xtest': Xtest, 'ytest': ytest, 'info': 'Synthetic data generated by Ripley for a two class classification problem.'}, data_set) + return data_details_return({'X': X, 'Y': y, 'Xtest': Xtest, 'Ytest': ytest, 'info': 'Synthetic data generated by Ripley for a two class classification problem.'}, data_set) + +def global_average_temperature(data_set='global_temperature', num_train=1000, refresh_data=False): + path = os.path.join(data_path, data_set) + if data_available(data_set) and not refresh_data: + print 'Using cached version of the data set, to use latest version set refresh_data to True' + else: + download_data(data_set) + data = np.loadtxt(os.path.join(data_path, data_set, 'GLBTS.long.data')) + print 'Most recent data observation from month ', data[-1, 1], ' in year ', data[-1, 0] + allX = data[data[:, 3]!=-99.99, 2:3] + allY = data[data[:, 3]!=-99.99, 3:4] + X = allX[:num_train, 0:1] + Xtest = allX[num_train:, 0:1] + Y = allY[:num_train, 0:1] + Ytest = allY[num_train:, 0:1] + return data_details_return({'X': X, 'Y': Y, 'Xtest': Xtest, 'Ytest': Ytest, 'info': "Mauna Loa data with " + str(num_train) + " values used as training points."}, data_set) + +def mauna_loa(data_set='mauna_loa', num_train=545, refresh_data=False): + path = os.path.join(data_path, data_set) + if data_available(data_set) and not refresh_data: + print 'Using cached version of the data set, to use latest version set refresh_data to True' + else: + download_data(data_set) + data = np.loadtxt(os.path.join(data_path, data_set, 'co2_mm_mlo.txt')) + print 'Most recent data observation from month ', data[-1, 1], ' in year ', data[-1, 0] + allX = data[data[:, 3]!=-99.99, 2:3] + allY = data[data[:, 3]!=-99.99, 3:4] + X = allX[:num_train, 0:1] + Xtest = allX[num_train:, 0:1] + Y = allY[:num_train, 0:1] + Ytest = allY[num_train:, 0:1] + return data_details_return({'X': X, 'Y': Y, 'Xtest': Xtest, 'Ytest': Ytest, 'info': "Mauna Loa data with " + str(num_train) + " values used as training points."}, data_set) + + +def boxjenkins_airline(data_set='boxjenkins_airline', num_train=96): + path = os.path.join(data_path, data_set) + if not data_available(data_set): + download_data(data_set) + data = np.loadtxt(os.path.join(data_path, data_set, 'boxjenkins_airline.csv'), delimiter=',') + Y = data[:num_train, 1:2] + X = data[:num_train, 0:1] + Xtest = data[num_train:, 0:1] + Ytest = data[num_train:, 1:2] + return data_details_return({'X': X, 'Y': Y, 'Xtest': Xtest, 'Ytest': Ytest, 'info': "Montly airline passenger data from Box & Jenkins 1976."}, data_set) + def osu_run1(data_set='osu_run1', sample_every=4): path = os.path.join(data_path, data_set) @@ -438,7 +733,7 @@ def osu_run1(data_set='osu_run1', sample_every=4): return data_details_return({'Y': Y, 'connect' : connect}, data_set) def swiss_roll_generated(num_samples=1000, sigma=0.0): - with open(os.path.join(data_path, 'swiss_roll.pickle')) as f: + with open(os.path.join(os.path.dirname(__file__), 'datasets', 'swiss_roll.pickle')) as f: data = pickle.load(f) Na = data['Y'].shape[0] perm = np.random.permutation(np.r_[:Na])[:num_samples] @@ -452,23 +747,61 @@ def swiss_roll_generated(num_samples=1000, sigma=0.0): return {'Y':Y, 't':t, 'colors':c} def hapmap3(data_set='hapmap3'): + """ + The HapMap phase three SNP dataset - 1184 samples out of 11 populations. + + SNP_matrix (A) encoding [see Paschou et all. 2007 (PCA-Correlated SNPs...)]: + Let (B1,B2) be the alphabetically sorted bases, which occur in the j-th SNP, then + + / 1, iff SNPij==(B1,B1) + Aij = | 0, iff SNPij==(B1,B2) + \ -1, iff SNPij==(B2,B2) + + The SNP data and the meta information (such as iid, sex and phenotype) are + stored in the dataframe datadf, index is the Individual ID, + with following columns for metainfo: + + * family_id -> Family ID + * paternal_id -> Paternal ID + * maternal_id -> Maternal ID + * sex -> Sex (1=male; 2=female; other=unknown) + * phenotype -> Phenotype (-9, or 0 for unknown) + * population -> Population string (e.g. 'ASW' - 'YRI') + * rest are SNP rs (ids) + + More information is given in infodf: + + * Chromosome: + - autosomal chromosemes -> 1-22 + - X X chromosome -> 23 + - Y Y chromosome -> 24 + - XY Pseudo-autosomal region of X -> 25 + - MT Mitochondrial -> 26 + * Relative Positon (to Chromosome) [base pairs] + """ try: from pandas import read_pickle, DataFrame from sys import stdout import bz2 except ImportError as i: raise i, "Need pandas for hapmap dataset, make sure to install pandas (http://pandas.pydata.org/) before loading the hapmap dataset" - if not data_available(data_set): - download_data(data_set) - dirpath = os.path.join(data_path,'hapmap3') + + dir_path = os.path.join(data_path,'hapmap3') hapmap_file_name = 'hapmap3_r2_b36_fwd.consensus.qc.poly' - preprocessed_data_paths = [os.path.join(dirpath,hapmap_file_name + file_name) for file_name in \ + unpacked_files = [os.path.join(dir_path, hapmap_file_name+ending) for ending in ['.ped', '.map']] + unpacked_files_exist = reduce(lambda a, b:a and b, map(os.path.exists, unpacked_files)) + + if not unpacked_files_exist and not data_available(data_set): + download_data(data_set) + + preprocessed_data_paths = [os.path.join(dir_path,hapmap_file_name + file_name) for file_name in \ ['.snps.pickle', '.info.pickle', '.nan.pickle']] + if not reduce(lambda a,b: a and b, map(os.path.exists, preprocessed_data_paths)): - if not overide_manual_authorize and prompt_user("Preprocessing requires 17GB " - "of memory and can take a long time, continue? [Y/n]\n"): + if not overide_manual_authorize and not prompt_user("Preprocessing requires ~25GB " + "of memory and can take a (very) long time, continue? [Y/n]"): print "Preprocessing required for further usage." return status = "Preprocessing data, please be patient..." @@ -479,8 +812,7 @@ def hapmap3(data_set='hapmap3'): perc="="*int(20.*progress/100.)) stdout.write(status); stdout.flush() return status - unpacked_files = [os.path.join(dirpath, hapmap_file_name+ending) for ending in ['.ped', '.map']] - if not reduce(lambda a,b: a and b, map(os.path.exists, unpacked_files)): + if not unpacked_files_exist: status=write_status('unpacking...', 0, '') curr = 0 for newfilepath in unpacked_files: @@ -494,17 +826,18 @@ def hapmap3(data_set='hapmap3'): for data in iter(lambda : f.read(buffsize), b''): new_file.write(decomp.decompress(data)) file_processed += len(data) - write_status('unpacking...', curr+12.*file_processed/(file_size), status) + status=write_status('unpacking...', curr+12.*file_processed/(file_size), status) curr += 12 status=write_status('unpacking...', curr, status) + os.remove(filepath) status=write_status('reading .ped...', 25, status) - # Preprocess data: - snpstrnp = np.loadtxt('hapmap3_r2_b36_fwd.consensus.qc.poly.ped', dtype=str) + # Preprocess data: + snpstrnp = np.loadtxt(unpacked_files[0], dtype=str) status=write_status('reading .map...', 33, status) - mapnp = np.loadtxt('hapmap3_r2_b36_fwd.consensus.qc.poly.map', dtype=str) + mapnp = np.loadtxt(unpacked_files[1], dtype=str) status=write_status('reading relationships.txt...', 42, status) # and metainfo: - infodf = DataFrame.from_csv('./relationships_w_pops_121708.txt', header=0, sep='\t') + infodf = DataFrame.from_csv(os.path.join(dir_path,'./relationships_w_pops_121708.txt'), header=0, sep='\t') infodf.set_index('IID', inplace=1) status=write_status('filtering nan...', 45, status) snpstr = snpstrnp[:,6:].astype('S1').reshape(snpstrnp.shape[0], -1, 2) @@ -519,8 +852,8 @@ def hapmap3(data_set='hapmap3'): snps = (snps*np.array([1,-1])[None,None,:]) status=write_status('encoding snps...', 78, status) snps = snps.sum(-1) - status=write_status('encoding snps', 81, status) - snps = snps.astype('S1') + status=write_status('encoding snps...', 81, status) + snps = snps.astype('i8') status=write_status('marking nan values...', 88, status) # put in nan values (masked as -128): snps[inan] = -128 @@ -534,7 +867,8 @@ def hapmap3(data_set='hapmap3'): # put everything together: status=write_status('setting up snps...', 96, status) snpsdf = DataFrame(index=metadf.index, data=snps, columns=mapnp[:,1]) - snpsdf.to_pickle(preprocessed_data_paths[0]) + with open(preprocessed_data_paths[0], 'wb') as f: + pickle.dump(f, snpsdf, protocoll=-1) status=write_status('setting up snps...', 98, status) inandf = DataFrame(index=metadf.index, data=inan, columns=mapnp[:,1]) inandf.to_pickle(preprocessed_data_paths[2]) @@ -562,7 +896,159 @@ def hapmap3(data_set='hapmap3'): inandf=inandf, populations=populations) return hapmap - + +def singlecell(data_set='singlecell'): + if not data_available(data_set): + download_data(data_set) + + from pandas import read_csv + dir_path = os.path.join(data_path, data_set) + filename = os.path.join(dir_path, 'singlecell.csv') + Y = read_csv(filename, header=0, index_col=0) + genes = Y.columns + labels = Y.index + # data = np.loadtxt(os.path.join(dir_path, 'singlecell.csv'), delimiter=",", dtype=str) + return data_details_return({'Y': Y, 'info' : "qPCR singlecell experiment in Mouse, measuring 48 gene expressions in 1-64 cell states. The labels have been created as in Guo et al. [2010]", + 'genes': genes, 'labels':labels, + }, data_set) + +def singlecell_rna_seq_islam(dataset='singlecell_islam'): + if not data_available(dataset): + download_data(dataset) + + from pandas import read_csv, DataFrame, concat + dir_path = os.path.join(data_path, dataset) + filename = os.path.join(dir_path, 'GSE29087_L139_expression_tab.txt.gz') + data = read_csv(filename, sep='\t', skiprows=6, compression='gzip', header=None) + header1 = read_csv(filename, sep='\t', header=None, skiprows=5, nrows=1, compression='gzip') + header2 = read_csv(filename, sep='\t', header=None, skiprows=3, nrows=1, compression='gzip') + data.columns = np.concatenate((header1.ix[0, :], header2.ix[0, 7:])) + Y = data.set_index("Feature").ix[8:, 6:-4].T.astype(float) + + # read the info .soft + filename = os.path.join(dir_path, 'GSE29087_family.soft.gz') + info = read_csv(filename, sep='\t', skiprows=0, compression='gzip', header=None) + # split at ' = ' + info = DataFrame(info.ix[:,0].str.split(' = ').tolist()) + # only take samples: + info = info[info[0].str.contains("!Sample")] + info[0] = info[0].apply(lambda row: row[len("!Sample_"):]) + + groups = info.groupby(0).groups + # remove 'GGG' from barcodes + barcode = info[1][groups['barcode']].apply(lambda row: row[:-3]) + + title = info[1][groups['title']] + title.index = barcode + title.name = 'title' + geo_accession = info[1][groups['geo_accession']] + geo_accession.index = barcode + geo_accession.name = 'geo_accession' + case_id = info[1][groups['source_name_ch1']] + case_id.index = barcode + case_id.name = 'source_name_ch1' + + info = concat([title, geo_accession, case_id], axis=1) + labels = info.join(Y).source_name_ch1[:-4] + labels[labels=='Embryonic stem cell'] = "ES" + labels[labels=='Embryonic fibroblast'] = "MEF" + + return data_details_return({'Y': Y, + 'info': '92 single cells (48 mouse ES cells, 44 mouse embryonic fibroblasts and 4 negative controls) were analyzed by single-cell tagged reverse transcription (STRT)', + 'genes': Y.columns, + 'labels': labels, + 'datadf': data, + 'infodf': info}, dataset) + +def singlecell_rna_seq_deng(dataset='singlecell_deng'): + if not data_available(dataset): + download_data(dataset) + + from pandas import read_csv, isnull + dir_path = os.path.join(data_path, dataset) + + # read the info .soft + filename = os.path.join(dir_path, 'GSE45719_series_matrix.txt.gz') + info = read_csv(filename, sep='\t', skiprows=0, compression='gzip', header=None, nrows=29, index_col=0) + summary = info.loc['!Series_summary'][1] + design = info.loc['!Series_overall_design'] + + # only take samples: + sample_info = read_csv(filename, sep='\t', skiprows=30, compression='gzip', header=0, index_col=0).T + sample_info.columns = sample_info.columns.to_series().apply(lambda row: row[len("!Sample_"):]) + sample_info.columns.name = sample_info.columns.name[len("!Sample_"):] + sample_info = sample_info[['geo_accession', 'characteristics_ch1', 'description']] + sample_info = sample_info.iloc[:, np.r_[0:4, 5:sample_info.shape[1]]] + c = sample_info.columns.to_series() + c[1:4] = ['strain', 'cross', 'developmental_stage'] + sample_info.columns = c + + # get the labels right: + rep = re.compile('\(.*\)') + def filter_dev_stage(row): + if isnull(row): + row = "2-cell stage embryo" + if row.startswith("developmental stage: "): + row = row[len("developmental stage: "):] + if row == 'adult': + row += " liver" + row = row.replace(' stage ', ' ') + row = rep.sub(' ', row) + row = row.strip(' ') + return row + labels = sample_info.developmental_stage.apply(filter_dev_stage) + + # Extract the tar file + filename = os.path.join(dir_path, 'GSE45719_Raw.tar') + with tarfile.open(filename, 'r') as files: + print "Extracting Archive {}...".format(files.name) + data = None + gene_info = None + message = '' + members = files.getmembers() + overall = len(members) + for i, file_info in enumerate(members): + f = files.extractfile(file_info) + inner = read_csv(f, sep='\t', header=0, compression='gzip', index_col=0) + print ' '*(len(message)+1) + '\r', + message = "{: >7.2%}: Extracting: {}".format(float(i+1)/overall, file_info.name[:20]+"...txt.gz") + print message, + if data is None: + data = inner.RPKM.to_frame() + data.columns = [file_info.name[:-18]] + gene_info = inner.Refseq_IDs.to_frame() + gene_info.columns = [file_info.name[:-18]] + else: + data[file_info.name[:-18]] = inner.RPKM + gene_info[file_info.name[:-18]] = inner.Refseq_IDs + + # Strip GSM number off data index + rep = re.compile('GSM\d+_') + data.columns = data.columns.to_series().apply(lambda row: row[rep.match(row).end():]) + data = data.T + + # make sure the same index gets used + sample_info.index = data.index + + # get the labels from the description + #rep = re.compile('fibroblast|\d+-cell|embryo|liver|early blastocyst|mid blastocyst|late blastocyst|blastomere|zygote', re.IGNORECASE) + + sys.stdout.write(' '*len(message) + '\r') + sys.stdout.flush() + print + print "Read Archive {}".format(files.name) + + return data_details_return({'Y': data, + 'series_info': info, + 'sample_info': sample_info, + 'gene_info': gene_info, + 'summary': summary, + 'design': design, + 'genes': data.columns, + 'labels': labels, + }, dataset) + + def swiss_roll_1000(): return swiss_roll(num_samples=1000) @@ -604,8 +1090,8 @@ def toy_rbf_1d(seed=default_seed, num_samples=500): num_in = 1 X = np.random.uniform(low= -1.0, high=1.0, size=(num_samples, num_in)) X.sort(axis=0) - rbf = GPy.kern.rbf(num_in, variance=1., lengthscale=np.array((0.25,))) - white = GPy.kern.white(num_in, variance=1e-2) + rbf = GPy.kern.RBF(num_in, variance=1., lengthscale=np.array((0.25,))) + white = GPy.kern.White(num_in, variance=1e-2) kernel = rbf + white K = kernel.K(X) y = np.reshape(np.random.multivariate_normal(np.zeros(num_samples), K), (num_samples, 1)) @@ -629,6 +1115,21 @@ def toy_linear_1d_classification(seed=default_seed): X = (np.r_[x1, x2])[:, None] return {'X': X, 'Y': sample_class(2.*X), 'F': 2.*X, 'seed' : seed} +def olivetti_glasses(data_set='olivetti_glasses', num_training=200, seed=default_seed): + path = os.path.join(data_path, data_set) + if not data_available(data_set): + download_data(data_set) + y = np.load(os.path.join(path, 'has_glasses.np')) + y = np.where(y=='y',1,0).reshape(-1,1) + faces = scipy.io.loadmat(os.path.join(path, 'olivettifaces.mat'))['faces'].T + np.random.seed(seed=seed) + index = np.random.permutation(faces.shape[0]) + X = faces[index[:num_training],:] + Xtest = faces[index[num_training:],:] + Y = y[index[:num_training],:] + Ytest = y[index[num_training:]] + return data_details_return({'X': X, 'Y': Y, 'Xtest': Xtest, 'Ytest': Ytest, 'seed' : seed, 'info': "ORL Faces with labels identifiying who is wearing glasses and who isn't. Data is randomly partitioned according to given seed. Presence or absence of glasses was labelled by James Hensman."}, 'olivetti_faces') + def olivetti_faces(data_set='olivetti_faces'): path = os.path.join(data_path, data_set) if not data_available(data_set): @@ -641,7 +1142,8 @@ def olivetti_faces(data_set='olivetti_faces'): for subject in range(40): for image in range(10): image_path = os.path.join(path, 'orl_faces', 's'+str(subject+1), str(image+1) + '.pgm') - Y.append(GPy.util.netpbmfile.imread(image_path).flatten()) + from GPy.util import netpbmfile + Y.append(netpbmfile.imread(image_path).flatten()) lbls.append(subject) Y = np.asarray(Y) lbls = np.asarray(lbls)[:, None] @@ -843,6 +1345,30 @@ def creep_data(data_set='creep_rupture'): X = all_data[:, features].copy() return data_details_return({'X': X, 'y': y}, data_set) +def cifar10_patches(data_set='cifar-10'): + """The Candian Institute for Advanced Research 10 image data set. Code for loading in this data is taken from this Boris Babenko's blog post, original code available here: http://bbabenko.tumblr.com/post/86756017649/learning-low-level-vision-feautres-in-10-lines-of-code""" + dir_path = os.path.join(data_path, data_set) + filename = os.path.join(dir_path, 'cifar-10-python.tar.gz') + if not data_available(data_set): + download_data(data_set) + import tarfile + # This code is from Boris Babenko's blog post. + # http://bbabenko.tumblr.com/post/86756017649/learning-low-level-vision-feautres-in-10-lines-of-code + tfile = tarfile.open(filename, 'r:gz') + tfile.extractall(dir_path) + + with open(os.path.join(dir_path, 'cifar-10-batches-py','data_batch_1'),'rb') as f: + data = pickle.load(f) + + images = data['data'].reshape((-1,3,32,32)).astype('float32')/255 + images = np.rollaxis(images, 1, 4) + patches = np.zeros((0,5,5,3)) + for x in range(0,32-5,5): + for y in range(0,32-5,5): + patches = np.concatenate((patches, images[:,x:x+5,y:y+5,:]), axis=0) + patches = patches.reshape((patches.shape[0],-1)) + return data_details_return({'Y': patches, "info" : "32x32 pixel patches extracted from the CIFAR-10 data by Boris Babenko to demonstrate k-means features."}, data_set) + def cmu_mocap_49_balance(data_set='cmu_mocap'): """Load CMU subject 49's one legged balancing motion that was used by Alvarez, Luengo and Lawrence at AISTATS 2009.""" train_motions = ['18', '19'] diff --git a/GPy/util/datasets/BGPLVMSimulation.mat b/GPy/util/datasets/BGPLVMSimulation.mat deleted file mode 100644 index c1cff0a0..00000000 Binary files a/GPy/util/datasets/BGPLVMSimulation.mat and /dev/null differ diff --git a/GPy/util/datasets/COPYRIGHT b/GPy/util/datasets/COPYRIGHT deleted file mode 100644 index b0c26f9d..00000000 --- a/GPy/util/datasets/COPYRIGHT +++ /dev/null @@ -1 +0,0 @@ -These datasets are reproduced for educational purposes only. No copyright infringement intended! diff --git a/GPy/util/datasets/banana.txt b/GPy/util/datasets/banana.txt deleted file mode 100644 index 7f50ce4f..00000000 --- a/GPy/util/datasets/banana.txt +++ /dev/null @@ -1,5301 +0,0 @@ --1 -3.0898387 -0.83168647 --1 -2.9808342 -0.15957534 --1 -2.8360574 -0.17708113 --1 -2.7678489 0.096217259 --1 -2.6003502 0.21677229 --1 -2.5624693 -0.078385908 --1 -2.4124094 0.25988449 --1 -2.3736195 -0.010002369 --1 -2.3424292 0.24560361 --1 -2.3212375 0.086108807 -1 -2.2843001 -1.0189387 -1 -2.2517489 -1.9629961 --1 -2.2499202 0.16699851 -1 -2.1905021 -1.3004049 --1 -2.1887042 0.099086783 -1 -2.1811689 -1.8767374 -1 -2.1690977 -0.52289999 -1 -2.1469883 -0.8576587 -1 -2.1430257 -0.47579202 -1 -2.1404626 -1.5866986 -1 -2.1396387 -1.4273546 -1 -2.1320511 -0.346628 -1 -2.1254684 -1.8510498 --1 -2.1253473 0.67801008 -1 -2.1190482 -0.57499502 -1 -2.1118612 -1.4534853 --1 -2.1093121 0.19263531 -1 -2.1061624 -1.5086741 -1 -2.0970666 -1.056122 -1 -2.095629 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1.4719528 -1 2.8133603 1.3016674 - diff --git a/GPy/util/datasets/column_2C b/GPy/util/datasets/column_2C deleted file mode 100644 index 40e55342..00000000 --- a/GPy/util/datasets/column_2C +++ /dev/null @@ -1,310 +0,0 @@ -63.03 22.55 39.61 40.48 98.67 -0.25 1 -39.06 10.06 25.02 29 114.41 4.56 1 -68.83 22.22 50.09 46.61 105.99 -3.53 1 -69.3 24.65 44.31 44.64 101.87 11.21 1 -49.71 9.65 28.32 40.06 108.17 7.92 1 -40.25 13.92 25.12 26.33 130.33 2.23 1 -53.43 15.86 37.17 37.57 120.57 5.99 1 -45.37 10.76 29.04 34.61 117.27 -10.68 1 -43.79 13.53 42.69 30.26 125 13.29 1 -36.69 5.01 41.95 31.68 84.24 0.66 1 -49.71 13.04 31.33 36.67 108.65 -7.83 1 -31.23 17.72 15.5 13.52 120.06 0.5 1 -48.92 19.96 40.26 28.95 119.32 8.03 1 -53.57 20.46 33.1 33.11 110.97 7.04 1 -57.3 24.19 47 33.11 116.81 5.77 1 -44.32 12.54 36.1 31.78 124.12 5.42 1 -63.83 20.36 54.55 43.47 112.31 -0.62 1 -31.28 3.14 32.56 28.13 129.01 3.62 1 -38.7 13.44 31 25.25 123.16 1.43 1 -41.73 12.25 30.12 29.48 116.59 -1.24 1 -43.92 14.18 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114.37 -0.42 -1 -61.45 22.69 46.17 38.75 125.67 -2.71 -1 -45.25 8.69 41.58 36.56 118.55 0.21 -1 -33.84 5.07 36.64 28.77 123.95 -0.2 -1 diff --git a/GPy/util/datasets/connections.txt b/GPy/util/datasets/connections.txt deleted file mode 100644 index e1886100..00000000 --- a/GPy/util/datasets/connections.txt +++ /dev/null @@ -1,22 +0,0 @@ -LFHD, RFHD -RFHD, RBHD -RBHD, LBHD -LBHD, LFHD -LELB, LWRB -LWRB, LFIN -LELB, LSHO -LSHO, RSHO -RSHO, STRN -LSHO, STRN -RSHO, RELB -RELB, RWRB -RWRB, RFIN -LSHO, LFWT -RSHO, RFWT -LFWT, RFWT -LFWT, LKNE -RFWT, RKNE -LKNE, LHEE -RKNE, RHEE -RMT5, RHEE -LMT5, LHEE diff --git a/GPy/util/datasets/diabetes.txt b/GPy/util/datasets/diabetes.txt deleted file mode 100644 index aae457f6..00000000 --- a/GPy/util/datasets/diabetes.txt +++ /dev/null @@ -1,769 +0,0 @@ -6,148,72,35,0,33.6,0.627,50,1 -1,85,66,29,0,26.6,0.351,31,0 -8,183,64,0,0,23.3,0.672,32,1 -1,89,66,23,94,28.1,0.167,21,0 -0,137,40,35,168,43.1,2.288,33,1 -5,116,74,0,0,25.6,0.201,30,0 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-3,139,4.2,0.7,4.3,6.3 -3,103,5.1,1.4,1.2,5.0 -3,97,4.7,1.1,2.1,12.6 -3,102,5.3,1.4,1.3,6.7 - diff --git a/GPy/util/debug.py b/GPy/util/debug.py new file mode 100644 index 00000000..00107f5e --- /dev/null +++ b/GPy/util/debug.py @@ -0,0 +1,35 @@ +# Copyright (c) 2012, GPy authors (see AUTHORS.txt). +# Licensed under the BSD 3-clause license (see LICENSE.txt) + +""" +The module for some general debug tools +""" + +import numpy as np + +def checkFinite(arr, name=None): + if name is None: + name = 'Array with ID['+str(id(arr))+']' + + if np.any(np.logical_not(np.isfinite(arr))): + idx = np.where(np.logical_not(np.isfinite(arr)))[0] + print name+' at indices '+str(idx)+' have not finite values: '+str(arr[idx])+'!' + return False + return True + +def checkFullRank(m, tol=1e-10, name=None, force_check=False): + if name is None: + name = 'Matrix with ID['+str(id(m))+']' + assert len(m.shape)==2 and m.shape[0]==m.shape[1], 'The input of checkFullRank has to be a square matrix!' + + if not force_check and m.shape[0]>=10000: + print 'The size of '+name+'is too big to check (>=10000)!' + return True + + s = np.real(np.linalg.eigvals(m)) + + if s.min()/s.max() - -''' -__updated__ = '2013-12-03' +# Copyright (c) 2012, GPy authors (see AUTHORS.txt). +# Licensed under the BSD 3-clause license (see LICENSE.txt) import numpy as np def view(A, offset=0): """ Get a view on the diagonal elements of a 2D array. - - This is actually a view (!) on the diagonal of the array, so you can + + This is actually a view (!) on the diagonal of the array, so you can in-place adjust the view. - + :param :class:`ndarray` A: 2 dimensional numpy array :param int offset: view offset to give back (negative entries allowed) :rtype: :class:`ndarray` view of diag(A) - + >>> import numpy as np >>> X = np.arange(9).reshape(3,3) >>> view(X) @@ -36,7 +31,7 @@ def view(A, offset=0): """ from numpy.lib.stride_tricks import as_strided assert A.ndim == 2, "only implemented for 2 dimensions" - assert A.shape[0] == A.shape[1], "attempting to get the view of non-square matrix?!" + assert A.shape[0] == A.shape[1], "attempting to get the view of non-square matrix?!" if offset > 0: return as_strided(A[0, offset:], shape=(A.shape[0] - offset, ), strides=((A.shape[0]+1)*A.itemsize, )) elif offset < 0: @@ -44,6 +39,12 @@ def view(A, offset=0): else: return as_strided(A, shape=(A.shape[0], ), strides=((A.shape[0]+1)*A.itemsize, )) +def offdiag_view(A, offset=0): + from numpy.lib.stride_tricks import as_strided + assert A.ndim == 2, "only implemented for 2 dimensions" + Af = as_strided(A, shape=(A.size,), strides=(A.itemsize,)) + return as_strided(Af[(1+offset):], shape=(A.shape[0]-1, A.shape[1]), strides=(A.strides[0] + A.itemsize, A.strides[1])) + def _diag_ufunc(A,b,offset,func): dA = view(A, offset); func(dA,b,dA) return A @@ -51,11 +52,11 @@ def _diag_ufunc(A,b,offset,func): def times(A, b, offset=0): """ Times the view of A with b in place (!). - Returns modified A + Returns modified A Broadcasting is allowed, thus b can be scalar. - + if offset is not zero, make sure b is of right shape! - + :param ndarray A: 2 dimensional array :param ndarray-like b: either one dimensional or scalar :param int offset: same as in view. @@ -67,11 +68,11 @@ multiply = times def divide(A, b, offset=0): """ Divide the view of A by b in place (!). - Returns modified A + Returns modified A Broadcasting is allowed, thus b can be scalar. - + if offset is not zero, make sure b is of right shape! - + :param ndarray A: 2 dimensional array :param ndarray-like b: either one dimensional or scalar :param int offset: same as in view. @@ -84,9 +85,9 @@ def add(A, b, offset=0): Add b to the view of A in place (!). Returns modified A. Broadcasting is allowed, thus b can be scalar. - + if offset is not zero, make sure b is of right shape! - + :param ndarray A: 2 dimensional array :param ndarray-like b: either one dimensional or scalar :param int offset: same as in view. @@ -99,16 +100,16 @@ def subtract(A, b, offset=0): Subtract b from the view of A in place (!). Returns modified A. Broadcasting is allowed, thus b can be scalar. - + if offset is not zero, make sure b is of right shape! - + :param ndarray A: 2 dimensional array :param ndarray-like b: either one dimensional or scalar :param int offset: same as in view. :rtype: view of A, which is adjusted inplace """ return _diag_ufunc(A, b, offset, np.subtract) - + if __name__ == '__main__': import doctest - doctest.testmod() \ No newline at end of file + doctest.testmod() diff --git a/GPy/util/football_teams.json b/GPy/util/football_teams.json new file mode 100644 index 00000000..a4eb9c38 --- /dev/null +++ b/GPy/util/football_teams.json @@ -0,0 +1 @@ +{"Canvey Island": 94, "Crewe": 21, "Fleetwood Town": 134, "Wrexham": 89, "Barnet": 69, "Ipswich": 29, "Rochdale": 84, "Bristol Rvs": 70, "Liverpool": 10, "Chelsea": 20, "York": 113, "Newcastle": 18, "QPR": 28, "Middlesboro": 116, "Tranmere": 68, "Bury": 72, "Luton": 24, "AFC Wimbledon": 126, "West Ham": 15, "Braintree Town": 135, "Bournemouth": 58, "Hayes & Yeading": 130, "Rushden & D": 81, "Weymouth": 120, "Chesterfield": 48, "Exeter": 104, "Barnsley": 45, "Aldershot": 95, "Gateshead": 129, "Hartlepool": 55, "Newport County": 132, "Crystal Palace": 23, "Ebbsfleet": 123, "Wigan": 19, "Shrewsbury": 83, "Hereford": 105, "Stevenage": 111, "Grimsby": 73, "Crawley Town": 114, "Morecambe": 109, "Oldham": 61, "Aston Villa": 1, "Bristol City": 51, "Gravesend": 103, "Huddersfield": 60, "Reading": 33, "Nuneaton Town": 140, "AFC Telford United": 137, "Wycombe": 91, "Leeds": 43, "Colchester": 54, "Rotherham": 63, "Southport": 100, "Southampton": 37, "Darlington": 82, "Blackburn": 16, "Bath City": 133, "Yeovil": 62, "Leyton Orient": 75, "Forest Green": 101, "Chester": 80, "Halifax": 110, "Portsmouth": 11, "Woking": 108, "Histon": 125, "Man City": 7, "Northampton": 78, "Arsenal": 17, "Charlton": 14, "Middlesbrough": 9, "Watford": 41, "Nott'm Forest": 59, "Eastbourne Borough": 131, "Hull": 27, "Barrow": 127, "Doncaster": 52, "Carlisle": 92, "Gillingham": 53, "Accrington": 93, "Dartford": 139, "Altrincham": 112, "Scarborough": 106, "Northwich": 117, "Farsley": 124, "Tamworth": 96, "St. Albans": 119, "Alfreton Town": 136, "Mansfield": 86, "Macclesfield": 76, "Torquay": 87, "Brighton": 26, "Bradford": 56, "Lincoln": 77, "Brentford": 49, "Everton": 3, "Cambridge": 102, "Sheffield United": 35, "Stockport": 85, "Bolton": 2, "Southend": 65, "Cheltenham": 71, "Walsall": 64, "Preston": 42, "Peterboro": 79, "Birmingham": 6, "Boston": 90, "Burton": 97, "West Brom": 8, "Man United": 4, "Stafford Rangers": 118, "Wimbledon": 115, "Scunthorpe": 50, "Kidderminster": 107, "Millwall": 44, "Swansea": 67, "Norwich": 31, "Burnley": 22, "Sunderland": 13, "Sheffield Weds": 40, "Fulham": 5, "Dag and Red": 99, "Oxford": 74, "Stoke": 39, "Tottenham": 12, "Kettering Town": 128, "Coventry": 32, "Wolves": 38, "Port Vale": 66, "Milton Keynes Dons": 57, "Plymouth": 34, "Derby": 25, "Notts County": 88, "Leicester": 36, "Droylsden": 121, "Blackpool": 47, "Salisbury": 122, "Cardiff": 30, "Grays": 98, "Swindon": 46, "Hyde United": 138} \ No newline at end of file diff --git a/GPy/util/functions.py b/GPy/util/functions.py new file mode 100644 index 00000000..be024aeb --- /dev/null +++ b/GPy/util/functions.py @@ -0,0 +1,27 @@ +# Copyright (c) 2012, GPy authors (see AUTHORS.txt). +# Licensed under the BSD 3-clause license (see LICENSE.txt) +import numpy as np +from scipy.special import erf, erfc, erfcx +import sys +epsilon = sys.float_info.epsilon +lim_val = -np.log(epsilon) + +def logisticln(x): + return np.where(x-lim_val, -np.log(1+np.exp(-x)), -x), -np.log(1+epsilon)) + +def logistic(x): + return np.where(x-lim_val, 1/(1+np.exp(-x)), epsilon/(epsilon+1)), 1/(1+epsilon)) + +def normcdf(x): + g=0.5*erfc(-x/np.sqrt(2)) + return np.where(g==0, epsilon, np.where(g==1, 1-epsilon, g)) + +def normcdfln(x): + return np.where(x < 0, -.5*x*x + np.log(.5) + np.log(erfcx(-x/np.sqrt(2))), np.log(normcdf(x))) + +def clip_exp(x): + return np.where(x-lim_val, np.exp(x), epsilon), 1/epsilon) + +def differfln(x0, x1): + # this is a, hopefully!, a numerically more stable variant of log(erf(x0)-erf(x1)) = log(erfc(x1)-erfc(x0)). + return np.where(x0>x1, -x1*x1 + np.log(erfcx(x1)-np.exp(-x0**2+x1**2)*erfcx(x0)), -x0*x0 + np.log(np.exp(-x1**2+x0**2)*erfcx(x1) - erfcx(x0))) diff --git a/GPy/util/gpu_init.py b/GPy/util/gpu_init.py new file mode 100644 index 00000000..b6a4a164 --- /dev/null +++ b/GPy/util/gpu_init.py @@ -0,0 +1,48 @@ +""" +The package for scikits.cuda initialization + +Global variables: initSuccess +providing CUBLAS handle: cublas_handle +""" + +gpu_initialized = False +gpu_device = None +gpu_context = None +MPI_enabled = False + +try: + from mpi4py import MPI + MPI_enabled = True +except: + pass + +try: + if MPI_enabled and MPI.COMM_WORLD.size>1: + from .parallel import get_id_within_node + gpuid = get_id_within_node() + import pycuda.driver + pycuda.driver.init() + if gpuid>=pycuda.driver.Device.count(): + print '['+MPI.Get_processor_name()+'] more processes than the GPU numbers!' + #MPI.COMM_WORLD.Abort() + raise + gpu_device = pycuda.driver.Device(gpuid) + gpu_context = gpu_device.make_context() + gpu_initialized = True + else: + import pycuda.autoinit + gpu_initialized = True +except: + pass + +try: + from scikits.cuda import cublas + import scikits.cuda.linalg as culinalg + culinalg.init() + cublas_handle = cublas.cublasCreate() +except: + pass + +def closeGPU(): + if gpu_context is not None: + gpu_context.detach() diff --git a/GPy/util/initialization.py b/GPy/util/initialization.py new file mode 100644 index 00000000..1cf9e846 --- /dev/null +++ b/GPy/util/initialization.py @@ -0,0 +1,23 @@ +''' +Created on 24 Feb 2014 + +@author: maxz +''' + +import numpy as np +from GPy.util.pca import PCA + +def initialize_latent(init, input_dim, Y): + Xr = np.asfortranarray(np.random.randn(Y.shape[0], input_dim)) + if init == 'PCA': + p = PCA(Y) + PC = p.project(Y, min(input_dim, Y.shape[1])) + Xr[:PC.shape[0], :PC.shape[1]] = PC + var = .1*p.fracs[:input_dim] + else: + var = Xr.var(0) + + Xr -= Xr.mean(0) + Xr /= Xr.std(0) + + return Xr, var/var.max() diff --git a/GPy/util/linalg.py b/GPy/util/linalg.py index 842178e2..dffd438a 100644 --- a/GPy/util/linalg.py +++ b/GPy/util/linalg.py @@ -10,60 +10,174 @@ from scipy import linalg, weave import types import ctypes from ctypes import byref, c_char, c_int, c_double # TODO -# import scipy.lib.lapack import scipy import warnings +import os +from config import config +import logging -if np.all(np.float64((scipy.__version__).split('.')[:2]) >= np.array([0, 12])): - import scipy.linalg.lapack as lapack +_scipyversion = np.float64((scipy.__version__).split('.')[:2]) +_fix_dpotri_scipy_bug = True +if np.all(_scipyversion >= np.array([0, 14])): + from scipy.linalg import lapack + _fix_dpotri_scipy_bug = False +elif np.all(_scipyversion >= np.array([0, 12])): + #import scipy.linalg.lapack.clapack as lapack + from scipy.linalg import lapack else: from scipy.linalg.lapack import flapack as lapack -try: - _blaslib = ctypes.cdll.LoadLibrary(np.core._dotblas.__file__) # @UndefinedVariable - _blas_available = True - assert hasattr(_blaslib, 'dsyrk_') - assert hasattr(_blaslib, 'dsyr_') -except AssertionError: - _blas_available = False -except AttributeError as e: - _blas_available = False - warnings.warn("warning: caught this exception:" + str(e)) +if config.getboolean('anaconda', 'installed') and config.getboolean('anaconda', 'MKL'): + try: + anaconda_path = str(config.get('anaconda', 'location')) + mkl_rt = ctypes.cdll.LoadLibrary(os.path.join(anaconda_path, 'DLLs', 'mkl_rt.dll')) + dsyrk = mkl_rt.dsyrk + dsyr = mkl_rt.dsyr + _blas_available = True + print 'anaconda installed and mkl is loaded' + except: + _blas_available = False +else: + try: + _blaslib = ctypes.cdll.LoadLibrary(np.core._dotblas.__file__) # @UndefinedVariable + dsyrk = _blaslib.dsyrk_ + dsyr = _blaslib.dsyr_ + _blas_available = True + except AttributeError as e: + _blas_available = False + warnings.warn("warning: caught this exception:" + str(e)) -def dtrtrs(A, B, lower=0, trans=0, unitdiag=0): +def force_F_ordered_symmetric(A): + """ + return a F ordered version of A, assuming A is symmetric + """ + if A.flags['F_CONTIGUOUS']: + return A + if A.flags['C_CONTIGUOUS']: + return A.T + else: + return np.asfortranarray(A) + +def force_F_ordered(A): + """ + return a F ordered version of A, assuming A is triangular + """ + if A.flags['F_CONTIGUOUS']: + return A + print "why are your arrays not F order?" + return np.asfortranarray(A) + +# def jitchol(A, maxtries=5): +# A = force_F_ordered_symmetric(A) +# L, info = lapack.dpotrf(A, lower=1) +# if info == 0: +# return L +# else: +# if maxtries==0: +# raise linalg.LinAlgError, "not positive definite, even with jitter." +# diagA = np.diag(A) +# if np.any(diagA <= 0.): +# raise linalg.LinAlgError, "not pd: non-positive diagonal elements" +# jitter = diagA.mean() * 1e-6 + +# return jitchol(A+np.eye(A.shape[0])*jitter, maxtries-1) + +def jitchol(A, maxtries=5): + A = np.ascontiguousarray(A) + L, info = lapack.dpotrf(A, lower=1) + if info == 0: + return L + else: + diagA = np.diag(A) + if np.any(diagA <= 0.): + raise linalg.LinAlgError, "not pd: non-positive diagonal elements" + jitter = diagA.mean() * 1e-6 + while maxtries > 0 and np.isfinite(jitter): + try: + L = linalg.cholesky(A + np.eye(A.shape[0]) * jitter, lower=True) + except: + jitter *= 10 + finally: + maxtries -= 1 + raise linalg.LinAlgError, "not positive definite, even with jitter." + import traceback + try: raise + except: + logging.warning('\n'.join(['Added jitter of {:.10e}'.format(jitter), + ' in '+traceback.format_list(traceback.extract_stack(limit=2)[-2:-1])[0][2:]])) + import ipdb;ipdb.set_trace() + return L + + + + + +# def dtrtri(L, lower=1): +# """ +# Wrapper for lapack dtrtri function +# Inverse of L +# +# :param L: Triangular Matrix L +# :param lower: is matrix lower (true) or upper (false) +# :returns: Li, info +# """ +# L = force_F_ordered(L) +# return lapack.dtrtri(L, lower=lower) + +def dtrtrs(A, B, lower=1, trans=0, unitdiag=0): """ Wrapper for lapack dtrtrs function - :param A: Matrix A + DTRTRS solves a triangular system of the form + + A * X = B or A**T * X = B, + + where A is a triangular matrix of order N, and B is an N-by-NRHS + matrix. A check is made to verify that A is nonsingular. + + :param A: Matrix A(triangular) :param B: Matrix B :param lower: is matrix lower (true) or upper (false) - :returns: + :returns: Solution to A * X = B or A**T * X = B """ + A = np.asfortranarray(A) + #Note: B does not seem to need to be F ordered! return lapack.dtrtrs(A, B, lower=lower, trans=trans, unitdiag=unitdiag) -def dpotrs(A, B, lower=0): +def dpotrs(A, B, lower=1): """ Wrapper for lapack dpotrs function - :param A: Matrix A :param B: Matrix B :param lower: is matrix lower (true) or upper (false) :returns: - """ + A = force_F_ordered(A) return lapack.dpotrs(A, B, lower=lower) -def dpotri(A, lower=0): +def dpotri(A, lower=1): """ Wrapper for lapack dpotri function + DPOTRI - compute the inverse of a real symmetric positive + definite matrix A using the Cholesky factorization A = + U**T*U or A = L*L**T computed by DPOTRF + :param A: Matrix A :param lower: is matrix lower (true) or upper (false) :returns: A inverse """ - return lapack.dpotri(A, lower=lower) + if _fix_dpotri_scipy_bug: + assert lower==1, "scipy linalg behaviour is very weird. please use lower, fortran ordered arrays" + lower = 0 + + A = force_F_ordered(A) + R, info = lapack.dpotri(A, lower=lower) #needs to be zero here, seems to be a scipy bug + + symmetrify(R) + return R, info def pddet(A): """ @@ -111,60 +225,8 @@ def _mdot_r(a, b): b = b[0] return np.dot(a, b) -def jitchol(A, maxtries=5): - A = np.asfortranarray(A) - L, info = lapack.dpotrf(A, lower=1) - if info == 0: - return L - else: - diagA = np.diag(A) - if np.any(diagA <= 0.): - raise linalg.LinAlgError, "not pd: non-positive diagonal elements" - jitter = diagA.mean() * 1e-6 - while maxtries > 0 and np.isfinite(jitter): - print 'Warning: adding jitter of {:.10e}'.format(jitter) - try: - return linalg.cholesky(A + np.eye(A.shape[0]).T * jitter, lower=True) - except: - jitter *= 10 - finally: - maxtries -= 1 - raise linalg.LinAlgError, "not positive definite, even with jitter." - - - -def jitchol_old(A, maxtries=5): - """ - :param A: An almost pd square matrix - - :rval L: the Cholesky decomposition of A - - .. note: - - Adds jitter to K, to enforce positive-definiteness - if stuff breaks, please check: - np.allclose(sp.linalg.cholesky(XXT, lower = True), np.triu(sp.linalg.cho_factor(XXT)[0]).T) - - """ - try: - return linalg.cholesky(A, lower=True) - except linalg.LinAlgError: - diagA = np.diag(A) - if np.any(diagA < 0.): - raise linalg.LinAlgError, "not pd: negative diagonal elements" - jitter = diagA.mean() * 1e-6 - for i in range(1, maxtries + 1): - print '\rWarning: adding jitter of {:.10e} '.format(jitter), - try: - return linalg.cholesky(A + np.eye(A.shape[0]).T * jitter, lower=True) - except: - jitter *= 10 - - raise linalg.LinAlgError, "not positive definite, even with jitter." - def pdinv(A, *args): """ - :param A: A DxD pd numpy array :rval Ai: the inverse of A @@ -179,15 +241,15 @@ def pdinv(A, *args): """ L = jitchol(A, *args) logdet = 2.*np.sum(np.log(np.diag(L))) - Li = chol_inv(L) - Ai, _ = lapack.dpotri(L) + Li = dtrtri(L) + Ai, _ = dpotri(L, lower=1) # Ai = np.tril(Ai) + np.tril(Ai,-1).T symmetrify(Ai) return Ai, L, Li, logdet -def chol_inv(L): +def dtrtri(L): """ Inverts a Cholesky lower triangular matrix @@ -196,7 +258,8 @@ def chol_inv(L): """ - return lapack.dtrtri(L, lower=True)[0] + L = force_F_ordered(L) + return lapack.dtrtri(L, lower=1)[0] def multiple_pdinv(A): @@ -212,7 +275,7 @@ def multiple_pdinv(A): N = A.shape[-1] chols = [jitchol(A[:, :, i]) for i in range(N)] halflogdets = [np.sum(np.log(np.diag(L[0]))) for L in chols] - invs = [lapack.dpotri(L[0], True)[0] for L in chols] + invs = [dpotri(L[0], True)[0] for L in chols] invs = [np.triu(I) + np.triu(I, 1).T for I in invs] return np.dstack(invs), np.array(halflogdets) @@ -265,101 +328,6 @@ def ppca(Y, Q, iterations=100): pass return np.asarray_chkfinite(exp_x), np.asarray_chkfinite(W) -def ppca_missing_data_at_random(Y, Q, iters=100): - """ - EM implementation of Probabilistic pca for when there is missing data. - - Taken from - - .. math: - \\mathbf{Y} = \mathbf{XW} + \\epsilon \\text{, where} - \\epsilon = \\mathcal{N}(0, \\sigma^2 \mathbf{I}) - - :returns: X, W, sigma^2 - """ - from numpy.ma import dot as madot - import diag - from GPy.util.subarray_and_sorting import common_subarrays - import time - debug = 1 - # Initialise W randomly - N, D = Y.shape - W = np.random.randn(Q, D) * 1e-3 - Y = np.ma.masked_invalid(Y, copy=1) - nu = 1. - #num_obs_i = 1./Y.count() - Ycentered = Y - Y.mean(0) - - X = np.zeros((N,Q)) - cs = common_subarrays(Y.mask) - cr = common_subarrays(Y.mask, 1) - Sigma = np.zeros((N, Q, Q)) - Sigma2 = np.zeros((N, Q, Q)) - mu = np.zeros(D) - if debug: - import matplotlib.pyplot as pylab - fig = pylab.figure("FIT MISSING DATA"); - ax = fig.gca() - ax.cla() - lines = pylab.plot(np.zeros((N,Q)).dot(W)) - W2 = np.zeros((Q,D)) - - for i in range(iters): -# Sigma = np.linalg.solve(diag.add(madot(W,W.T), nu), diag.times(np.eye(Q),nu)) -# exp_x = madot(madot(Ycentered, W.T),Sigma)/nu -# Ycentered = (Y - exp_x.dot(W).mean(0)) -# #import ipdb;ipdb.set_trace() -# #Ycentered = mu -# W = np.linalg.solve(madot(exp_x.T,exp_x) + Sigma, madot(exp_x.T, Ycentered)) -# nu = (((Ycentered - madot(exp_x, W))**2).sum(0) + madot(W.T,madot(Sigma,W)).sum(0)).sum()/N - for csi, (mask, index) in enumerate(cs.iteritems()): - mask = ~np.array(mask) - Sigma2[index, :, :] = nu * np.linalg.inv(diag.add(W2[:,mask].dot(W2[:,mask].T), nu)) - #X[index,:] = madot((Sigma[csi]/nu),madot(W,Ycentered[index].T))[:,0] - X2 = ((Sigma2/nu) * (madot(Ycentered,W2.T).base)[:,:,None]).sum(-1) - mu2 = (Y - X.dot(W)).mean(0) - for n in range(N): - Sigma[n] = nu * np.linalg.inv(diag.add(W[:,~Y.mask[n]].dot(W[:,~Y.mask[n]].T), nu)) - X[n, :] = (Sigma[n]/nu).dot(W[:,~Y.mask[n]].dot(Ycentered[n,~Y.mask[n]].T)) - for d in range(D): - mu[d] = (Y[~Y.mask[:,d], d] - X[~Y.mask[:,d]].dot(W[:, d])).mean() - Ycentered = (Y - mu) - nu3 = 0. - for cri, (mask, index) in enumerate(cr.iteritems()): - mask = ~np.array(mask) - W2[:,index] = np.linalg.solve(X[mask].T.dot(X[mask]) + Sigma[mask].sum(0), madot(X[mask].T, Ycentered[mask,index]))[:,None] - W2[:,index] = np.linalg.solve(X.T.dot(X) + Sigma.sum(0), madot(X.T, Ycentered[:,index])) - #nu += (((Ycentered[mask,index] - X[mask].dot(W[:,index]))**2).sum(0) + W[:,index].T.dot(Sigma[mask].sum(0).dot(W[:,index])).sum(0)).sum() - nu3 += (((Ycentered[index] - X.dot(W[:,index]))**2).sum(0) + W[:,index].T.dot(Sigma.sum(0).dot(W[:,index])).sum(0)).sum() - nu3 /= N - nu = 0. - nu2 = 0. - W = np.zeros((Q,D)) - for j in range(D): - W[:,j] = np.linalg.solve(X[~Y.mask[:,j]].T.dot(X[~Y.mask[:,j]]) + Sigma[~Y.mask[:,j]].sum(0), madot(X[~Y.mask[:,j]].T, Ycentered[~Y.mask[:,j],j])) - nu2f = np.tensordot(W[:,j].T, Sigma[~Y.mask[:,j],:,:], [0,1]).dot(W[:,j]) - nu2s = W[:,j].T.dot(Sigma[~Y.mask[:,j],:,:].sum(0).dot(W[:,j])) - nu2 += (((Ycentered[~Y.mask[:,j],j] - X[~Y.mask[:,j],:].dot(W[:,j]))**2) + nu2f).sum() - for i in range(N): - if not Y.mask[i,j]: - nu += ((Ycentered[i,j] - X[i,:].dot(W[:,j]))**2) + W[:,j].T.dot(Sigma[i,:,:].dot(W[:,j])) - nu /= N - nu2 /= N - nu4 = (((Ycentered - X.dot(W))**2).sum(0) + W.T.dot(Sigma.sum(0).dot(W)).sum(0)).sum()/N - import ipdb;ipdb.set_trace() - if debug: - #print Sigma[0] - print "nu:", nu, "sum(X):", X.sum() - pred_y = X.dot(W) - for x, l in zip(pred_y.T, lines): - l.set_ydata(x) - ax.autoscale_view() - ax.set_ylim(pred_y.min(), pred_y.max()) - fig.canvas.draw() - time.sleep(.3) - return np.asarray_chkfinite(X), np.asarray_chkfinite(W), nu - - def tdot_numpy(mat, out=None): return np.dot(mat, mat.T, out) @@ -394,12 +362,13 @@ def tdot_blas(mat, out=None): BETA = c_double(0.0) C = out.ctypes.data_as(ctypes.c_void_p) LDC = c_int(np.max(out.strides) / 8) - _blaslib.dsyrk_(byref(UPLO), byref(TRANS), byref(N), byref(K), + dsyrk(byref(UPLO), byref(TRANS), byref(N), byref(K), byref(ALPHA), A, byref(LDA), byref(BETA), C, byref(LDC)) symmetrify(out, upper=True) - return out + + return np.ascontiguousarray(out) def tdot(*args, **kwargs): if _blas_available: @@ -424,7 +393,7 @@ def DSYR_blas(A, x, alpha=1.): A_ = A.ctypes.data_as(ctypes.c_void_p) x_ = x.ctypes.data_as(ctypes.c_void_p) INCX = c_int(1) - _blaslib.dsyr_(byref(UPLO), byref(N), byref(ALPHA), + dsyr(byref(UPLO), byref(N), byref(ALPHA), x_, byref(INCX), A_, byref(LDA)) symmetrify(A, upper=True) @@ -452,10 +421,31 @@ def symmetrify(A, upper=False): Take the square matrix A and make it symmetrical by copting elements from the lower half to the upper works IN PLACE. + + note: tries to use weave, falls back to a slower numpy version + """ + if config.getboolean('weave', 'working'): + try: + symmetrify_weave(A, upper) + except: + print "\n Weave compilation failed. Falling back to (slower) numpy implementation\n" + config.set('weave', 'working', 'False') + symmetrify_numpy(A, upper) + else: + symmetrify_numpy(A, upper) + + +def symmetrify_weave(A, upper=False): + """ + Take the square matrix A and make it symmetrical by copting elements from the lower half to the upper + + works IN PLACE. + + """ N, M = A.shape assert N == M - + c_contig_code = """ int iN; for (int i=1; inab',m1,m2) a=dim1, b=dim2 ) + join_prod = ElementwiseKernel("double *out, double *m1, double *m2, int dim1, int dim2", "out[i] = m1[(i%dim1)*dim1+(i%(dim1*dim2))/dim1]*m2[(i%dim1)*dim1+i/(dim1*dim2)]", "join_prod") + +except: + pass + +try: + import scikits.cuda.linalg as culinalg + from scikits.cuda import cublas + from scikits.cuda.cula import culaExceptions +except: + pass + + + diff --git a/GPy/util/misc.py b/GPy/util/misc.py index 2b825597..bf37159d 100644 --- a/GPy/util/misc.py +++ b/GPy/util/misc.py @@ -2,7 +2,6 @@ # Licensed under the BSD 3-clause license (see LICENSE.txt) import numpy as np -from scipy import weave from config import * def chain_1(df_dg, dg_dx): @@ -84,146 +83,16 @@ def kmm_init(X, m = 10): inducing = np.array(inducing) return X[inducing] -def fast_array_equal(A, B): - - if config.getboolean('parallel', 'openmp'): - pragma_string = '#pragma omp parallel for private(i, j)' - else: - pragma_string = '' - - code2=""" - int i, j; - return_val = 1; - - %s - for(i=0;i - """ % pragma_string - - - weave_options_openmp = {'headers' : [''], - 'extra_compile_args': ['-fopenmp -O3'], - 'extra_link_args' : ['-lgomp'], - 'libraries': ['gomp']} - weave_options_noopenmp = {'extra_compile_args': ['-O3']} - - if config.getboolean('parallel', 'openmp'): - weave_options = weave_options_openmp - else: - weave_options = weave_options_noopenmp - - value = False - - - if (A == None) and (B == None): - return True - elif ((A == None) and (B != None)) or ((A != None) and (B == None)): - return False - elif A.shape == B.shape: - if A.ndim == 2: - N, D = [int(i) for i in A.shape] - value = weave.inline(code2, support_code=support_code, - arg_names=['A', 'B', 'N', 'D'], - type_converters=weave.converters.blitz, **weave_options) - elif A.ndim == 3: - N, D, Q = [int(i) for i in A.shape] - value = weave.inline(code3, support_code=support_code, - arg_names=['A', 'B', 'N', 'D', 'Q'], - type_converters=weave.converters.blitz, **weave_options) - else: - value = np.array_equal(A,B) - - return value - -def fast_array_equal2(A, B): - if (A == None) and (B == None): - return True - elif ((A == None) and (B != None)) or ((A != None) and (B == None)): - return False - elif not (A.shape == B.shape): - return False - - if config.getboolean('parallel', 'openmp'): - pragma_string = '#include ' - weave_options = {'headers' : [''], - 'extra_compile_args': ['-fopenmp -O3'], - 'extra_link_args' : ['-lgomp'], - 'libraries' : ['gomp']} - else: - weave_options = {'extra_compile_args': ['-O3']} - pragma_string = '' - - support_code = """ - %s - #include - """ % pragma_string - - code = """ - int i; - return_val = 1; - - %s - for(i=0;i 0, "At least one parameter needed" + if len(param) == 1: + return param[0].view(np.ndarray) + return [x.view(np.ndarray) for x in param] diff --git a/GPy/util/multioutput.py b/GPy/util/multioutput.py index a57593a7..cc9af29e 100644 --- a/GPy/util/multioutput.py +++ b/GPy/util/multioutput.py @@ -1,35 +1,100 @@ import numpy as np import warnings -from .. import kern +import GPy -def build_lcm(input_dim, num_outputs, CK = [], NC = [], W_columns=1,W=None,kappa=None): - #TODO build_icm or build_lcm + +def get_slices(input_list): + num_outputs = len(input_list) + _s = [0] + [ _x.shape[0] for _x in input_list ] + _s = np.cumsum(_s) + slices = [slice(a,b) for a,b in zip(_s[:-1],_s[1:])] + return slices + +def build_XY(input_list,output_list=None,index=None): + num_outputs = len(input_list) + if output_list is not None: + assert num_outputs == len(output_list) + Y = np.vstack(output_list) + else: + Y = None + + if index is not None: + assert len(index) == num_outputs + I = np.hstack( [np.repeat(j,_x.shape[0]) for _x,j in zip(input_list,index)] ) + else: + I = np.hstack( [np.repeat(j,_x.shape[0]) for _x,j in zip(input_list,range(num_outputs))] ) + + X = np.vstack(input_list) + X = np.hstack([X,I[:,None]]) + + return X,Y,I[:,None]#slices + +def build_likelihood(Y_list,noise_index,likelihoods_list=None): + Ny = len(Y_list) + if likelihoods_list is None: + likelihoods_list = [GPy.likelihoods.Gaussian(name="Gaussian_noise_%s" %j) for y,j in zip(Y_list,range(Ny))] + else: + assert len(likelihoods_list) == Ny + #likelihood = GPy.likelihoods.mixed_noise.MixedNoise(likelihoods_list=likelihoods_list, noise_index=noise_index) + likelihood = GPy.likelihoods.mixed_noise.MixedNoise(likelihoods_list=likelihoods_list) + return likelihood + + +def ICM(input_dim, num_outputs, kernel, W_rank=1,W=None,kappa=None,name='ICM'): """ - Builds a kernel for a linear coregionalization model + Builds a kernel for an Intrinsic Coregionalization Model + + :input_dim: Input dimensionality (does not include dimension of indices) + :num_outputs: Number of outputs + :param kernel: kernel that will be multiplied by the coregionalize kernel (matrix B). + :type kernel: a GPy kernel + :param W_rank: number tuples of the corregionalization parameters 'W' + :type W_rank: integer + """ + if kernel.input_dim <> input_dim: + kernel.input_dim = input_dim + warnings.warn("kernel's input dimension overwritten to fit input_dim parameter.") + + K = kernel.prod(GPy.kern.Coregionalize(1, num_outputs, active_dims=[input_dim], rank=W_rank,W=W,kappa=kappa,name='B'),name=name) + return K + + +def LCM(input_dim, num_outputs, kernels_list, W_rank=1,name='ICM'): + """ + Builds a kernel for an Linear Coregionalization Model + + :input_dim: Input dimensionality (does not include dimension of indices) + :num_outputs: Number of outputs + :param kernel: kernel that will be multiplied by the coregionalize kernel (matrix B). + :type kernel: a GPy kernel + :param W_rank: number tuples of the corregionalization parameters 'W' + :type W_rank: integer + """ + Nk = len(kernels_list) + K = ICM(input_dim,num_outputs,kernels_list[0],W_rank,name='%s%s' %(name,0)) + j = 1 + for kernel in kernels_list[1:]: + K += ICM(input_dim,num_outputs,kernel,W_rank,name='%s%s' %(name,j)) + j += 1 + return K + + +def Private(input_dim, num_outputs, kernel, output, kappa=None,name='X'): + """ + Builds a kernel for an Intrinsic Coregionalization Model :input_dim: Input dimensionality :num_outputs: Number of outputs - :param CK: List of coregionalized kernels (i.e., this will be multiplied by a coregionalize kernel). - :param K: List of kernels that will be added up together with CK, but won't be multiplied by a coregionalize kernel - :param W_columns: number tuples of the corregionalization parameters 'coregion_W' - :type W_columns: integer + :param kernel: kernel that will be multiplied by the coregionalize kernel (matrix B). + :type kernel: a GPy kernel + :param W_rank: number tuples of the corregionalization parameters 'W' + :type W_rank: integer """ - - for k in CK: - if k.input_dim <> input_dim: - k.input_dim = input_dim - warnings.warn("kernel's input dimension overwritten to fit input_dim parameter.") - - for k in NC: - if k.input_dim <> input_dim + 1: - k.input_dim = input_dim + 1 - warnings.warn("kernel's input dimension overwritten to fit input_dim parameter.") - - kernel = CK[0].prod(kern.coregionalize(num_outputs,W_columns,W,kappa),tensor=True) - for k in CK[1:]: - k_coreg = kern.coregionalize(num_outputs,W_columns,W,kappa) - kernel += k.prod(k_coreg,tensor=True) - for k in NC: - kernel += k - - return kernel + K = ICM(input_dim,num_outputs,kernel,W_rank=1,kappa=kappa,name=name) + K.B.W.fix(0) + _range = range(num_outputs) + _range.pop(output) + for j in _range: + K.B.kappa[j] = 0 + K.B.kappa[j].fix() + return K diff --git a/GPy/util/normalizer.py b/GPy/util/normalizer.py new file mode 100644 index 00000000..854726c4 --- /dev/null +++ b/GPy/util/normalizer.py @@ -0,0 +1,45 @@ +''' +Created on Aug 27, 2014 + +@author: t-mazwie +''' +import logging +import numpy as np + +class Norm(object): + def __init__(self): + pass + def scale_by(self, Y): + """ + Use data matrix Y as normalization space to work in. + """ + raise NotImplementedError + def normalize(self, Y): + """ + Project Y into normalized space + """ + raise NotImplementedError + def inverse_mean(self, X): + """ + Project the normalized object X into space of Y + """ + raise NotImplementedError + def inverse_variance(self, var): + return var + def scaled(self): + """ + Whether this Norm object has been initialized. + """ + raise NotImplementedError +class MeanNorm(Norm): + def __init__(self): + self.mean = None + def scale_by(self, Y): + Y = np.ma.masked_invalid(Y, copy=False) + self.mean = Y.mean(0).view(np.ndarray) + def normalize(self, Y): + return Y-self.mean + def inverse_mean(self, X): + return X+self.mean + def scaled(self): + return self.mean is not None diff --git a/GPy/util/parallel.py b/GPy/util/parallel.py new file mode 100644 index 00000000..fab43936 --- /dev/null +++ b/GPy/util/parallel.py @@ -0,0 +1,41 @@ +""" +The module of tools for parallelization (MPI) +""" +import numpy as np +try: + from mpi4py import MPI + def get_id_within_node(comm=MPI.COMM_WORLD): + rank = comm.rank + nodename = MPI.Get_processor_name() + nodelist = comm.allgather(nodename) + return len([i for i in nodelist[:rank] if i==nodename]) + + numpy_to_MPI_typemap = { + np.dtype(np.float64) : MPI.DOUBLE, + np.dtype(np.float32) : MPI.FLOAT, + np.dtype(np.int) : MPI.INT, + np.dtype(np.int8) : MPI.CHAR, + np.dtype(np.uint8) : MPI.UNSIGNED_CHAR, + np.dtype(np.int32) : MPI.INT, + np.dtype(np.uint32) : MPI.UNSIGNED_INT, + } +except: + pass + +def divide_data(datanum, rank, size): + assert rank0 + + residue = (datanum)%size + datanum_list = np.empty((size),dtype=np.int32) + for i in xrange(size): + if i= X.shape[1]: + # print "N >= D: using primal" + self.eigvals, self.eigvectors = self._primal_eig(X) + else: + # print "N < D: using dual" + self.eigvals, self.eigvectors = self._dual_eig(X) + self.sort = numpy.argsort(self.eigvals)[::-1] + self.eigvals = self.eigvals[self.sort] + self.eigvectors = self.eigvectors[:, self.sort] + self.fracs = self.eigvals / self.eigvals.sum() + self.Q = self.eigvals.shape[0] + + def center(self, X): + """ + Center `X` in PCA space. + """ + X = X.copy() + inan = numpy.isnan(X) + if self.mu is None: + X_ = numpy.ma.masked_array(X, inan) + self.mu = X_.mean(0).base + self.sigma = X_.std(0).base + reduce(lambda y,x: setitem(x[0], x[1], x[2]), itertools.izip(X.T, inan.T, self.mu), None) + X = X - self.mu + X = X / numpy.where(self.sigma == 0, 1e-30, self.sigma) + return X + + def _primal_eig(self, X): + return numpy.linalg.eigh(numpy.einsum('ji,jk->ik',X,X)) + + def _dual_eig(self, X): + dual_eigvals, dual_eigvects = numpy.linalg.eigh(numpy.einsum('ij,kj->ik',X,X)) + relevant_dimensions = numpy.argsort(numpy.abs(dual_eigvals))[-X.shape[1]:] + eigvals = dual_eigvals[relevant_dimensions] + eigvects = dual_eigvects[:, relevant_dimensions] + eigvects = (1. / numpy.sqrt(X.shape[0] * numpy.abs(eigvals))) * X.T.dot(eigvects) + eigvects /= numpy.sqrt(numpy.diag(eigvects.T.dot(eigvects))) + return eigvals, eigvects + + def project(self, X, Q=None): + """ + Project X into PCA space, defined by the Q highest eigenvalues. + Y = X dot V + """ + if Q is None: + Q = self.Q + if Q > X.shape[1]: + raise IndexError("requested dimension larger then input dimension") + X = self.center(X) + return X.dot(self.eigvectors[:, :Q]) + + def plot_fracs(self, Q=None, ax=None, fignum=None): + """ + Plot fractions of Eigenvalues sorted in descending order. + """ + from GPy.plotting.matplot_dep import Tango + Tango.reset() + col = Tango.nextMedium() + if ax is None: + fig = pylab.figure(fignum) + ax = fig.add_subplot(111) + if Q is None: + Q = self.Q + ticks = numpy.arange(Q) + bar = ax.bar(ticks - .4, self.fracs[:Q], color=col) + ax.set_xticks(ticks, map(lambda x: r"${}$".format(x), ticks + 1)) + ax.set_ylabel("Eigenvalue fraction") + ax.set_xlabel("PC") + ax.set_ylim(0, ax.get_ylim()[1]) + ax.set_xlim(ticks.min() - .5, ticks.max() + .5) + try: + pylab.tight_layout() + except: + pass + return bar + + def plot_2d(self, X, labels=None, s=20, marker='o', + dimensions=(0, 1), ax=None, colors=None, + fignum=None, cmap=None, # @UndefinedVariable + ** kwargs): + """ + Plot dimensions `dimensions` with given labels against each other in + PC space. Labels can be any sequence of labels of dimensions X.shape[0]. + Labels can be drawn with a subsequent call to legend() + """ + if cmap is None: + cmap = matplotlib.cm.jet + if ax is None: + fig = pylab.figure(fignum) + ax = fig.add_subplot(111) + if labels is None: + labels = numpy.zeros(X.shape[0]) + ulabels = [] + for lab in labels: + if not lab in ulabels: + ulabels.append(lab) + nlabels = len(ulabels) + if colors is None: + colors = iter([cmap(float(i) / nlabels) for i in range(nlabels)]) + else: + colors = iter(colors) + X_ = self.project(X, self.Q)[:,dimensions] + kwargs.update(dict(s=s)) + plots = list() + for i, l in enumerate(ulabels): + kwargs.update(dict(color=colors.next(), marker=marker[i % len(marker)])) + plots.append(ax.scatter(*X_[labels == l, :].T, label=str(l), **kwargs)) + ax.set_xlabel(r"PC$_1$") + ax.set_ylabel(r"PC$_2$") + try: + pylab.tight_layout() + except: + pass + return plots \ No newline at end of file diff --git a/GPy/util/plot_latent.py b/GPy/util/plot_latent.py deleted file mode 100644 index 9ebc5a4e..00000000 --- a/GPy/util/plot_latent.py +++ /dev/null @@ -1,182 +0,0 @@ -import pylab as pb -import numpy as np -from .. import util -from .latent_space_visualizations.controllers.imshow_controller import ImshowController -import itertools - -def most_significant_input_dimensions(model, which_indices): - if which_indices is None: - if model.input_dim == 1: - input_1 = 0 - input_2 = None - if model.input_dim == 2: - input_1, input_2 = 0, 1 - else: - try: - input_1, input_2 = np.argsort(model.input_sensitivity())[::-1][:2] - except: - raise ValueError, "cannot automatically determine which dimensions to plot, please pass 'which_indices'" - else: - input_1, input_2 = which_indices - return input_1, input_2 - -def plot_latent(model, labels=None, which_indices=None, - resolution=50, ax=None, marker='o', s=40, - fignum=None, plot_inducing=False, legend=True, - aspect='auto', updates=False): - """ - :param labels: a np.array of size model.num_data containing labels for the points (can be number, strings, etc) - :param resolution: the resolution of the grid on which to evaluate the predictive variance - """ - if ax is None: - fig = pb.figure(num=fignum) - ax = fig.add_subplot(111) - util.plot.Tango.reset() - - if labels is None: - labels = np.ones(model.num_data) - - input_1, input_2 = most_significant_input_dimensions(model, which_indices) - - # first, plot the output variance as a function of the latent space - Xtest, xx, yy, xmin, xmax = util.plot.x_frame2D(model.X[:, [input_1, input_2]], resolution=resolution) - #Xtest_full = np.zeros((Xtest.shape[0], model.X.shape[1])) - Xtest_full = np.zeros((Xtest.shape[0], model.X.shape[1])) - def plot_function(x): - Xtest_full[:, [input_1, input_2]] = x - mu, var, low, up = model.predict(Xtest_full) - var = var[:, :1] - return np.log(var) - - xmi, ymi = xmin - xma, yma = xmax - - view = ImshowController(ax, plot_function, - (xmi, ymi, xma, yma), - resolution, aspect=aspect, interpolation='bilinear', - cmap=pb.cm.binary) - -# ax.imshow(var.reshape(resolution, resolution).T, -# extent=[xmin[0], xmax[0], xmin[1], xmax[1]], cmap=pb.cm.binary, interpolation='bilinear', origin='lower') - - # make sure labels are in order of input: - ulabels = [] - for lab in labels: - if not lab in ulabels: - ulabels.append(lab) - - marker = itertools.cycle(list(marker)) - - for i, ul in enumerate(ulabels): - if type(ul) is np.string_: - this_label = ul - elif type(ul) is np.int64: - this_label = 'class %i' % ul - else: - this_label = 'class %i' % i - m = marker.next() - - index = np.nonzero(labels == ul)[0] - if model.input_dim == 1: - x = model.X[index, input_1] - y = np.zeros(index.size) - else: - x = model.X[index, input_1] - y = model.X[index, input_2] - ax.scatter(x, y, marker=m, s=s, color=util.plot.Tango.nextMedium(), label=this_label) - - ax.set_xlabel('latent dimension %i' % input_1) - ax.set_ylabel('latent dimension %i' % input_2) - - if not np.all(labels == 1.) and legend: - ax.legend(loc=0, numpoints=1) - - ax.set_xlim(xmin[0], xmax[0]) - ax.set_ylim(xmin[1], xmax[1]) - ax.grid(b=False) # remove the grid if present, it doesn't look good - ax.set_aspect('auto') # set a nice aspect ratio - - if plot_inducing: - ax.plot(model.Z[:, input_1], model.Z[:, input_2], '^w') - - if updates: - ax.figure.canvas.show() - raw_input('Enter to continue') - return ax - -def plot_magnification(model, labels=None, which_indices=None, - resolution=60, ax=None, marker='o', s=40, - fignum=None, plot_inducing=False, legend=True, - aspect='auto', updates=False): - """ - :param labels: a np.array of size model.num_data containing labels for the points (can be number, strings, etc) - :param resolution: the resolution of the grid on which to evaluate the predictive variance - """ - if ax is None: - fig = pb.figure(num=fignum) - ax = fig.add_subplot(111) - util.plot.Tango.reset() - - if labels is None: - labels = np.ones(model.num_data) - - input_1, input_2 = most_significant_input_dimensions(model, which_indices) - - # first, plot the output variance as a function of the latent space - Xtest, xx, yy, xmin, xmax = util.plot.x_frame2D(model.X[:, [input_1, input_2]], resolution=resolution) - Xtest_full = np.zeros((Xtest.shape[0], model.X.shape[1])) - def plot_function(x): - Xtest_full[:, [input_1, input_2]] = x - mf=model.magnification(Xtest_full) - return mf - view = ImshowController(ax, plot_function, - tuple(model.X.min(0)[:, [input_1, input_2]]) + tuple(model.X.max(0)[:, [input_1, input_2]]), - resolution, aspect=aspect, interpolation='bilinear', - cmap=pb.cm.gray) - - # make sure labels are in order of input: - ulabels = [] - for lab in labels: - if not lab in ulabels: - ulabels.append(lab) - - marker = itertools.cycle(list(marker)) - - for i, ul in enumerate(ulabels): - if type(ul) is np.string_: - this_label = ul - elif type(ul) is np.int64: - this_label = 'class %i' % ul - else: - this_label = 'class %i' % i - m = marker.next() - - index = np.nonzero(labels == ul)[0] - if model.input_dim == 1: - x = model.X[index, input_1] - y = np.zeros(index.size) - else: - x = model.X[index, input_1] - y = model.X[index, input_2] - ax.scatter(x, y, marker=m, s=s, color=util.plot.Tango.nextMedium(), label=this_label) - - ax.set_xlabel('latent dimension %i' % input_1) - ax.set_ylabel('latent dimension %i' % input_2) - - if not np.all(labels == 1.) and legend: - ax.legend(loc=0, numpoints=1) - - ax.set_xlim(xmin[0], xmax[0]) - ax.set_ylim(xmin[1], xmax[1]) - ax.grid(b=False) # remove the grid if present, it doesn't look good - ax.set_aspect('auto') # set a nice aspect ratio - - if plot_inducing: - ax.plot(model.Z[:, input_1], model.Z[:, input_2], '^w') - - if updates: - ax.figure.canvas.show() - raw_input('Enter to continue') - - pb.title('Magnification Factor') - return ax diff --git a/GPy/util/subarray_and_sorting.py b/GPy/util/subarray_and_sorting.py index 49385771..0966084c 100644 --- a/GPy/util/subarray_and_sorting.py +++ b/GPy/util/subarray_and_sorting.py @@ -4,9 +4,9 @@ .. moduleauthor:: Max Zwiessele ''' -__updated__ = '2013-12-02' +__updated__ = '2014-05-21' -import numpy as np +import numpy as np, logging def common_subarrays(X, axis=0): """ @@ -14,15 +14,15 @@ def common_subarrays(X, axis=0): Common subarrays are returned as a dictionary of pairs, where the subarray is a tuple representing the subarray and the index is the index for the subarray in X, where index is the index to the remaining axis. - + :param :class:`np.ndarray` X: 2d array to check for common subarrays in - :param int axis: axis to apply subarray detection over. - When the index is 0, compare rows, columns, otherwise. - + :param int axis: axis to apply subarray detection over. + When the index is 0, compare rows -- columns, otherwise. + Examples: ========= - In a 2d array: + In a 2d array: >>> import numpy as np >>> X = np.zeros((3,6), dtype=bool) >>> X[[1,1,1],[0,4,5]] = 1; X[1:,[2,3]] = 1 @@ -48,9 +48,15 @@ def common_subarrays(X, axis=0): assert X.ndim == 2 and axis in (0,1), "Only implemented for 2D arrays" subarrays = defaultdict(list) cnt = count() - np.apply_along_axis(lambda x: iadd(subarrays[tuple(x)], [cnt.next()]), 1-axis, X) + def accumulate(x, s, c): + t = tuple(x) + col = c.next() + iadd(s[t], [col]) + return None + if axis == 0: [accumulate(x, subarrays, cnt) for x in X] + else: [accumulate(x, subarrays, cnt) for x in X.T] return subarrays if __name__ == '__main__': import doctest - doctest.testmod() \ No newline at end of file + doctest.testmod() diff --git a/GPy/util/symbolic.py b/GPy/util/symbolic.py deleted file mode 100644 index 49c8c33a..00000000 --- a/GPy/util/symbolic.py +++ /dev/null @@ -1,239 +0,0 @@ -from sympy import Function, S, oo, I, cos, sin, asin, log, erf, pi, exp, sqrt, sign - - -class ln_diff_erf(Function): - nargs = 2 - - def fdiff(self, argindex=2): - if argindex == 2: - x0, x1 = self.args - return -2*exp(-x1**2)/(sqrt(pi)*(erf(x0)-erf(x1))) - elif argindex == 1: - x0, x1 = self.args - return 2.*exp(-x0**2)/(sqrt(pi)*(erf(x0)-erf(x1))) - else: - raise ArgumentIndexError(self, argindex) - - @classmethod - def eval(cls, x0, x1): - if x0.is_Number and x1.is_Number: - return log(erf(x0)-erf(x1)) - -class dh_dd_i(Function): - nargs = 5 - @classmethod - def eval(cls, t, tprime, d_i, d_j, l): - if (t.is_Number - and tprime.is_Number - and d_i.is_Number - and d_j.is_Number - and l.is_Number): - - diff_t = (t-tprime) - l2 = l*l - h = h(t, tprime, d_i, d_j, l) - half_l_di = 0.5*l*d_i - arg_1 = half_l_di + tprime/l - arg_2 = half_l_di - (t-tprime)/l - ln_part_1 = ln_diff_erf(arg_1, arg_2) - arg_1 = half_l_di - arg_2 = half_l_di - t/l - sign_val = sign(t/l) - ln_part_2 = ln_diff_erf(half_l_di, half_l_di - t/l) - - base = ((0.5*d_i*l2*(d_i+d_j)-1)*h - + (-diff_t*sign_val*exp(half_l_di*half_l_di - -d_i*diff_t - +ln_part_1) - +t*sign_val*exp(half_l_di*half_l_di - -d_i*t-d_j*tprime - +ln_part_2)) - + l/sqrt(pi)*(-exp(-diff_t*diff_t/l2) - +exp(-tprime*tprime/l2-d_i*t) - +exp(-t*t/l2-d_j*tprime) - -exp(-(d_i*t + d_j*tprime)))) - return base/(d_i+d_j) - -class dh_dd_j(Function): - nargs = 5 - @classmethod - def eval(cls, t, tprime, d_i, d_j, l): - if (t.is_Number - and tprime.is_Number - and d_i.is_Number - and d_j.is_Number - and l.is_Number): - diff_t = (t-tprime) - l2 = l*l - half_l_di = 0.5*l*d_i - h = h(t, tprime, d_i, d_j, l) - arg_1 = half_l_di + tprime/l - arg_2 = half_l_di - (t-tprime)/l - ln_part_1 = ln_diff_erf(arg_1, arg_2) - arg_1 = half_l_di - arg_2 = half_l_di - t/l - sign_val = sign(t/l) - ln_part_2 = ln_diff_erf(half_l_di, half_l_di - t/l) - sign_val = sign(t/l) - base = tprime*sign_val*exp(half_l_di*half_l_di-(d_i*t+d_j*tprime)+ln_part_2)-h - return base/(d_i+d_j) - -class dh_dl(Function): - nargs = 5 - @classmethod - def eval(cls, t, tprime, d_i, d_j, l): - if (t.is_Number - and tprime.is_Number - and d_i.is_Number - and d_j.is_Number - and l.is_Number): - - diff_t = (t-tprime) - l2 = l*l - h = h(t, tprime, d_i, d_j, l) - return 0.5*d_i*d_i*l*h + 2./(sqrt(pi)*(d_i+d_j))*((-diff_t/l2-d_i/2.)*exp(-diff_t*diff_t/l2)+(-tprime/l2+d_i/2.)*exp(-tprime*tprime/l2-d_i*t)-(-t/l2-d_i/2.)*exp(-t*t/l2-d_j*tprime)-d_i/2.*exp(-(d_i*t+d_j*tprime))) - -class dh_dt(Function): - nargs = 5 - @classmethod - def eval(cls, t, tprime, d_i, d_j, l): - if (t.is_Number - and tprime.is_Number - and d_i.is_Number - and d_j.is_Number - and l.is_Number): - if (t is S.NaN - or tprime is S.NaN - or d_i is S.NaN - or d_j is S.NaN - or l is S.NaN): - return S.NaN - else: - half_l_di = 0.5*l*d_i - arg_1 = half_l_di + tprime/l - arg_2 = half_l_di - (t-tprime)/l - ln_part_1 = ln_diff_erf(arg_1, arg_2) - arg_1 = half_l_di - arg_2 = half_l_di - t/l - sign_val = sign(t/l) - ln_part_2 = ln_diff_erf(half_l_di, half_l_di - t/l) - - - return (sign_val*exp(half_l_di*half_l_di - - d_i*(t-tprime) - + ln_part_1 - - log(d_i + d_j)) - - sign_val*exp(half_l_di*half_l_di - - d_i*t - d_j*tprime - + ln_part_2 - - log(d_i + d_j))).diff(t) - -class dh_dtprime(Function): - nargs = 5 - @classmethod - def eval(cls, t, tprime, d_i, d_j, l): - if (t.is_Number - and tprime.is_Number - and d_i.is_Number - and d_j.is_Number - and l.is_Number): - if (t is S.NaN - or tprime is S.NaN - or d_i is S.NaN - or d_j is S.NaN - or l is S.NaN): - return S.NaN - else: - half_l_di = 0.5*l*d_i - arg_1 = half_l_di + tprime/l - arg_2 = half_l_di - (t-tprime)/l - ln_part_1 = ln_diff_erf(arg_1, arg_2) - arg_1 = half_l_di - arg_2 = half_l_di - t/l - sign_val = sign(t/l) - ln_part_2 = ln_diff_erf(half_l_di, half_l_di - t/l) - - - return (sign_val*exp(half_l_di*half_l_di - - d_i*(t-tprime) - + ln_part_1 - - log(d_i + d_j)) - - sign_val*exp(half_l_di*half_l_di - - d_i*t - d_j*tprime - + ln_part_2 - - log(d_i + d_j))).diff(tprime) - - -class h(Function): - nargs = 5 - def fdiff(self, argindex=5): - t, tprime, d_i, d_j, l = self.args - if argindex == 1: - return dh_dt(t, tprime, d_i, d_j, l) - elif argindex == 2: - return dh_dtprime(t, tprime, d_i, d_j, l) - elif argindex == 3: - return dh_dd_i(t, tprime, d_i, d_j, l) - elif argindex == 4: - return dh_dd_j(t, tprime, d_i, d_j, l) - elif argindex == 5: - return dh_dl(t, tprime, d_i, d_j, l) - - - @classmethod - def eval(cls, t, tprime, d_i, d_j, l): - # putting in the is_Number stuff forces it to look for a fdiff method for derivative. If it's left out, then when asking for self.diff, it just does the diff on the eval symbolic terms directly. We want to avoid that because we are looking to ensure everything is numerically stable. Maybe it's because of the if statement that this happens? - if (t.is_Number - and tprime.is_Number - and d_i.is_Number - and d_j.is_Number - and l.is_Number): - if (t is S.NaN - or tprime is S.NaN - or d_i is S.NaN - or d_j is S.NaN - or l is S.NaN): - return S.NaN - else: - half_l_di = 0.5*l*d_i - arg_1 = half_l_di + tprime/l - arg_2 = half_l_di - (t-tprime)/l - ln_part_1 = ln_diff_erf(arg_1, arg_2) - arg_1 = half_l_di - arg_2 = half_l_di - t/l - sign_val = sign(t/l) - ln_part_2 = ln_diff_erf(half_l_di, half_l_di - t/l) - - - return (sign_val*exp(half_l_di*half_l_di - - d_i*(t-tprime) - + ln_part_1 - - log(d_i + d_j)) - - sign_val*exp(half_l_di*half_l_di - - d_i*t - d_j*tprime - + ln_part_2 - - log(d_i + d_j))) - - - # return (exp((d_j/2.*l)**2)/(d_i+d_j) - # *(exp(-d_j*(tprime - t)) - # *(erf((tprime-t)/l - d_j/2.*l) - # + erf(t/l + d_j/2.*l)) - # - exp(-(d_j*tprime + d_i)) - # *(erf(tprime/l - d_j/2.*l) - # + erf(d_j/2.*l)))) - -class erfc(Function): - nargs = 1 - - @classmethod - def eval(cls, arg): - return 1-erf(arg) - -class erfcx(Function): - nargs = 1 - - @classmethod - def eval(cls, arg): - return erfc(arg)*exp(arg*arg) - diff --git a/GPy/util/univariate_Gaussian.py b/GPy/util/univariate_Gaussian.py index 702ab25c..09b2e99c 100644 --- a/GPy/util/univariate_Gaussian.py +++ b/GPy/util/univariate_Gaussian.py @@ -12,6 +12,39 @@ def std_norm_cdf(x): """ Cumulative standard Gaussian distribution Based on Abramowitz, M. and Stegun, I. (1970) + """ + x_shape = np.asarray(x).shape + + if len(x_shape) == 0 or x_shape[0] == 1: + sign = np.sign(x) + x *= sign + x /= np.sqrt(2.) + t = 1.0/(1.0 + 0.3275911*x) + erf = 1. - np.exp(-x**2)*t*(0.254829592 + t*(-0.284496736 + t*(1.421413741 + t*(-1.453152027 + t*(1.061405429))))) + cdf_x = 0.5*(1.0 + sign*erf) + return cdf_x + else: + x = np.atleast_1d(x).copy() + cdf_x = np.zeros_like(x) + sign = np.ones_like(x) + neg_x_ind = x<0 + sign[neg_x_ind] = -1.0 + x[neg_x_ind] = -x[neg_x_ind] + x /= np.sqrt(2.) + t = 1.0/(1.0 + 0.3275911*x) + erf = 1. - np.exp(-x**2)*t*(0.254829592 + t*(-0.284496736 + t*(1.421413741 + t*(-1.453152027 + t*(1.061405429))))) + cdf_x = 0.5*(1.0 + sign*erf) + cdf_x = cdf_x.reshape(x_shape) + return cdf_x + +def std_norm_cdf_weave(x): + """ + Cumulative standard Gaussian distribution + Based on Abramowitz, M. and Stegun, I. (1970) + + A weave implementation of std_norm_cdf, which is faster. this is unused, + because of the difficulties of a weave dependency. (see github issue #94) + """ #Generalize for many x x = np.asarray(x).copy() diff --git a/GPy/util/warping_functions.py b/GPy/util/warping_functions.py index 35ad3b80..a0a385e0 100644 --- a/GPy/util/warping_functions.py +++ b/GPy/util/warping_functions.py @@ -3,8 +3,6 @@ import numpy as np -import scipy as sp -import pylab as plt class WarpingFunction(object): """ @@ -39,6 +37,7 @@ class WarpingFunction(object): def plot(self, psi, xmin, xmax): y = np.arange(xmin, xmax, 0.01) f_y = self.f(y, psi) + from matplotlib import pyplot as plt plt.figure() plt.plot(y, f_y) plt.xlabel('y') diff --git a/MANIFEST.in b/MANIFEST.in index 8d5b2304..bcbf3583 100644 --- a/MANIFEST.in +++ b/MANIFEST.in @@ -4,3 +4,5 @@ include *.md recursive-include doc *.md include *.cfg recursive-include doc *.cfg +include *.json +recursive-include doc *.json diff --git a/README.md b/README.md index b7635b0d..6a880209 100644 --- a/README.md +++ b/README.md @@ -3,13 +3,27 @@ GPy A Gaussian processes framework in Python. +* [GPy homepage](http://sheffieldml.github.io/GPy/) * [User mailing list](https://lists.shef.ac.uk/sympa/subscribe/gpy-users) * [Online documentation](https://gpy.readthedocs.org/en/latest/) * [Unit tests (Travis-CI)](https://travis-ci.org/SheffieldML/GPy) - Continuous integration status: ![CI status](https://travis-ci.org/SheffieldML/GPy.png) +Citation +======== + + @Misc{gpy2014, + author = {The GPy authors}, + title = {{GPy}: A Gaussian process framework in python}, + howpublished = {\url{http://github.com/SheffieldML/GPy}}, + year = {2012--2014} + } + +Pronounciation +============== +We like to pronounce it 'Gee-pie'. + Getting started =============== Installing with pip diff --git a/doc/GPy.core.parameterization.rst b/doc/GPy.core.parameterization.rst new file mode 100644 index 00000000..4877a06d --- /dev/null +++ b/doc/GPy.core.parameterization.rst @@ -0,0 +1,102 @@ +GPy.core.parameterization package +================================= + +Submodules +---------- + +GPy.core.parameterization.domains module +---------------------------------------- + +.. automodule:: GPy.core.parameterization.domains + :members: + :undoc-members: + :show-inheritance: + +GPy.core.parameterization.index_operations module +------------------------------------------------- + +.. automodule:: GPy.core.parameterization.index_operations + :members: + :undoc-members: + :show-inheritance: + +GPy.core.parameterization.lists_and_dicts module +------------------------------------------------ + +.. automodule:: GPy.core.parameterization.lists_and_dicts + :members: + :undoc-members: + :show-inheritance: + +GPy.core.parameterization.observable_array module +------------------------------------------------- + +.. automodule:: GPy.core.parameterization.observable_array + :members: + :undoc-members: + :show-inheritance: + +GPy.core.parameterization.param module +-------------------------------------- + +.. automodule:: GPy.core.parameterization.param + :members: + :undoc-members: + :show-inheritance: + +GPy.core.parameterization.parameter_core module +----------------------------------------------- + +.. automodule:: GPy.core.parameterization.parameter_core + :members: + :undoc-members: + :show-inheritance: + +GPy.core.parameterization.parameterized module +---------------------------------------------- + +.. automodule:: GPy.core.parameterization.parameterized + :members: + :undoc-members: + :show-inheritance: + +GPy.core.parameterization.priors module +--------------------------------------- + +.. automodule:: GPy.core.parameterization.priors + :members: + :undoc-members: + :show-inheritance: + +GPy.core.parameterization.ties_and_remappings module +---------------------------------------------------- + +.. automodule:: GPy.core.parameterization.ties_and_remappings + :members: + :undoc-members: + :show-inheritance: + +GPy.core.parameterization.transformations module +------------------------------------------------ + +.. automodule:: GPy.core.parameterization.transformations + :members: + :undoc-members: + :show-inheritance: + +GPy.core.parameterization.variational module +-------------------------------------------- + +.. automodule:: GPy.core.parameterization.variational + :members: + :undoc-members: + :show-inheritance: + + +Module contents +--------------- + +.. automodule:: GPy.core.parameterization + :members: + :undoc-members: + :show-inheritance: diff --git a/doc/GPy.core.rst b/doc/GPy.core.rst index c4f1849d..3c236612 100644 --- a/doc/GPy.core.rst +++ b/doc/GPy.core.rst @@ -1,25 +1,16 @@ GPy.core package ================ +Subpackages +----------- + +.. toctree:: + + GPy.core.parameterization + Submodules ---------- -GPy.core.domains module ------------------------ - -.. automodule:: GPy.core.domains - :members: - :undoc-members: - :show-inheritance: - -GPy.core.fitc module --------------------- - -.. automodule:: GPy.core.fitc - :members: - :undoc-members: - :show-inheritance: - GPy.core.gp module ------------------ @@ -28,14 +19,6 @@ GPy.core.gp module :undoc-members: :show-inheritance: -GPy.core.gp_base module ------------------------ - -.. automodule:: GPy.core.gp_base - :members: - :undoc-members: - :show-inheritance: - GPy.core.mapping module ----------------------- @@ -52,22 +35,6 @@ GPy.core.model module :undoc-members: :show-inheritance: -GPy.core.parameterized module ------------------------------ - -.. automodule:: GPy.core.parameterized - :members: - :undoc-members: - :show-inheritance: - -GPy.core.priors module ----------------------- - -.. automodule:: GPy.core.priors - :members: - :undoc-members: - :show-inheritance: - GPy.core.sparse_gp module ------------------------- @@ -76,6 +43,14 @@ GPy.core.sparse_gp module :undoc-members: :show-inheritance: +GPy.core.sparse_gp_mpi module +----------------------------- + +.. automodule:: GPy.core.sparse_gp_mpi + :members: + :undoc-members: + :show-inheritance: + GPy.core.svigp module --------------------- @@ -84,10 +59,10 @@ GPy.core.svigp module :undoc-members: :show-inheritance: -GPy.core.transformations module -------------------------------- +GPy.core.symbolic module +------------------------ -.. automodule:: GPy.core.transformations +.. automodule:: GPy.core.symbolic :members: :undoc-members: :show-inheritance: diff --git a/doc/GPy.examples.rst b/doc/GPy.examples.rst index bde015dd..7fc8a123 100644 --- a/doc/GPy.examples.rst +++ b/doc/GPy.examples.rst @@ -12,6 +12,14 @@ GPy.examples.classification module :undoc-members: :show-inheritance: +GPy.examples.coreg_example module +--------------------------------- + +.. automodule:: GPy.examples.coreg_example + :members: + :undoc-members: + :show-inheritance: + GPy.examples.dimensionality_reduction module -------------------------------------------- diff --git a/doc/GPy.inference.latent_function_inference.rst b/doc/GPy.inference.latent_function_inference.rst new file mode 100644 index 00000000..98d16705 --- /dev/null +++ b/doc/GPy.inference.latent_function_inference.rst @@ -0,0 +1,102 @@ +GPy.inference.latent_function_inference package +=============================================== + +Submodules +---------- + +GPy.inference.latent_function_inference.dtc module +-------------------------------------------------- + +.. automodule:: GPy.inference.latent_function_inference.dtc + :members: + :undoc-members: + :show-inheritance: + +GPy.inference.latent_function_inference.exact_gaussian_inference module +----------------------------------------------------------------------- + +.. automodule:: GPy.inference.latent_function_inference.exact_gaussian_inference + :members: + :undoc-members: + :show-inheritance: + +GPy.inference.latent_function_inference.expectation_propagation module +---------------------------------------------------------------------- + +.. automodule:: GPy.inference.latent_function_inference.expectation_propagation + :members: + :undoc-members: + :show-inheritance: + +GPy.inference.latent_function_inference.expectation_propagation_dtc module +-------------------------------------------------------------------------- + +.. automodule:: GPy.inference.latent_function_inference.expectation_propagation_dtc + :members: + :undoc-members: + :show-inheritance: + +GPy.inference.latent_function_inference.fitc module +--------------------------------------------------- + +.. automodule:: GPy.inference.latent_function_inference.fitc + :members: + :undoc-members: + :show-inheritance: + +GPy.inference.latent_function_inference.inferenceX module +--------------------------------------------------------- + +.. automodule:: GPy.inference.latent_function_inference.inferenceX + :members: + :undoc-members: + :show-inheritance: + +GPy.inference.latent_function_inference.laplace module +------------------------------------------------------ + +.. automodule:: GPy.inference.latent_function_inference.laplace + :members: + :undoc-members: + :show-inheritance: + +GPy.inference.latent_function_inference.posterior module +-------------------------------------------------------- + +.. automodule:: GPy.inference.latent_function_inference.posterior + :members: + :undoc-members: + :show-inheritance: + +GPy.inference.latent_function_inference.var_dtc module +------------------------------------------------------ + +.. automodule:: GPy.inference.latent_function_inference.var_dtc + :members: + :undoc-members: + :show-inheritance: + +GPy.inference.latent_function_inference.var_dtc_gpu module +---------------------------------------------------------- + +.. automodule:: GPy.inference.latent_function_inference.var_dtc_gpu + :members: + :undoc-members: + :show-inheritance: + +GPy.inference.latent_function_inference.var_dtc_parallel module +--------------------------------------------------------------- + +.. automodule:: GPy.inference.latent_function_inference.var_dtc_parallel + :members: + :undoc-members: + :show-inheritance: + + +Module contents +--------------- + +.. automodule:: GPy.inference.latent_function_inference + :members: + :undoc-members: + :show-inheritance: diff --git a/doc/GPy.inference.mcmc.rst b/doc/GPy.inference.mcmc.rst new file mode 100644 index 00000000..273658b7 --- /dev/null +++ b/doc/GPy.inference.mcmc.rst @@ -0,0 +1,30 @@ +GPy.inference.mcmc package +========================== + +Submodules +---------- + +GPy.inference.mcmc.hmc module +----------------------------- + +.. automodule:: GPy.inference.mcmc.hmc + :members: + :undoc-members: + :show-inheritance: + +GPy.inference.mcmc.samplers module +---------------------------------- + +.. automodule:: GPy.inference.mcmc.samplers + :members: + :undoc-members: + :show-inheritance: + + +Module contents +--------------- + +.. automodule:: GPy.inference.mcmc + :members: + :undoc-members: + :show-inheritance: diff --git a/doc/GPy.inference.optimization.rst b/doc/GPy.inference.optimization.rst new file mode 100644 index 00000000..a81a8e68 --- /dev/null +++ b/doc/GPy.inference.optimization.rst @@ -0,0 +1,62 @@ +GPy.inference.optimization package +================================== + +Submodules +---------- + +GPy.inference.optimization.conjugate_gradient_descent module +------------------------------------------------------------ + +.. automodule:: GPy.inference.optimization.conjugate_gradient_descent + :members: + :undoc-members: + :show-inheritance: + +GPy.inference.optimization.gradient_descent_update_rules module +--------------------------------------------------------------- + +.. automodule:: GPy.inference.optimization.gradient_descent_update_rules + :members: + :undoc-members: + :show-inheritance: + +GPy.inference.optimization.optimization module +---------------------------------------------- + +.. automodule:: GPy.inference.optimization.optimization + :members: + :undoc-members: + :show-inheritance: + +GPy.inference.optimization.scg module +------------------------------------- + +.. automodule:: GPy.inference.optimization.scg + :members: + :undoc-members: + :show-inheritance: + +GPy.inference.optimization.sgd module +------------------------------------- + +.. automodule:: GPy.inference.optimization.sgd + :members: + :undoc-members: + :show-inheritance: + +GPy.inference.optimization.stochastics module +--------------------------------------------- + +.. automodule:: GPy.inference.optimization.stochastics + :members: + :undoc-members: + :show-inheritance: + + +Module contents +--------------- + +.. automodule:: GPy.inference.optimization + :members: + :undoc-members: + :show-inheritance: diff --git a/doc/GPy.inference.rst b/doc/GPy.inference.rst index 28f42994..235f804b 100644 --- a/doc/GPy.inference.rst +++ b/doc/GPy.inference.rst @@ -1,57 +1,14 @@ GPy.inference package ===================== -Submodules ----------- +Subpackages +----------- -GPy.inference.conjugate_gradient_descent module ------------------------------------------------ - -.. automodule:: GPy.inference.conjugate_gradient_descent - :members: - :undoc-members: - :show-inheritance: - -GPy.inference.gradient_descent_update_rules module --------------------------------------------------- - -.. automodule:: GPy.inference.gradient_descent_update_rules - :members: - :undoc-members: - :show-inheritance: - -GPy.inference.optimization module ---------------------------------- - -.. automodule:: GPy.inference.optimization - :members: - :undoc-members: - :show-inheritance: - -GPy.inference.samplers module ------------------------------ - -.. automodule:: GPy.inference.samplers - :members: - :undoc-members: - :show-inheritance: - -GPy.inference.scg module ------------------------- - -.. automodule:: GPy.inference.scg - :members: - :undoc-members: - :show-inheritance: - -GPy.inference.sgd module ------------------------- - -.. automodule:: GPy.inference.sgd - :members: - :undoc-members: - :show-inheritance: +.. toctree:: + GPy.inference.latent_function_inference + GPy.inference.mcmc + GPy.inference.optimization Module contents --------------- diff --git a/doc/GPy.kern._src.psi_comp.rst b/doc/GPy.kern._src.psi_comp.rst new file mode 100644 index 00000000..d84eeaa0 --- /dev/null +++ b/doc/GPy.kern._src.psi_comp.rst @@ -0,0 +1,62 @@ +GPy.kern._src.psi_comp package +============================== + +Submodules +---------- + +GPy.kern._src.psi_comp.linear_psi_comp module +--------------------------------------------- + +.. automodule:: GPy.kern._src.psi_comp.linear_psi_comp + :members: + :undoc-members: + :show-inheritance: + +GPy.kern._src.psi_comp.rbf_psi_comp module +------------------------------------------ + +.. automodule:: GPy.kern._src.psi_comp.rbf_psi_comp + :members: + :undoc-members: + :show-inheritance: + +GPy.kern._src.psi_comp.rbf_psi_gpucomp module +--------------------------------------------- + +.. automodule:: GPy.kern._src.psi_comp.rbf_psi_gpucomp + :members: + :undoc-members: + :show-inheritance: + +GPy.kern._src.psi_comp.sslinear_psi_comp module +----------------------------------------------- + +.. automodule:: GPy.kern._src.psi_comp.sslinear_psi_comp + :members: + :undoc-members: + :show-inheritance: + +GPy.kern._src.psi_comp.ssrbf_psi_comp module +-------------------------------------------- + +.. automodule:: GPy.kern._src.psi_comp.ssrbf_psi_comp + :members: + :undoc-members: + :show-inheritance: + +GPy.kern._src.psi_comp.ssrbf_psi_gpucomp module +----------------------------------------------- + +.. automodule:: GPy.kern._src.psi_comp.ssrbf_psi_gpucomp + :members: + :undoc-members: + :show-inheritance: + + +Module contents +--------------- + +.. automodule:: GPy.kern._src.psi_comp + :members: + :undoc-members: + :show-inheritance: diff --git a/doc/GPy.kern._src.rst b/doc/GPy.kern._src.rst new file mode 100644 index 00000000..93dc0058 --- /dev/null +++ b/doc/GPy.kern._src.rst @@ -0,0 +1,197 @@ +GPy.kern._src package +===================== + +Subpackages +----------- + +.. toctree:: + + GPy.kern._src.psi_comp + +Submodules +---------- + +GPy.kern._src.ODE_UY module +--------------------------- + +.. automodule:: GPy.kern._src.ODE_UY + :members: + :undoc-members: + :show-inheritance: + +GPy.kern._src.ODE_UYC module +---------------------------- + +.. automodule:: GPy.kern._src.ODE_UYC + :members: + :undoc-members: + :show-inheritance: + +GPy.kern._src.ODE_st module +--------------------------- + +.. automodule:: GPy.kern._src.ODE_st + :members: + :undoc-members: + :show-inheritance: + +GPy.kern._src.ODE_t module +-------------------------- + +.. automodule:: GPy.kern._src.ODE_t + :members: + :undoc-members: + :show-inheritance: + +GPy.kern._src.add module +------------------------ + +.. automodule:: GPy.kern._src.add + :members: + :undoc-members: + :show-inheritance: + +GPy.kern._src.brownian module +----------------------------- + +.. automodule:: GPy.kern._src.brownian + :members: + :undoc-members: + :show-inheritance: + +GPy.kern._src.coregionalize module +---------------------------------- + +.. automodule:: GPy.kern._src.coregionalize + :members: + :undoc-members: + :show-inheritance: + +GPy.kern._src.hierarchical module +--------------------------------- + +.. automodule:: GPy.kern._src.hierarchical + :members: + :undoc-members: + :show-inheritance: + +GPy.kern._src.independent_outputs module +---------------------------------------- + +.. automodule:: GPy.kern._src.independent_outputs + :members: + :undoc-members: + :show-inheritance: + +GPy.kern._src.kern module +------------------------- + +.. automodule:: GPy.kern._src.kern + :members: + :undoc-members: + :show-inheritance: + +GPy.kern._src.kernel_slice_operations module +-------------------------------------------- + +.. automodule:: GPy.kern._src.kernel_slice_operations + :members: + :undoc-members: + :show-inheritance: + +GPy.kern._src.linear module +--------------------------- + +.. automodule:: GPy.kern._src.linear + :members: + :undoc-members: + :show-inheritance: + +GPy.kern._src.mlp module +------------------------ + +.. automodule:: GPy.kern._src.mlp + :members: + :undoc-members: + :show-inheritance: + +GPy.kern._src.periodic module +----------------------------- + +.. automodule:: GPy.kern._src.periodic + :members: + :undoc-members: + :show-inheritance: + +GPy.kern._src.poly module +------------------------- + +.. automodule:: GPy.kern._src.poly + :members: + :undoc-members: + :show-inheritance: + +GPy.kern._src.prod module +------------------------- + +.. automodule:: GPy.kern._src.prod + :members: + :undoc-members: + :show-inheritance: + +GPy.kern._src.rbf module +------------------------ + +.. automodule:: GPy.kern._src.rbf + :members: + :undoc-members: + :show-inheritance: + +GPy.kern._src.splitKern module +------------------------------ + +.. automodule:: GPy.kern._src.splitKern + :members: + :undoc-members: + :show-inheritance: + +GPy.kern._src.static module +--------------------------- + +.. automodule:: GPy.kern._src.static + :members: + :undoc-members: + :show-inheritance: + +GPy.kern._src.stationary module +------------------------------- + +.. automodule:: GPy.kern._src.stationary + :members: + :undoc-members: + :show-inheritance: + +GPy.kern._src.symbolic module +----------------------------- + +.. automodule:: GPy.kern._src.symbolic + :members: + :undoc-members: + :show-inheritance: + +GPy.kern._src.trunclinear module +-------------------------------- + +.. automodule:: GPy.kern._src.trunclinear + :members: + :undoc-members: + :show-inheritance: + + +Module contents +--------------- + +.. automodule:: GPy.kern._src + :members: + :undoc-members: + :show-inheritance: diff --git a/doc/GPy.kern.parts.rst b/doc/GPy.kern.parts.rst deleted file mode 100644 index 59c48d96..00000000 --- a/doc/GPy.kern.parts.rst +++ /dev/null @@ -1,278 +0,0 @@ -GPy.kern.parts package -====================== - -Submodules ----------- - -GPy.kern.parts.Brownian module ------------------------------- - -.. automodule:: GPy.kern.parts.Brownian - :members: - :undoc-members: - :show-inheritance: - -GPy.kern.parts.Matern32 module ------------------------------- - -.. automodule:: GPy.kern.parts.Matern32 - :members: - :undoc-members: - :show-inheritance: - -GPy.kern.parts.Matern52 module ------------------------------- - -.. automodule:: GPy.kern.parts.Matern52 - :members: - :undoc-members: - :show-inheritance: - -GPy.kern.parts.ODE_1 module ---------------------------- - -.. automodule:: GPy.kern.parts.ODE_1 - :members: - :undoc-members: - :show-inheritance: - -GPy.kern.parts.ODE_UY module ----------------------------- - -.. automodule:: GPy.kern.parts.ODE_UY - :members: - :undoc-members: - :show-inheritance: - -GPy.kern.parts.bias module --------------------------- - -.. automodule:: GPy.kern.parts.bias - :members: - :undoc-members: - :show-inheritance: - -GPy.kern.parts.coregionalize module ------------------------------------ - -.. automodule:: GPy.kern.parts.coregionalize - :members: - :undoc-members: - :show-inheritance: - -GPy.kern.parts.eq_ode1 module ------------------------------ - -.. automodule:: GPy.kern.parts.eq_ode1 - :members: - :undoc-members: - :show-inheritance: - -GPy.kern.parts.exponential module ---------------------------------- - -.. automodule:: GPy.kern.parts.exponential - :members: - :undoc-members: - :show-inheritance: - -GPy.kern.parts.finite_dimensional module ----------------------------------------- - -.. automodule:: GPy.kern.parts.finite_dimensional - :members: - :undoc-members: - :show-inheritance: - -GPy.kern.parts.fixed module ---------------------------- - -.. automodule:: GPy.kern.parts.fixed - :members: - :undoc-members: - :show-inheritance: - -GPy.kern.parts.gibbs module ---------------------------- - -.. automodule:: GPy.kern.parts.gibbs - :members: - :undoc-members: - :show-inheritance: - -GPy.kern.parts.hetero module ----------------------------- - -.. automodule:: GPy.kern.parts.hetero - :members: - :undoc-members: - :show-inheritance: - -GPy.kern.parts.hierarchical module ----------------------------------- - -.. automodule:: GPy.kern.parts.hierarchical - :members: - :undoc-members: - :show-inheritance: - -GPy.kern.parts.independent_outputs module ------------------------------------------ - -.. automodule:: GPy.kern.parts.independent_outputs - :members: - :undoc-members: - :show-inheritance: - -GPy.kern.parts.kernpart module ------------------------------- - -.. automodule:: GPy.kern.parts.kernpart - :members: - :undoc-members: - :show-inheritance: - -GPy.kern.parts.linear module ----------------------------- - -.. automodule:: GPy.kern.parts.linear - :members: - :undoc-members: - :show-inheritance: - -GPy.kern.parts.mlp module -------------------------- - -.. automodule:: GPy.kern.parts.mlp - :members: - :undoc-members: - :show-inheritance: - -GPy.kern.parts.periodic_Matern32 module ---------------------------------------- - -.. automodule:: GPy.kern.parts.periodic_Matern32 - :members: - :undoc-members: - :show-inheritance: - -GPy.kern.parts.periodic_Matern52 module ---------------------------------------- - -.. automodule:: GPy.kern.parts.periodic_Matern52 - :members: - :undoc-members: - :show-inheritance: - -GPy.kern.parts.periodic_exponential module ------------------------------------------- - -.. automodule:: GPy.kern.parts.periodic_exponential - :members: - :undoc-members: - :show-inheritance: - -GPy.kern.parts.poly module --------------------------- - -.. automodule:: GPy.kern.parts.poly - :members: - :undoc-members: - :show-inheritance: - -GPy.kern.parts.prod module --------------------------- - -.. automodule:: GPy.kern.parts.prod - :members: - :undoc-members: - :show-inheritance: - -GPy.kern.parts.prod_orthogonal module -------------------------------------- - -.. automodule:: GPy.kern.parts.prod_orthogonal - :members: - :undoc-members: - :show-inheritance: - -GPy.kern.parts.rational_quadratic module ----------------------------------------- - -.. automodule:: GPy.kern.parts.rational_quadratic - :members: - :undoc-members: - :show-inheritance: - -GPy.kern.parts.rbf module -------------------------- - -.. automodule:: GPy.kern.parts.rbf - :members: - :undoc-members: - :show-inheritance: - -GPy.kern.parts.rbf_inv module ------------------------------ - -.. automodule:: GPy.kern.parts.rbf_inv - :members: - :undoc-members: - :show-inheritance: - -GPy.kern.parts.rbfcos module ----------------------------- - -.. automodule:: GPy.kern.parts.rbfcos - :members: - :undoc-members: - :show-inheritance: - -GPy.kern.parts.spline module ----------------------------- - -.. automodule:: GPy.kern.parts.spline - :members: - :undoc-members: - :show-inheritance: - -GPy.kern.parts.symmetric module -------------------------------- - -.. automodule:: GPy.kern.parts.symmetric - :members: - :undoc-members: - :show-inheritance: - -GPy.kern.parts.sympy_helpers module ------------------------------------ - -.. automodule:: GPy.kern.parts.sympy_helpers - :members: - :undoc-members: - :show-inheritance: - -GPy.kern.parts.sympykern module -------------------------------- - -.. automodule:: GPy.kern.parts.sympykern - :members: - :undoc-members: - :show-inheritance: - -GPy.kern.parts.white module ---------------------------- - -.. automodule:: GPy.kern.parts.white - :members: - :undoc-members: - :show-inheritance: - - -Module contents ---------------- - -.. automodule:: GPy.kern.parts - :members: - :undoc-members: - :show-inheritance: diff --git a/doc/GPy.kern.rst b/doc/GPy.kern.rst index b4b9d9aa..5a0c61c2 100644 --- a/doc/GPy.kern.rst +++ b/doc/GPy.kern.rst @@ -6,27 +6,7 @@ Subpackages .. toctree:: - GPy.kern.parts - -Submodules ----------- - -GPy.kern.constructors module ----------------------------- - -.. automodule:: GPy.kern.constructors - :members: - :undoc-members: - :show-inheritance: - -GPy.kern.kern module --------------------- - -.. automodule:: GPy.kern.kern - :members: - :undoc-members: - :show-inheritance: - + GPy.kern._src Module contents --------------- diff --git a/doc/GPy.likelihoods.noise_models.rst b/doc/GPy.likelihoods.noise_models.rst deleted file mode 100644 index 6fec5aff..00000000 --- a/doc/GPy.likelihoods.noise_models.rst +++ /dev/null @@ -1,78 +0,0 @@ -GPy.likelihoods.noise_models package -==================================== - -Submodules ----------- - -GPy.likelihoods.noise_models.bernoulli_noise module ---------------------------------------------------- - -.. automodule:: GPy.likelihoods.noise_models.bernoulli_noise - :members: - :undoc-members: - :show-inheritance: - -GPy.likelihoods.noise_models.exponential_noise module ------------------------------------------------------ - -.. automodule:: GPy.likelihoods.noise_models.exponential_noise - :members: - :undoc-members: - :show-inheritance: - -GPy.likelihoods.noise_models.gamma_noise module ------------------------------------------------ - -.. automodule:: GPy.likelihoods.noise_models.gamma_noise - :members: - :undoc-members: - :show-inheritance: - -GPy.likelihoods.noise_models.gaussian_noise module --------------------------------------------------- - -.. automodule:: GPy.likelihoods.noise_models.gaussian_noise - :members: - :undoc-members: - :show-inheritance: - -GPy.likelihoods.noise_models.gp_transformations module ------------------------------------------------------- - -.. automodule:: GPy.likelihoods.noise_models.gp_transformations - :members: - :undoc-members: - :show-inheritance: - -GPy.likelihoods.noise_models.noise_distributions module -------------------------------------------------------- - -.. automodule:: GPy.likelihoods.noise_models.noise_distributions - :members: - :undoc-members: - :show-inheritance: - -GPy.likelihoods.noise_models.poisson_noise module -------------------------------------------------- - -.. automodule:: GPy.likelihoods.noise_models.poisson_noise - :members: - :undoc-members: - :show-inheritance: - -GPy.likelihoods.noise_models.student_t_noise module ---------------------------------------------------- - -.. automodule:: GPy.likelihoods.noise_models.student_t_noise - :members: - :undoc-members: - :show-inheritance: - - -Module contents ---------------- - -.. automodule:: GPy.likelihoods.noise_models - :members: - :undoc-members: - :show-inheritance: diff --git a/doc/GPy.likelihoods.rst b/doc/GPy.likelihoods.rst index 34d98739..323bb609 100644 --- a/doc/GPy.likelihoods.rst +++ b/doc/GPy.likelihoods.rst @@ -1,28 +1,29 @@ GPy.likelihoods package ======================= -Subpackages ------------ - -.. toctree:: - - GPy.likelihoods.noise_models - Submodules ---------- -GPy.likelihoods.ep module -------------------------- +GPy.likelihoods.bernoulli module +-------------------------------- -.. automodule:: GPy.likelihoods.ep +.. automodule:: GPy.likelihoods.bernoulli :members: :undoc-members: :show-inheritance: -GPy.likelihoods.ep_mixed_noise module -------------------------------------- +GPy.likelihoods.exponential module +---------------------------------- -.. automodule:: GPy.likelihoods.ep_mixed_noise +.. automodule:: GPy.likelihoods.exponential + :members: + :undoc-members: + :show-inheritance: + +GPy.likelihoods.gamma module +---------------------------- + +.. automodule:: GPy.likelihoods.gamma :members: :undoc-members: :show-inheritance: @@ -35,22 +36,6 @@ GPy.likelihoods.gaussian module :undoc-members: :show-inheritance: -GPy.likelihoods.gaussian_mixed_noise module -------------------------------------------- - -.. automodule:: GPy.likelihoods.gaussian_mixed_noise - :members: - :undoc-members: - :show-inheritance: - -GPy.likelihoods.laplace module ------------------------------- - -.. automodule:: GPy.likelihoods.laplace - :members: - :undoc-members: - :show-inheritance: - GPy.likelihoods.likelihood module --------------------------------- @@ -59,10 +44,34 @@ GPy.likelihoods.likelihood module :undoc-members: :show-inheritance: -GPy.likelihoods.noise_model_constructors module ------------------------------------------------ +GPy.likelihoods.link_functions module +------------------------------------- -.. automodule:: GPy.likelihoods.noise_model_constructors +.. automodule:: GPy.likelihoods.link_functions + :members: + :undoc-members: + :show-inheritance: + +GPy.likelihoods.mixed_noise module +---------------------------------- + +.. automodule:: GPy.likelihoods.mixed_noise + :members: + :undoc-members: + :show-inheritance: + +GPy.likelihoods.poisson module +------------------------------ + +.. automodule:: GPy.likelihoods.poisson + :members: + :undoc-members: + :show-inheritance: + +GPy.likelihoods.student_t module +-------------------------------- + +.. automodule:: GPy.likelihoods.student_t :members: :undoc-members: :show-inheritance: diff --git a/doc/GPy.mappings.rst b/doc/GPy.mappings.rst index c48cb06e..c13642cc 100644 --- a/doc/GPy.mappings.rst +++ b/doc/GPy.mappings.rst @@ -4,6 +4,14 @@ GPy.mappings package Submodules ---------- +GPy.mappings.additive module +---------------------------- + +.. automodule:: GPy.mappings.additive + :members: + :undoc-members: + :show-inheritance: + GPy.mappings.kernel module -------------------------- diff --git a/doc/GPy.models.rst b/doc/GPy.models.rst new file mode 100644 index 00000000..cb043afa --- /dev/null +++ b/doc/GPy.models.rst @@ -0,0 +1,198 @@ +GPy.models package +================== + +Submodules +---------- + +GPy.models.bayesian_gplvm module +-------------------------------- + +.. automodule:: GPy.models.bayesian_gplvm + :members: + :undoc-members: + :show-inheritance: + +GPy.models.bayesian_gplvm_minibatch module +------------------------------------------ + +.. automodule:: GPy.models.bayesian_gplvm_minibatch + :members: + :undoc-members: + :show-inheritance: + +GPy.models.bcgplvm module +------------------------- + +.. automodule:: GPy.models.bcgplvm + :members: + :undoc-members: + :show-inheritance: + +GPy.models.gp_classification module +----------------------------------- + +.. automodule:: GPy.models.gp_classification + :members: + :undoc-members: + :show-inheritance: + +GPy.models.gp_coregionalized_regression module +---------------------------------------------- + +.. automodule:: GPy.models.gp_coregionalized_regression + :members: + :undoc-members: + :show-inheritance: + +GPy.models.gp_heteroscedastic_regression module +----------------------------------------------- + +.. automodule:: GPy.models.gp_heteroscedastic_regression + :members: + :undoc-members: + :show-inheritance: + +GPy.models.gp_kronecker_gaussian_regression module +-------------------------------------------------- + +.. automodule:: GPy.models.gp_kronecker_gaussian_regression + :members: + :undoc-members: + :show-inheritance: + +GPy.models.gp_multioutput_regression module +------------------------------------------- + +.. automodule:: GPy.models.gp_multioutput_regression + :members: + :undoc-members: + :show-inheritance: + +GPy.models.gp_regression module +------------------------------- + +.. automodule:: GPy.models.gp_regression + :members: + :undoc-members: + :show-inheritance: + +GPy.models.gp_var_gauss module +------------------------------ + +.. automodule:: GPy.models.gp_var_gauss + :members: + :undoc-members: + :show-inheritance: + +GPy.models.gplvm module +----------------------- + +.. automodule:: GPy.models.gplvm + :members: + :undoc-members: + :show-inheritance: + +GPy.models.gradient_checker module +---------------------------------- + +.. automodule:: GPy.models.gradient_checker + :members: + :undoc-members: + :show-inheritance: + +GPy.models.mrd module +--------------------- + +.. automodule:: GPy.models.mrd + :members: + :undoc-members: + :show-inheritance: + +GPy.models.sparse_gp_classification module +------------------------------------------ + +.. automodule:: GPy.models.sparse_gp_classification + :members: + :undoc-members: + :show-inheritance: + +GPy.models.sparse_gp_coregionalized_regression module +----------------------------------------------------- + +.. automodule:: GPy.models.sparse_gp_coregionalized_regression + :members: + :undoc-members: + :show-inheritance: + +GPy.models.sparse_gp_minibatch module +------------------------------------- + +.. automodule:: GPy.models.sparse_gp_minibatch + :members: + :undoc-members: + :show-inheritance: + +GPy.models.sparse_gp_multioutput_regression module +-------------------------------------------------- + +.. automodule:: GPy.models.sparse_gp_multioutput_regression + :members: + :undoc-members: + :show-inheritance: + +GPy.models.sparse_gp_regression module +-------------------------------------- + +.. automodule:: GPy.models.sparse_gp_regression + :members: + :undoc-members: + :show-inheritance: + +GPy.models.sparse_gplvm module +------------------------------ + +.. automodule:: GPy.models.sparse_gplvm + :members: + :undoc-members: + :show-inheritance: + +GPy.models.ss_gplvm module +-------------------------- + +.. automodule:: GPy.models.ss_gplvm + :members: + :undoc-members: + :show-inheritance: + +GPy.models.ss_mrd module +------------------------ + +.. automodule:: GPy.models.ss_mrd + :members: + :undoc-members: + :show-inheritance: + +GPy.models.svigp_regression module +---------------------------------- + +.. automodule:: GPy.models.svigp_regression + :members: + :undoc-members: + :show-inheritance: + +GPy.models.warped_gp module +--------------------------- + +.. automodule:: GPy.models.warped_gp + :members: + :undoc-members: + :show-inheritance: + + +Module contents +--------------- + +.. automodule:: GPy.models + :members: + :undoc-members: + :show-inheritance: diff --git a/doc/GPy.plotting.matplot_dep.latent_space_visualizations.controllers.rst b/doc/GPy.plotting.matplot_dep.latent_space_visualizations.controllers.rst new file mode 100644 index 00000000..71826ed6 --- /dev/null +++ b/doc/GPy.plotting.matplot_dep.latent_space_visualizations.controllers.rst @@ -0,0 +1,30 @@ +GPy.plotting.matplot_dep.latent_space_visualizations.controllers package +======================================================================== + +Submodules +---------- + +GPy.plotting.matplot_dep.latent_space_visualizations.controllers.axis_event_controller module +--------------------------------------------------------------------------------------------- + +.. automodule:: GPy.plotting.matplot_dep.latent_space_visualizations.controllers.axis_event_controller + :members: + :undoc-members: + :show-inheritance: + +GPy.plotting.matplot_dep.latent_space_visualizations.controllers.imshow_controller module +----------------------------------------------------------------------------------------- + +.. automodule:: GPy.plotting.matplot_dep.latent_space_visualizations.controllers.imshow_controller + :members: + :undoc-members: + :show-inheritance: + + +Module contents +--------------- + +.. automodule:: GPy.plotting.matplot_dep.latent_space_visualizations.controllers + :members: + :undoc-members: + :show-inheritance: diff --git a/doc/GPy.plotting.matplot_dep.latent_space_visualizations.rst b/doc/GPy.plotting.matplot_dep.latent_space_visualizations.rst new file mode 100644 index 00000000..6e5cf4bd --- /dev/null +++ b/doc/GPy.plotting.matplot_dep.latent_space_visualizations.rst @@ -0,0 +1,17 @@ +GPy.plotting.matplot_dep.latent_space_visualizations package +============================================================ + +Subpackages +----------- + +.. toctree:: + + GPy.plotting.matplot_dep.latent_space_visualizations.controllers + +Module contents +--------------- + +.. automodule:: GPy.plotting.matplot_dep.latent_space_visualizations + :members: + :undoc-members: + :show-inheritance: diff --git a/doc/GPy.plotting.matplot_dep.rst b/doc/GPy.plotting.matplot_dep.rst new file mode 100644 index 00000000..77780708 --- /dev/null +++ b/doc/GPy.plotting.matplot_dep.rst @@ -0,0 +1,141 @@ +GPy.plotting.matplot_dep package +================================ + +Subpackages +----------- + +.. toctree:: + + GPy.plotting.matplot_dep.latent_space_visualizations + +Submodules +---------- + +GPy.plotting.matplot_dep.Tango module +------------------------------------- + +.. automodule:: GPy.plotting.matplot_dep.Tango + :members: + :undoc-members: + :show-inheritance: + +GPy.plotting.matplot_dep.base_plots module +------------------------------------------ + +.. automodule:: GPy.plotting.matplot_dep.base_plots + :members: + :undoc-members: + :show-inheritance: + +GPy.plotting.matplot_dep.dim_reduction_plots module +--------------------------------------------------- + +.. automodule:: GPy.plotting.matplot_dep.dim_reduction_plots + :members: + :undoc-members: + :show-inheritance: + +GPy.plotting.matplot_dep.img_plots module +----------------------------------------- + +.. automodule:: GPy.plotting.matplot_dep.img_plots + :members: + :undoc-members: + :show-inheritance: + +GPy.plotting.matplot_dep.inference_plots module +----------------------------------------------- + +.. automodule:: GPy.plotting.matplot_dep.inference_plots + :members: + :undoc-members: + :show-inheritance: + +GPy.plotting.matplot_dep.kernel_plots module +-------------------------------------------- + +.. automodule:: GPy.plotting.matplot_dep.kernel_plots + :members: + :undoc-members: + :show-inheritance: + +GPy.plotting.matplot_dep.mapping_plots module +--------------------------------------------- + +.. automodule:: GPy.plotting.matplot_dep.mapping_plots + :members: + :undoc-members: + :show-inheritance: + +GPy.plotting.matplot_dep.maps module +------------------------------------ + +.. automodule:: GPy.plotting.matplot_dep.maps + :members: + :undoc-members: + :show-inheritance: + +GPy.plotting.matplot_dep.models_plots module +-------------------------------------------- + +.. automodule:: GPy.plotting.matplot_dep.models_plots + :members: + :undoc-members: + :show-inheritance: + +GPy.plotting.matplot_dep.netpbmfile module +------------------------------------------ + +.. automodule:: GPy.plotting.matplot_dep.netpbmfile + :members: + :undoc-members: + :show-inheritance: + +GPy.plotting.matplot_dep.priors_plots module +-------------------------------------------- + +.. automodule:: GPy.plotting.matplot_dep.priors_plots + :members: + :undoc-members: + :show-inheritance: + +GPy.plotting.matplot_dep.ssgplvm module +--------------------------------------- + +.. automodule:: GPy.plotting.matplot_dep.ssgplvm + :members: + :undoc-members: + :show-inheritance: + +GPy.plotting.matplot_dep.svig_plots module +------------------------------------------ + +.. automodule:: GPy.plotting.matplot_dep.svig_plots + :members: + :undoc-members: + :show-inheritance: + +GPy.plotting.matplot_dep.variational_plots module +------------------------------------------------- + +.. automodule:: GPy.plotting.matplot_dep.variational_plots + :members: + :undoc-members: + :show-inheritance: + +GPy.plotting.matplot_dep.visualize module +----------------------------------------- + +.. automodule:: GPy.plotting.matplot_dep.visualize + :members: + :undoc-members: + :show-inheritance: + + +Module contents +--------------- + +.. automodule:: GPy.plotting.matplot_dep + :members: + :undoc-members: + :show-inheritance: diff --git a/doc/GPy.plotting.rst b/doc/GPy.plotting.rst new file mode 100644 index 00000000..af035515 --- /dev/null +++ b/doc/GPy.plotting.rst @@ -0,0 +1,17 @@ +GPy.plotting package +==================== + +Subpackages +----------- + +.. toctree:: + + GPy.plotting.matplot_dep + +Module contents +--------------- + +.. automodule:: GPy.plotting + :members: + :undoc-members: + :show-inheritance: diff --git a/doc/GPy.rst b/doc/GPy.rst index cd1afd29..7f74fb5b 100644 --- a/doc/GPy.rst +++ b/doc/GPy.rst @@ -13,6 +13,8 @@ Subpackages GPy.likelihoods GPy.mappings GPy.models_modules + GPy.models + GPy.plotting GPy.testing GPy.util diff --git a/doc/GPy.testing.rst b/doc/GPy.testing.rst index fcf9dc30..45bb307f 100644 --- a/doc/GPy.testing.rst +++ b/doc/GPy.testing.rst @@ -4,30 +4,6 @@ GPy.testing package Submodules ---------- -GPy.testing.bcgplvm_tests module --------------------------------- - -.. automodule:: GPy.testing.bcgplvm_tests - :members: - :undoc-members: - :show-inheritance: - -GPy.testing.bgplvm_tests module -------------------------------- - -.. automodule:: GPy.testing.bgplvm_tests - :members: - :undoc-members: - :show-inheritance: - -GPy.testing.cgd_tests module ----------------------------- - -.. automodule:: GPy.testing.cgd_tests - :members: - :undoc-members: - :show-inheritance: - GPy.testing.examples_tests module --------------------------------- @@ -36,18 +12,26 @@ GPy.testing.examples_tests module :undoc-members: :show-inheritance: -GPy.testing.gp_transformation_tests module ------------------------------------------- +GPy.testing.fitc module +----------------------- -.. automodule:: GPy.testing.gp_transformation_tests +.. automodule:: GPy.testing.fitc :members: :undoc-members: :show-inheritance: -GPy.testing.gplvm_tests module ------------------------------- +GPy.testing.index_operations_tests module +----------------------------------------- -.. automodule:: GPy.testing.gplvm_tests +.. automodule:: GPy.testing.index_operations_tests + :members: + :undoc-members: + :show-inheritance: + +GPy.testing.inference_tests module +---------------------------------- + +.. automodule:: GPy.testing.inference_tests :members: :undoc-members: :show-inheritance: @@ -68,18 +52,34 @@ GPy.testing.likelihood_tests module :undoc-members: :show-inheritance: -GPy.testing.mapping_tests module --------------------------------- +GPy.testing.model_tests module +------------------------------ -.. automodule:: GPy.testing.mapping_tests +.. automodule:: GPy.testing.model_tests :members: :undoc-members: :show-inheritance: -GPy.testing.mrd_tests module ----------------------------- +GPy.testing.observable_tests module +----------------------------------- -.. automodule:: GPy.testing.mrd_tests +.. automodule:: GPy.testing.observable_tests + :members: + :undoc-members: + :show-inheritance: + +GPy.testing.parameterized_tests module +-------------------------------------- + +.. automodule:: GPy.testing.parameterized_tests + :members: + :undoc-members: + :show-inheritance: + +GPy.testing.pickle_tests module +------------------------------- + +.. automodule:: GPy.testing.pickle_tests :members: :undoc-members: :show-inheritance: @@ -92,38 +92,6 @@ GPy.testing.prior_tests module :undoc-members: :show-inheritance: -GPy.testing.psi_stat_expectation_tests module ---------------------------------------------- - -.. automodule:: GPy.testing.psi_stat_expectation_tests - :members: - :undoc-members: - :show-inheritance: - -GPy.testing.psi_stat_gradient_tests module ------------------------------------------- - -.. automodule:: GPy.testing.psi_stat_gradient_tests - :members: - :undoc-members: - :show-inheritance: - -GPy.testing.sparse_gplvm_tests module -------------------------------------- - -.. automodule:: GPy.testing.sparse_gplvm_tests - :members: - :undoc-members: - :show-inheritance: - -GPy.testing.unit_tests module ------------------------------ - -.. automodule:: GPy.testing.unit_tests - :members: - :undoc-members: - :show-inheritance: - Module contents --------------- diff --git a/doc/GPy.util.latent_space_visualizations.controllers.rst b/doc/GPy.util.latent_space_visualizations.controllers.rst deleted file mode 100644 index a88c1f5c..00000000 --- a/doc/GPy.util.latent_space_visualizations.controllers.rst +++ /dev/null @@ -1,30 +0,0 @@ -GPy.util.latent_space_visualizations.controllers package -======================================================== - -Submodules ----------- - -GPy.util.latent_space_visualizations.controllers.axis_event_controller module ------------------------------------------------------------------------------ - -.. automodule:: GPy.util.latent_space_visualizations.controllers.axis_event_controller - :members: - :undoc-members: - :show-inheritance: - -GPy.util.latent_space_visualizations.controllers.imshow_controller module -------------------------------------------------------------------------- - -.. automodule:: GPy.util.latent_space_visualizations.controllers.imshow_controller - :members: - :undoc-members: - :show-inheritance: - - -Module contents ---------------- - -.. automodule:: GPy.util.latent_space_visualizations.controllers - :members: - :undoc-members: - :show-inheritance: diff --git a/doc/GPy.util.latent_space_visualizations.rst b/doc/GPy.util.latent_space_visualizations.rst deleted file mode 100644 index d8cbd843..00000000 --- a/doc/GPy.util.latent_space_visualizations.rst +++ /dev/null @@ -1,17 +0,0 @@ -GPy.util.latent_space_visualizations package -============================================ - -Subpackages ------------ - -.. toctree:: - - GPy.util.latent_space_visualizations.controllers - -Module contents ---------------- - -.. automodule:: GPy.util.latent_space_visualizations - :members: - :undoc-members: - :show-inheritance: diff --git a/doc/GPy.util.rst b/doc/GPy.util.rst index 1c35a7ba..e50efdfb 100644 --- a/doc/GPy.util.rst +++ b/doc/GPy.util.rst @@ -1,24 +1,9 @@ GPy.util package ================ -Subpackages ------------ - -.. toctree:: - - GPy.util.latent_space_visualizations - Submodules ---------- -GPy.util.Tango module ---------------------- - -.. automodule:: GPy.util.Tango - :members: - :undoc-members: - :show-inheritance: - GPy.util.block_matrices module ------------------------------ @@ -27,6 +12,14 @@ GPy.util.block_matrices module :undoc-members: :show-inheritance: +GPy.util.caching module +----------------------- + +.. automodule:: GPy.util.caching + :members: + :undoc-members: + :show-inheritance: + GPy.util.classification module ------------------------------ @@ -51,6 +44,14 @@ GPy.util.datasets module :undoc-members: :show-inheritance: +GPy.util.debug module +--------------------- + +.. automodule:: GPy.util.debug + :members: + :undoc-members: + :show-inheritance: + GPy.util.decorators module -------------------------- @@ -75,6 +76,30 @@ GPy.util.erfcx module :undoc-members: :show-inheritance: +GPy.util.functions module +------------------------- + +.. automodule:: GPy.util.functions + :members: + :undoc-members: + :show-inheritance: + +GPy.util.gpu_init module +------------------------ + +.. automodule:: GPy.util.gpu_init + :members: + :undoc-members: + :show-inheritance: + +GPy.util.initialization module +------------------------------ + +.. automodule:: GPy.util.initialization + :members: + :undoc-members: + :show-inheritance: + GPy.util.linalg module ---------------------- @@ -83,6 +108,14 @@ GPy.util.linalg module :undoc-members: :show-inheritance: +GPy.util.linalg_gpu module +-------------------------- + +.. automodule:: GPy.util.linalg_gpu + :members: + :undoc-members: + :show-inheritance: + GPy.util.ln_diff_erfs module ---------------------------- @@ -107,6 +140,14 @@ GPy.util.mocap module :undoc-members: :show-inheritance: +GPy.util.mpi module +------------------- + +.. automodule:: GPy.util.mpi + :members: + :undoc-members: + :show-inheritance: + GPy.util.multioutput module --------------------------- @@ -123,18 +164,26 @@ GPy.util.netpbmfile module :undoc-members: :show-inheritance: -GPy.util.plot module --------------------- +GPy.util.normalizer module +-------------------------- -.. automodule:: GPy.util.plot +.. automodule:: GPy.util.normalizer :members: :undoc-members: :show-inheritance: -GPy.util.plot_latent module ---------------------------- +GPy.util.parallel module +------------------------ -.. automodule:: GPy.util.plot_latent +.. automodule:: GPy.util.parallel + :members: + :undoc-members: + :show-inheritance: + +GPy.util.pca module +------------------- + +.. automodule:: GPy.util.pca :members: :undoc-members: :show-inheritance: @@ -155,14 +204,6 @@ GPy.util.subarray_and_sorting module :undoc-members: :show-inheritance: -GPy.util.symbolic module ------------------------- - -.. automodule:: GPy.util.symbolic - :members: - :undoc-members: - :show-inheritance: - GPy.util.univariate_Gaussian module ----------------------------------- @@ -171,14 +212,6 @@ GPy.util.univariate_Gaussian module :undoc-members: :show-inheritance: -GPy.util.visualize module -------------------------- - -.. automodule:: GPy.util.visualize - :members: - :undoc-members: - :show-inheritance: - GPy.util.warping_functions module --------------------------------- diff --git a/doc/conf.py b/doc/conf.py index 7b71a897..91a6c75b 100644 --- a/doc/conf.py +++ b/doc/conf.py @@ -11,6 +11,30 @@ # All configuration values have a default; values that are commented out # serve to show the default. +#autodoc_default_flags = ['members', 'show-inheritance', 'private-members', 'special-members'] +#autodoc_default_flags = ['private-members', 'special-members'] +#autodoc_default_flags = 'private-members' +#autodoc_member_order = "source" + +#def autodoc_skip_member(app, what, name, obj, skip, options): + #exclusions = ('__weakref__', # special-members + #'__doc__', '__module__', '__dict__', # undoc-members + #) + #exclude = name in exclusions + + #inclusions = ('_src') + #include = name in inclusions + #if include: + #print app, what, name, obj, skip, options + #return False + #return skip or exclude + +#def setup(app): + ##app.connect('autodoc-process-docstring', cut_lines(2)) + ##app.connect('autodoc_default_flags', autodoc_default_flags) + ##app.connect('autodoc_member_order', autodoc_member_order) + #app.connect('autodoc-skip-member', autodoc_skip_member) + import sys import os @@ -111,10 +135,11 @@ MOCK_MODULES = ['sympy', for mod_name in MOCK_MODULES: sys.modules[mod_name] = Mock() + # ----------------------- READTHEDOCS ------------------ on_rtd = os.environ.get('READTHEDOCS', None) == 'True' -on_rtd = True +#on_rtd = True if on_rtd: sys.path.append(os.path.abspath('../GPy')) @@ -126,7 +151,8 @@ if on_rtd: proc = subprocess.Popen("ls ../", stdout=subprocess.PIPE, shell=True) (out, err) = proc.communicate() print "program output:", out - proc = subprocess.Popen("sphinx-apidoc -f -o . ../GPy", stdout=subprocess.PIPE, shell=True) + #Lets regenerate our rst files from the source, -P adds private modules (i.e kern._src) + proc = subprocess.Popen("sphinx-apidoc -P -f -o . ../GPy", stdout=subprocess.PIPE, shell=True) (out, err) = proc.communicate() print "program output:", out #proc = subprocess.Popen("whereis numpy", stdout=subprocess.PIPE, shell=True) @@ -397,5 +423,3 @@ epub_copyright = u'2013, Author' # Allow duplicate toc entries. #epub_tocdup = True - -autodoc_member_order = "source" diff --git a/doc/index.rst b/doc/index.rst index f6207963..f72a860e 100644 --- a/doc/index.rst +++ b/doc/index.rst @@ -5,15 +5,22 @@ Welcome to GPy's documentation! =============================== -For a quick start, you can have a look at one of the tutorials: -* `Basic Gaussian process regression `_ -* `Interacting with models `_ -* `A kernel overview `_ -* `Writing new kernels `_ -* `Writing new models `_ +`GPy `_ is a Gaussian Process (GP) framework written in Python, from the Sheffield machine learning group. -You may also be interested by some examples in the GPy/examples folder. +The `GPy homepage `_ contains tutorials for users and further information on the project, including installation instructions. +This documentation is mostly aimed at developers interacting closely with the code-base. + +The code can be found on our `Github project page `_. It is open source and provided under the BSD license. + +.. * `Basic Gaussian process regression `_ +.. * `Interacting with models `_ +.. * `A kernel overview `_ +.. * `Writing new kernels `_ +.. * `Writing new models `_ +.. * `Parameterization handles `_ + +.. You may also be interested by some examples in the GPy/examples folder. The detailed Developers Documentation is listed below ===================================================== @@ -21,8 +28,8 @@ The detailed Developers Documentation is listed below Contents: .. toctree:: - :maxdepth: 4 - + :maxdepth: 2 + GPy diff --git a/doc/installation.rst b/doc/installation.rst new file mode 100644 index 00000000..35352272 --- /dev/null +++ b/doc/installation.rst @@ -0,0 +1,31 @@ +============== + Installation +============== + + +Linux +============ + + +Windows +====================== +One easy way to get a Python distribution with the required packages is to use the Anaconda environment from Continuum Analytics. + +* Download and install the free version of Anaconda according to your operating system from `their website `_. +* Open a (new) terminal window: + + * Navigate to Applications/Accessories/cmd, or + * open *anaconda Command Prompt* from windows *start* + +You should now be able to launch a Python interpreter by typing *ipython* in the terminal. In the ipython prompt, you can check your installation by importing the libraries we will need later: +:: + $ import numpy + $ import pylab + +To install the latest version of GPy, *git* is required. A *git* client on Windows can be found `here `_. It is recommened to install with the option "*Use Git from the Windows Command Prompt*". Then, GPy can be installed with the following command +:: + pip install git+https://github.com/SheffieldML/GPy.git@devel + +MacOSX +=================================== + diff --git a/doc/log.txt b/doc/log.txt new file mode 100644 index 00000000..1b563edd --- /dev/null +++ b/doc/log.txt @@ -0,0 +1,176 @@ +/home/alans/Work/GPy/GPy/__init__.py:docstring of GPy.load:1: WARNING: Inline interpreted text or phrase reference start-string without end-string. +/home/alans/Work/GPy/GPy/core/gp.py:docstring of GPy.core.gp.GP.optimize:8: ERROR: Unknown interpreted text role "module". +/home/alans/Work/GPy/GPy/core/gp.py:docstring of GPy.core.gp.GP.predictive_gradients:5: ERROR: Unexpected indentation. +/home/alans/Work/GPy/GPy/core/gp.py:docstring of GPy.core.gp.GP.predictive_gradients:8: WARNING: Block quote ends without a blank line; unexpected unindent. +/home/alans/Work/GPy/GPy/core/model.py:docstring of GPy.core.model.Model.optimize_restarts:29: WARNING: Explicit markup ends without a blank line; unexpected unindent. +/home/alans/Work/GPy/doc/GPy.core.rst:65: WARNING: autodoc: failed to import module u'GPy.core.symbolic'; the following exception was raised: +Traceback (most recent call last): + File "/home/alans/anaconda/envs/GPy/lib/python2.7/site-packages/sphinx/ext/autodoc.py", line 335, in import_object + __import__(self.modname) + File "/home/alans/Work/GPy/GPy/core/symbolic.py", line 10, in + from sympy.utilities.lambdify import lambdastr, _imp_namespace, _get_namespace +ImportError: No module named lambdify +/home/alans/Work/GPy/GPy/core/parameterization/parameter_core.py:docstring of GPy.core.parameterization.parameter_core.Indexable.unset_priors:1: WARNING: Inline emphasis start-string without end-string. +/home/alans/Work/GPy/GPy/core/parameterization/parameter_core.py:docstring of GPy.core.parameterization.parameter_core.Nameable.hierarchy_name:4: WARNING: Field list ends without a blank line; unexpected unindent. +/home/alans/Work/GPy/GPy/core/parameterization/parameter_core.py:docstring of GPy.core.parameterization.parameter_core.Observable.notify_observers:5: SEVERE: Unexpected section title or transition. + +^^^^^^^^^^^^^^^^ +/home/alans/Work/GPy/GPy/core/parameterization/parameter_core.py:docstring of GPy.core.parameterization.parameter_core.Observable.notify_observers:6: WARNING: Definition list ends without a blank line; unexpected unindent. +/home/alans/Work/GPy/GPy/core/parameterization/parameter_core.py:docstring of GPy.core.parameterization.parameter_core.Parameterizable.traverse:1: WARNING: Inline emphasis start-string without end-string. +/home/alans/Work/GPy/GPy/core/parameterization/parameter_core.py:docstring of GPy.core.parameterization.parameter_core.Parameterizable.traverse:1: WARNING: Inline strong start-string without end-string. +/home/alans/Work/GPy/GPy/core/parameterization/parameterized.py:docstring of GPy.core.parameterization.parameterized.Parameterized:18: ERROR: Unexpected indentation. +/home/alans/Work/GPy/GPy/core/parameterization/parameterized.py:docstring of GPy.core.parameterization.parameterized.Parameterized:20: WARNING: Block quote ends without a blank line; unexpected unindent. +/home/alans/Work/GPy/GPy/core/parameterization/ties_and_remappings.py:docstring of GPy.core.parameterization.ties_and_remappings.Tie:18: SEVERE: Unexpected section title or transition. + +================================ +/home/alans/Work/GPy/GPy/kern/_src/coregionalize.py:docstring of GPy.kern._src.coregionalize.Coregionalize:5: ERROR: Unexpected indentation. +/home/alans/Work/GPy/doc/GPy.kern._src.rst:73: WARNING: autodoc: failed to import module u'GPy.kern._src.hierarchical'; the following exception was raised: +Traceback (most recent call last): + File "/home/alans/anaconda/envs/GPy/lib/python2.7/site-packages/sphinx/ext/autodoc.py", line 335, in import_object + __import__(self.modname) + File "/home/alans/Work/GPy/GPy/kern/_src/hierarchical.py", line 4, in + from kernpart import Kernpart +ImportError: No module named kernpart +/home/alans/Work/GPy/GPy/kern/_src/independent_outputs.py:docstring of GPy.kern._src.independent_outputs.IndependentOutputs:9: WARNING: Field list ends without a blank line; unexpected unindent. +/home/alans/Work/GPy/GPy/kern/_src/stationary.py:docstring of GPy.kern._src.stationary.Stationary:12: WARNING: Block quote ends without a blank line; unexpected unindent. +/home/alans/Work/GPy/GPy/kern/_src/stationary.py:docstring of GPy.kern._src.stationary.Stationary:22: ERROR: Unexpected indentation. +/home/alans/Work/GPy/GPy/kern/_src/stationary.py:docstring of GPy.kern._src.stationary.Stationary:23: WARNING: Block quote ends without a blank line; unexpected unindent. +/home/alans/Work/GPy/doc/GPy.kern._src.rst:177: WARNING: autodoc: failed to import module u'GPy.kern._src.symbolic'; the following exception was raised: +Traceback (most recent call last): + File "/home/alans/anaconda/envs/GPy/lib/python2.7/site-packages/sphinx/ext/autodoc.py", line 335, in import_object + __import__(self.modname) + File "/home/alans/Work/GPy/GPy/kern/_src/symbolic.py", line 5, in + from ...core.symbolic import Symbolic_core + File "/home/alans/Work/GPy/GPy/core/symbolic.py", line 10, in + from sympy.utilities.lambdify import lambdastr, _imp_namespace, _get_namespace +ImportError: No module named lambdify +/home/alans/Work/GPy/GPy/models/gp_kronecker_gaussian_regression.py:docstring of GPy.models.gp_kronecker_gaussian_regression.GPKroneckerGaussianRegression:13: ERROR: Unexpected indentation. +/home/alans/Work/GPy/GPy/models/gp_kronecker_gaussian_regression.py:docstring of GPy.models.gp_kronecker_gaussian_regression.GPKroneckerGaussianRegression:18: WARNING: Block quote ends without a blank line; unexpected unindent. +/home/alans/Work/GPy/GPy/models/gp_var_gauss.py:docstring of GPy.models.gp_var_gauss.GPVariationalGaussianApproximation:9: WARNING: Definition list ends without a blank line; unexpected unindent. +/home/alans/Work/GPy/GPy/models/mrd.py:docstring of GPy.models.mrd.MRD:32: WARNING: Field list ends without a blank line; unexpected unindent. +/home/alans/Work/GPy/GPy/models/mrd.py:docstring of GPy.models.mrd.MRD:32: WARNING: Inline interpreted text or phrase reference start-string without end-string. +/home/alans/Work/GPy/GPy/models/mrd.py:docstring of GPy.models.mrd.MRD:34: WARNING: Definition list ends without a blank line; unexpected unindent. +/home/alans/Work/GPy/GPy/models/sparse_gp_minibatch.py:docstring of GPy.models.sparse_gp_minibatch.SparseGPMiniBatch:2: WARNING: Block quote ends without a blank line; unexpected unindent. +/home/alans/Work/GPy/GPy/plotting/matplot_dep/netpbmfile.py:docstring of GPy.plotting.matplot_dep.netpbmfile.imread:6: SEVERE: Unexpected section title. + +Examples +-------- +/home/alans/Work/GPy/GPy/plotting/matplot_dep/netpbmfile.py:docstring of GPy.plotting.matplot_dep.netpbmfile.imsave:4: SEVERE: Unexpected section title. + +Examples +-------- +/home/alans/Work/GPy/GPy/testing/likelihood_tests.py:docstring of GPy.testing.likelihood_tests.dparam_checkgrad:6: ERROR: Unexpected indentation. +/home/alans/Work/GPy/GPy/testing/likelihood_tests.py:docstring of GPy.testing.likelihood_tests.dparam_checkgrad:7: WARNING: Block quote ends without a blank line; unexpected unindent. +/home/alans/Work/GPy/GPy/testing/likelihood_tests.py:docstring of GPy.testing.likelihood_tests.dparam_partial:7: WARNING: Definition list ends without a blank line; unexpected unindent. +/home/alans/Work/GPy/GPy/testing/likelihood_tests.py:docstring of GPy.testing.likelihood_tests.dparam_partial:9: ERROR: Unexpected indentation. +/home/alans/Work/GPy/GPy/util/datasets.py:docstring of GPy.util.datasets.hapmap3:7: WARNING: Block quote ends without a blank line; unexpected unindent. +/home/alans/Work/GPy/doc/GPy.util.rst:2: SEVERE: Duplicate ID: "module-GPy.util.diag". +/home/alans/Work/GPy/GPy/util/netpbmfile.py:docstring of GPy.util.netpbmfile.imread:6: SEVERE: Unexpected section title. + +Examples +-------- +/home/alans/Work/GPy/GPy/util/netpbmfile.py:docstring of GPy.util.netpbmfile.imsave:4: SEVERE: Unexpected section title. + +Examples +-------- +/home/alans/Work/GPy/doc/GPy.util.rst:2: SEVERE: Duplicate ID: "module-GPy.util.subarray_and_sorting". +/home/alans/Work/GPy/GPy/util/subarray_and_sorting.py:docstring of GPy.util.subarray_and_sorting.common_subarrays:8: ERROR: Unexpected indentation. +/home/alans/Work/GPy/GPy/util/subarray_and_sorting.py:docstring of GPy.util.subarray_and_sorting.common_subarrays:11: SEVERE: Unexpected section title. + +Examples: +========= +/home/alans/Work/GPy/GPy/util/subarray_and_sorting.py:docstring of GPy.util.subarray_and_sorting.common_subarrays:19: ERROR: Unexpected indentation. +/home/alans/Work/GPy/GPy/util/subarray_and_sorting.py:docstring of GPy.util.subarray_and_sorting.common_subarrays:21: WARNING: Block quote ends without a blank line; unexpected unindent. +/home/alans/Work/GPy/doc/installation.rst:22: ERROR: Unexpected indentation. +/home/alans/Work/GPy/doc/installation.rst:27: ERROR: Unexpected indentation. +/home/alans/Work/GPy/doc/tuto_creating_new_kernels.rst:58: WARNING: Inline literal start-string without end-string. +/home/alans/Work/GPy/doc/tuto_creating_new_models.rst:24: ERROR: Unknown target name: "parameterized". +/home/alans/Work/GPy/doc/tuto_interacting_with_models.rst:83: WARNING: Title underline too short. + +Interacting with Parameters: +======================= +/home/alans/Work/GPy/doc/tuto_interacting_with_models.rst:83: WARNING: Title underline too short. + +Interacting with Parameters: +======================= +/home/alans/Work/GPy/doc/tuto_interacting_with_models.rst:109: WARNING: Title underline too short. + +Regular expressions +---------------- +/home/alans/Work/GPy/doc/tuto_interacting_with_models.rst:164: WARNING: Title underline too short. + +Setting and fetching parameters `parameter_array` +------------------------------------------ +/home/alans/Work/GPy/doc/tuto_interacting_with_models.rst:164: WARNING: Title underline too short. + +Setting and fetching parameters `parameter_array` +------------------------------------------ +/home/alans/Work/GPy/doc/tuto_interacting_with_models.rst:220: WARNING: Title underline too short. + +Getting the model parameter's gradients +============================ +/home/alans/Work/GPy/doc/tuto_interacting_with_models.rst:220: WARNING: Title underline too short. + +Getting the model parameter's gradients +============================ +/home/alans/Work/GPy/doc/tuto_interacting_with_models.rst:236: WARNING: Title underline too short. + +Adjusting the model's constraints +================================ +/home/alans/Work/GPy/doc/tuto_interacting_with_models.rst:236: WARNING: Title underline too short. + +Adjusting the model's constraints +================================ +/home/alans/Work/GPy/doc/tuto_interacting_with_models.rst:287: WARNING: Title underline too short. + +Available Constraints +============== +/home/alans/Work/GPy/doc/tuto_interacting_with_models.rst:287: WARNING: Title underline too short. + +Available Constraints +============== +/home/alans/Work/GPy/doc/tuto_interacting_with_models.rst:299: WARNING: Title underline too short. + +Tying Parameters +============ +/home/alans/Work/GPy/doc/tuto_interacting_with_models.rst:299: WARNING: Title underline too short. + +Tying Parameters +============ +/home/alans/Work/GPy/doc/tuto_parameterized.rst:3: WARNING: Title overline too short. + +******************* +Parameterization handling +******************* +/home/alans/Work/GPy/doc/tuto_parameterized.rst:10: WARNING: Title underline too short. + +Parameter handles +============== +/home/alans/Work/GPy/doc/tuto_parameterized.rst:16: WARNING: Title underline too short. + +:py:class:`~GPy.core.parameterization.parameterized.Parameterized` +========== +/home/alans/Work/GPy/doc/tuto_parameterized.rst:16: WARNING: Title underline too short. + +:py:class:`~GPy.core.parameterization.parameterized.Parameterized` +========== +/home/alans/Work/GPy/doc/tuto_parameterized.rst:21: WARNING: Title underline too short. + +:py:class:`~GPy.core.parameterization.param.Param` +=========== +/home/alans/Work/GPy/doc/tuto_parameterized.rst:21: WARNING: Title underline too short. + +:py:class:`~GPy.core.parameterization.param.Param` +=========== +/home/alans/Work/GPy/doc/installation.rst:: WARNING: document isn't included in any toctree +/home/alans/Work/GPy/doc/kernel_implementation.rst:: WARNING: document isn't included in any toctree +/home/alans/Work/GPy/doc/modules.rst:: WARNING: document isn't included in any toctree +/home/alans/Work/GPy/doc/tuto_GP_regression.rst:: WARNING: document isn't included in any toctree +/home/alans/Work/GPy/doc/tuto_creating_new_kernels.rst:: WARNING: document isn't included in any toctree +/home/alans/Work/GPy/doc/tuto_creating_new_models.rst:: WARNING: document isn't included in any toctree +/home/alans/Work/GPy/doc/tuto_interacting_with_models.rst:: WARNING: document isn't included in any toctree +/home/alans/Work/GPy/doc/tuto_kernel_overview.rst:: WARNING: document isn't included in any toctree +/home/alans/Work/GPy/doc/tuto_parameterized.rst:: WARNING: document isn't included in any toctree +WARNING: dvipng command 'dvipng' cannot be run (needed for math display), check the pngmath_dvipng setting +/home/alans/Work/GPy/doc/tuto_interacting_with_models.rst:336: WARNING: undefined label: creating_new_kernels (if the link has no caption the label must precede a section header) +WARNING: html_static_path entry u'/home/alans/Work/GPy/doc/_static' does not exist diff --git a/doc/tuto_GP_regression.rst b/doc/tuto_GP_regression.rst index fe0bdca1..85c53fb4 100644 --- a/doc/tuto_GP_regression.rst +++ b/doc/tuto_GP_regression.rst @@ -23,15 +23,15 @@ Note that the observations Y include some noise. The first step is to define the covariance kernel we want to use for the model. We choose here a kernel based on Gaussian kernel (i.e. rbf or square exponential):: - kernel = GPy.kern.rbf(input_dim=1, variance=1., lengthscale=1.) + kernel = GPy.kern.RBF(input_dim=1, variance=1., lengthscale=1.) The parameter ``input_dim`` stands for the dimension of the input space. The parameters ``variance`` and ``lengthscale`` are optional. Many other kernels are implemented such as: -* linear (``GPy.kern.linear``) -* exponential kernel (``GPy.kern.exponential``) -* Matern 3/2 (``GPy.kern.Matern32``) -* Matern 5/2 (``GPy.kern.Matern52``) -* spline (``GPy.kern.spline``) +* linear (:py:class:`~GPy.kern.Linear`) +* exponential kernel (:py:class:`GPy.kern.Exponential`) +* Matern 3/2 (:py:class:`GPy.kern.Matern32`) +* Matern 5/2 (:py:class:`GPy.kern.Matern52`) +* spline (:py:class:`GPy.kern.Spline`) * and many others... The inputs required for building the model are the observations and the kernel:: @@ -45,38 +45,28 @@ By default, some observation noise is added to the modle. The functions ``print` gives the following output: :: - Marginal log-likelihood: -4.479e+00 - Name | Value | Constraints | Ties | Prior - ----------------------------------------------------------------- - rbf_variance | 1.0000 | | | - rbf_lengthscale | 1.0000 | | | - noise_variance | 1.0000 | | | - + Name : GP regression + Log-likelihood : -22.8178418808 + Number of Parameters : 3 + Parameters: + GP_regression. | Value | Constraint | Prior | Tied to + rbf.variance | 1.0 | +ve | | + rbf.lengthscale | 1.0 | +ve | | + Gaussian_noise.variance | 1.0 | +ve | | + .. figure:: Figures/tuto_GP_regression_m1.png :align: center :height: 350px - GP regression model before optimization of the parameters. The shaded region corresponds to 95% confidence intervals (ie +/- 2 standard deviation). + GP regression model before optimization of the parameters. The shaded region corresponds to ~95% confidence intervals (ie +/- 2 standard deviation). -The default values of the kernel parameters may not be relevant for the current data (for example, the confidence intervals seems too wide on the previous figure). A common approach is to find the values of the parameters that maximize the likelihood of the data. There are two steps for doing that with GPy: +The default values of the kernel parameters may not be relevant for +the current data (for example, the confidence intervals seems too wide +on the previous figure). A common approach is to find the values of +the parameters that maximize the likelihood of the data. It as easy as +calling ``m.optimize`` in GPy:: -* Constrain the parameters of the kernel to ensure the kernel will always be a valid covariance structure (For example, we don\'t want some variances to be negative!). -* Run the optimization - -There are various ways to constrain the parameters of the kernel. The most basic is to constrain all the parameters to be positive:: - - m.ensure_default_constraints() # or similarly m.constrain_positive('') - -but it is also possible to set a range on to constrain one parameter to be fixed. The parameter of ``m.constrain_positive`` is a regular expression that matches the name of the parameters to be constrained (as seen in ``print m``). For example, if we want the variance to be positive, the lengthscale to be in [1,10] and the noise variance to be fixed we can write:: - - m.unconstrain('') # may be used to remove the previous constrains - m.constrain_positive('.*rbf_variance') - m.constrain_bounded('.*lengthscale',1.,10. ) - m.constrain_fixed('.*noise',0.0025) - -Once the constrains have been imposed, the model can be optimized:: - - m.optimize() + m.optimize() If we want to perform some restarts to try to improve the result of the optimization, we can use the ``optimize_restart`` function:: @@ -84,13 +74,15 @@ If we want to perform some restarts to try to improve the result of the optimiza Once again, we can use ``print(m)`` and ``m.plot()`` to look at the resulting model resulting model:: - Marginal log-likelihood: 3.603e+01 - Name | Value | Constraints | Ties | Prior - ----------------------------------------------------------------- - rbf_variance | 0.8151 | (+ve) | | - rbf_lengthscale | 1.8037 | (1.0, 10.0) | | - noise_variance | 0.0025 | Fixed | | - + Name : GP regression + Log-likelihood : 11.947469082 + Number of Parameters : 3 + Parameters: + GP_regression. | Value | Constraint | Prior | Tied to + rbf.variance | 0.74229417323 | +ve | | + rbf.lengthscale | 1.43020495724 | +ve | | + Gaussian_noise.variance | 0.00325654460991 | +ve | | + .. figure:: Figures/tuto_GP_regression_m2.png :align: center :height: 350px @@ -113,30 +105,36 @@ Here is a 2 dimensional example:: Y = np.sin(X[:,0:1]) * np.sin(X[:,1:2])+np.random.randn(50,1)*0.05 # define kernel - ker = GPy.kern.Matern52(2,ARD=True) + GPy.kern.white(2) + ker = GPy.kern.Matern52(2,ARD=True) + GPy.kern.White(2) # create simple GP model m = GPy.models.GPRegression(X,Y,ker) - # contrain all parameters to be positive - m.constrain_positive('') - # optimize and plot - m.optimize('tnc', max_f_eval = 1000) + m.optimize(max_f_eval = 1000) m.plot() print(m) The flag ``ARD=True`` in the definition of the Matern kernel specifies that we want one lengthscale parameter per dimension (ie the GP is not isotropic). The output of the last two lines is:: - Marginal log-likelihood: 6.682e+01 - Name | Value | Constraints | Ties | Prior - --------------------------------------------------------------------- - Mat52_variance | 0.3860 | (+ve) | | - Mat52_lengthscale_0 | 2.0578 | (+ve) | | - Mat52_lengthscale_1 | 1.8542 | (+ve) | | - white_variance | 0.0023 | (+ve) | | - noise variance | 0.0000 | (+ve) | | + Name : GP regression + Log-likelihood : 26.787156248 + Number of Parameters : 5 + Parameters: + GP_regression. | Value | Constraint | Prior | Tied to + add.Mat52.variance | 0.385463739076 | +ve | | + add.Mat52.lengthscale | (2,) | +ve | | + add.white.variance | 0.000835329608514 | +ve | | + Gaussian_noise.variance | 0.000835329608514 | +ve | | +If you want to see the ``ARD`` parameters explicitly print them +directly:: + + >>> print m.add.Mat52.lengthscale + Index | GP_regression.add.Mat52.lengthscale | Constraint | Prior | Tied to + [0] | 1.9575587 | +ve | | N/A + [1] | 1.9689948 | +ve | | N/A + .. figure:: Figures/tuto_GP_regression_m3.png :align: center :height: 350px diff --git a/doc/tuto_creating_new_kernels.rst b/doc/tuto_creating_new_kernels.rst index 6d30fe05..a8197596 100644 --- a/doc/tuto_creating_new_kernels.rst +++ b/doc/tuto_creating_new_kernels.rst @@ -35,45 +35,74 @@ The implementation of this function in mandatory. For all kernparts the first parameter ``input_dim`` corresponds to the dimension of the input space, and the following parameters stand for the parameterization of the kernel. -The following attributes are compulsory: ``self.input_dim`` (the dimension, integer), ``self.name`` (name of the kernel, string), ``self.num_params`` (number of parameters, integer). :: +You have to call ``super(, self).__init__(input_dim, +name)`` to make sure the input dimension and name of the kernel are +stored in the right place. These attributes are available as +``self.input_dim`` and ``self.name`` at runtime. +.. The following attributes are compulsory: ``self.input_dim`` (the dimension, integer), ``self.name`` (name of the kernel, string), ``self.num_params`` (number of parameters, integer). :: +Parameterization is done by adding +:py:class:``GPy.core.parameter.Param`` objects to ``self`` and use +them as normal numpy ``array-like``s in yout code. The parameters have +to be added by calling +:py:function:``GPy.core.parameterized:Parameterized.add_parameters`` +with the :py:class:``GPy.core.parameter.Param`` objects as arguments. def __init__(self,input_dim,variance=1.,lengthscale=1.,power=1.): - assert input_dim == 1, "For this kernel we assume input_dim=1" - self.input_dim = input_dim - self.num_params = 3 - self.name = 'rat_quad' - self.variance = variance - self.lengthscale = lengthscale - self.power = power + super(RationalQuadratic, self).__init__(input_dim, 'rat_quad') + assert input_dim == 1, "For this kernel we assume input_dim=1" + self.variance = Param('variance', variance) + self.lengthscale = Param('lengtscale', lengthscale) + self.power = Param('power', power) + self.add_parameters(self.variance, self.lengthscale, self.power) -**_get_params(self)** +From now on you can use the parameters ``self.variance, +self.lengthscale, self.power`` as normal numpy ``array-like``s in your +code. Updates from the optimization routine will be done +automatically. -The implementation of this function in mandatory. +**parameters_changed(self)** -This function returns a one dimensional array of length ``self.num_params`` containing the value of the parameters. :: +The implementation of this function is optional. - def _get_params(self): - return np.hstack((self.variance,self.lengthscale,self.power)) +This functions deals as a callback for each optimization iteration. If +one optimization step was successfull and the parameters (added by +:py:function:``GPy.core.parameterized:Parameterized.add_parameters``) +this callback function will be called to be able to update any +precomputations for the kernel. -**_set_params(self,x)** + def parameters_changed(self): + # nothing todo here -The implementation of this function in mandatory. -The input is a one dimensional array of length ``self.num_params`` containing the value of the parameters. The function has no output but it updates the values of the attribute associated to the parameters (such as ``self.variance``, ``self.lengthscale``, ...). :: - def _set_params(self,x): - self.variance = x[0] - self.lengthscale = x[1] - self.power = x[2] +.. **_get_params(self)** -**_get_param_names(self)** +.. The implementation of this function in mandatory. -The implementation of this function in mandatory. +.. This function returns a one dimensional array of length ``self.num_params`` containing the value of the parameters. :: -It returns a list of strings of length ``self.num_params`` corresponding to the parameter names. :: +.. def _get_params(self): +.. return np.hstack((self.variance,self.lengthscale,self.power)) - def _get_param_names(self): - return ['variance','lengthscale','power'] +.. **_set_params(self,x)** + +.. The implementation of this function in mandatory. + +.. The input is a one dimensional array of length ``self.num_params`` containing the value of the parameters. The function has no output but it updates the values of the attribute associated to the parameters (such as ``self.variance``, ``self.lengthscale``, ...). :: + +.. def _set_params(self,x): +.. self.variance = x[0] +.. self.lengthscale = x[1] +.. self.power = x[2] + +.. **_get_param_names(self)** + +.. The implementation of this function in mandatory. + +.. It returns a list of strings of length ``self.num_params`` corresponding to the parameter names. :: + +.. def _get_param_names(self): +.. return ['variance','lengthscale','power'] **K(self,X,X2,target)** diff --git a/doc/tuto_creating_new_models.rst b/doc/tuto_creating_new_models.rst index 021b4950..07f6194f 100644 --- a/doc/tuto_creating_new_models.rst +++ b/doc/tuto_creating_new_models.rst @@ -8,57 +8,93 @@ In GPy all models inherit from the base class :py:class:`~GPy.core.parameterized The :py:class:`~GPy.core.model.Model` class provides parameter introspection, objective function and optimization. -In order to fully use all functionality of :py:class:`~GPy.core.model.Model` some methods need to be implemented / overridden. In order to explain the functionality of those methods we will use a wrapper to the numpy ``rosen`` function, which holds input parameters :math:`\mathbf{X}`. Where :math:`\mathbf{X}\in\mathbb{R}^{N\times 1}`. +In order to fully use all functionality of +:py:class:`~GPy.core.model.Model` some methods need to be implemented +/ overridden. And the model needs to be told its parameters, such +that it can provide optimized parameter distribution and handling. +In order to explain the functionality of those methods +we will use a wrapper to the numpy ``rosen`` function, which holds +input parameters :math:`\mathbf{X}`. Where +:math:`\mathbf{X}\in\mathbb{R}^{N\times 1}`. Obligatory methods ================== -:py:meth:`~GPy.core.model.Model.__init__` : - Initialize the model with the given parameters. In our example we have to store shape information of :math:`\mathbf X` and the parameters themselves:: +:py:func:`~GPy.core.model.Model.__init__` : + Initialize the model with the given parameters. These need to + be added to the model by calling + `self.add_parameter()`, where param needs to be a + parameter handle (See parameterized_ for details).:: - self.X = X - self.num_inputs = self.X.shape[0] - assert self.X.ndim == 1, only vector inputs allowed - -:py:meth:`~GPy.core.model.Model._get_params` : - Return parameters of the model as a flattened numpy array-like. So, in our example we have to return the input parameters:: - - return self.X.flatten() - -:py:meth:`~GPy.core.model.Model._set_params` : - Set parameters, which have been fetched through :py:meth:`~GPy.core.model.Model._get_params`. In other words, "invert" the functionality of :py:meth:`~GPy.core.model.Model._get_params`:: - - self.X = params[:self.num_inputs*self.input_dim].reshape(self.num_inputs) - + self.X = GPy.Param("input", X) + self.add_parameter(self.X) + :py:meth:`~GPy.core.model.Model.log_likelihood` : - Returns the log-likelihood of the new model. For our example this is just the call to ``rosen``:: + Returns the log-likelihood of the new model. For our example + this is just the call to ``rosen`` and as we want to minimize + it, we need to negate the objective.:: - return scipy.optimize.rosen(self.X) + return -scipy.optimize.rosen(self.X) -:py:meth:`~GPy.core.model.Model._log_likelihood_gradients` : - Returns the gradients with respect to all parameters:: +:py:meth:`~GPy.core.model.Model.parameters_changed` : + Updates the internal state of the model and sets the gradient of + each parameter handle in the hierarchy with respect to the + log_likelihod. Thus here we need to set the negative derivative of + the rosenbrock function for the parameters. In this case it is the + gradient for self.X.:: - return scipy.optimize.rosen_der(self.X) + self.X.gradient = -scipy.optimize.rosen_der(self.X) +Here the full code for the `Rosen` class:: + + from GPy import Model, Param + import scipy + class Rosen(Model): + def __init__(self, X, name='rosenbrock'): + super(Rosen, self).__init__(name=name) + self.X = Param("input", X) + self.add_parameter(self.X) + def log_likelihood(self): + return -scipy.optimize.rosen(self.X) + def parameters_changed(self): + self.X.gradient = -scipy.optimize.rosen_der(self.X) + +In order to test the newly created model, we can check the gradients +and optimize a standard rosenbrock run:: + + >>> m = Rosen(np.array([-1,-1])) + >>> print m + Name : rosenbrock + Log-likelihood : -404.0 + Number of Parameters : 2 + Parameters: + rosenbrock. | Value | Constraint | Prior | Tied to + input | (2,) | | | + >>> m.checkgrad(verbose=True) + Name | Ratio | Difference | Analytical | Numerical + ------------------------------------------------------------------------------------------ + rosenbrock.input[[0]] | 1.000000 | 0.000000 | -804.000000 | -804.000000 + rosenbrock.input[[1]] | 1.000000 | 0.000000 | -400.000000 | -400.000000 + >>> m.optimize() + >>> print m + Name : rosenbrock + Log-likelihood : -6.52150088871e-15 + Number of Parameters : 2 + Parameters: + rosenbrock. | Value | Constraint | Prior | Tied to + input | (2,) | | | + >>> print m.input + Index | rosenbrock.input | Constraint | Prior | Tied to + [0] | 0.99999994 | | | N/A + [1] | 0.99999987 | | | N/A + >>> print m.gradient + [ -1.91169809e-06, 1.01852309e-06] + +This is the optimium for the 2D Rosenbrock function, as expected, and +the gradient of the inputs are almost zero. + Optional methods ================ -If you want some special functionality please provide the following methods: - -Using the pickle functionality ------------------------------- - -To be able to use the pickle functionality ``m.pickle()`` the methods ``getstate(self)`` and ``setstate(self, state)`` have to be provided. The convention for a ``state`` in ``GPy`` is a list of all parameters, which are needed to restore the model. All classes provided in ``GPy`` follow this convention, thus you can just append to the state of the inherited class and call the inherited class' ``setstate`` with the appropriate state. - -:py:meth:`~GPy.core.model.Model.getstate` : - This method returns a state of the model, following the memento pattern. As we are inheriting from :py:class:`~GPy.core.model.Model`, we have to return the state of Model as well. In out example we have `X` and `num_inputs` as state:: - - return Model.getstate(self) + [self.X, self.num_inputs] - -:py:meth:`~GPy.core.model.Model.setstate` : - This method restores this model with the given ``state``:: - - self.num_inputs = state.pop() - self.X = state.pop() - return Model.setstate(self, state) \ No newline at end of file +Currently none. diff --git a/doc/tuto_interacting_with_models.rst b/doc/tuto_interacting_with_models.rst index 5bd0511e..80b2ac77 100644 --- a/doc/tuto_interacting_with_models.rst +++ b/doc/tuto_interacting_with_models.rst @@ -40,89 +40,199 @@ is shown. For each parameter, the table contains the name of the parameter, the current value, and in case there are defined: constraints, ties and prior distrbutions associated. :: - Log-likelihood: 6.309e+02 + Name : sparse gp + Log-likelihood : 588.947189413 + Number of Parameters : 8 + Parameters: + sparse_gp. | Value | Constraint | Prior | Tied to + inducing inputs | (5, 1) | | | + rbf.variance | 1.91644016819 | +ve | | + rbf.lengthscale | 2.62103621347 | +ve | | + Gaussian_noise.variance | 0.00269870373421 | +ve | | - Name | Value | Constraints | Ties | Prior - ------------------------------------------------------------------ - iip_0_0 | -1.4671 | | | - iip_1_0 | 2.6378 | | | - iip_2_0 | -0.0396 | | | - iip_3_0 | -2.6372 | | | - iip_4_0 | 1.4704 | | | - rbf_variance | 1.5672 | (+ve) | | - rbf_lengthscale | 2.5625 | (+ve) | | - white_variance | 0.0000 | (+ve) | | - noise_variance | 0.0022 | (+ve) | | - -In this case the kernel parameters (``rbf_variance``, -``rbf_lengthscale`` and ``white_variance``) as well as -the noise parameter (``noise_variance``), are constrained -to be positive, while the inducing inputs have not +In this case the kernel parameters (``rbf.variance``, +``rbf.lengthscale``) as well as +the likelihood noise parameter (``Gaussian_noise.variance``), are constrained +to be positive, while the inducing inputs have no constraints associated. Also there are no ties or prior defined. -Setting and fetching parameters by name -======================================= -Another way to interact with the model's parameters is through -the functions ``_get_param_names()``, ``_get_params()`` and -``_set_params()``. +You can also print all subparts of the model, by printing the +subcomponents individually:: -``_get_param_names()`` returns a list of the parameters names :: + print m.rbf - ['iip_0_0', - 'iip_1_0', - 'iip_2_0', - 'iip_3_0', - 'iip_4_0', - 'rbf_variance', - 'rbf_lengthscale', - 'white_variance', - 'noise_variance'] +This will print the details of this particular parameter handle:: -``_get_params()`` returns an array of the parameters values :: + rbf. | Value | Constraint | Prior | Tied to + variance | 1.91644016819 | +ve | | + lengthscale | 2.62103621347 | +ve | | - array([ -1.46705227e+00, 2.63782176e+00, -3.96422982e-02, - -2.63715255e+00, 1.47038653e+00, 1.56724596e+00, - 2.56248679e+00, 2.20963633e-10, 2.18379922e-03]) +When you want to get a closer look into +multivalue parameters, print them directly:: -``_set_params()`` takes an array as input and substitutes -the current values of the parameters for those of the array. For example, -we can define a new array of values and change the parameters as follows: :: + print m.inducing_inputs - new_params = np.array([1.,2.,3.,4.,1.,1.,1.,1.,1.]) - m._set_params(new_params) + Index | sparse_gp.inducing_inputs | Constraint | Prior | Tied to + [0 0] | 2.7189499 | | | N/A + [1 0] | 0.02006533 | | | N/A + [2 0] | -1.5299386 | | | N/A + [3 0] | -2.7001675 | | | N/A + [4 0] | 1.4654162 | | | N/A -If we call the function ``_get_params()`` again, we will obtain the new -parameters we have just set. +Interacting with Parameters: +======================= +The preferred way of interacting with parameters is to act on the +parameter handle itself. +Interacting with parameter handles is simple. The names, printed by `print m` +are accessible interactively and programatically. For example try to +set kernels (`rbf`) `lengthscale` to `.2` and print the result:: -Parameters can be also set by name using dictionary notations. For example, -let's change the lengthscale to .5: :: + m.rbf.lengthscale = .2 + print m - m['rbf_lengthscale'] = .5 +You should see this:: -Here, the matching accepts a regular expression and therefore all parameters matching that regular expression are set to the given value. In this case rather -than passing as second output a single value, we can also -use a list of arrays. For example, lets change the inducing -inputs: :: + Name : sparse gp + Log-likelihood : 588.947189413 + Number of Parameters : 8 + Parameters: + sparse_gp. | Value | Constraint | Prior | Tied to + inducing inputs | (5, 1) | | | + rbf.variance | 1.91644016819 | +ve | | + rbf.lengthscale | 0.2 | +ve | | + Gaussian_noise.variance | 0.00269870373421 | +ve | | - m['iip'] = np.arange(-5,0) +This will already have updated the model's inner state, so you can +plot it or see the changes in the posterior `m.posterior` of the model. -Getting the model's likelihood and gradients +Regular expressions +---------------- +The model's parameters can also be accessed through regular +expressions, by 'indexing' the model with a regular expression, +matching the parameter name. Through indexing by regular expression, +you can only retrieve leafs of the hierarchy, and you can retrieve the +values matched by calling `values()` on the returned object:: + + >>> print m['.*var'] + Index | sparse_gp.rbf.variance | Constraint | Prior | Tied to + [0] | 2.1500132 | | | N/A + ----- | sparse_gp.Gaussian_noise.variance | ---------- | ---------- | ------- + [0] | 0.0024268215 | | | N/A + >>> print m['.*var'].values() + [ 2.1500132 0.00242682] + >>> print m['rbf'] + Index | sparse_gp.rbf.variance | Constraint | Prior | Tied to + [0] | 2.1500132 | | | N/A + ----- | sparse_gp.rbf.lengthscale | ---------- | ---------- | ------- + [0] | 2.6782803 | | | N/A + +There is access to setting parameters by regular expression, +as well. Here are a few examples of how to set parameters by regular expression:: + + >>> m['.*var'] = .1 + >>> print m['.*var'] + Index | sparse_gp.rbf.variance | Constraint | Prior | Tied to + [0] | 0.1 | | | N/A + ----- | sparse_gp.Gaussian_noise.variance | ---------- | ---------- | ------- + [0] | 0.1 | | | N/A + >>> m['.*var'] = [.1, .2] + >>> print m['.*var'] + Index | sparse_gp.rbf.variance | Constraint | Prior | Tied to + [0] | 0.1 | | | N/A + ----- | sparse_gp.Gaussian_noise.variance | ---------- | ---------- | ------- + [0] | 0.2 | | | N/A + +The fact that only leaf nodes can be accesses we can print all +parameters in a flattened view, by printing the regular expression +match of matching all objects:: + + >>> print m[''] + Index | sparse_gp.inducing_inputs | Constraint | Prior | Tied to + [0 0] | -2.6716041 | | | N/A + [1 0] | -1.4665111 | | | N/A + [2 0] | -0.031010293 | | | N/A + [3 0] | 1.4563711 | | | N/A + [4 0] | 2.6803046 | | | N/A + ----- | sparse_gp.rbf.variance | ---------- | ---------- | ------- + [0] | 0.1 | | | N/A + ----- | sparse_gp.rbf.lengthscale | ---------- | ---------- | ------- + [0] | 2.6782803 | | | N/A + ----- | sparse_gp.Gaussian_noise.variance | ---------- | ---------- | ------- + [0] | 0.2 | | | N/A + +Setting and fetching parameters `parameter_array` +------------------------------------------ +Another way to interact with the model's parameters is through the +`parameter_array`. The Parameter array holds all the parameters of the +model in one place and is editable. It can be accessed through +indexing the model for example you can set all the parameters through +this mechanism:: + + >>> new_params = np.r_[[-4,-2,0,2,4], [.5,2], [.3]] + >>> print new_params + array([-4. , -2. , 0. , 2. , 4. , 0.5, 2. , 0.3]) + >>> m[:] = new_params + >>> print m + Name : sparse gp + Log-likelihood : -147.561160209 + Number of Parameters : 8 + Parameters: + sparse_gp. | Value | Constraint | Prior | Tied to + inducing inputs | (5, 1) | | | + rbf.variance | 0.5 | +sq | | + rbf.lengthscale | 2.0 | +ve | | + Gaussian_noise.variance | 0.3 | +sq | | + +Parameters themselves (leafs of the hierarchy) can be indexed and used +the same way as numpy arrays. First let us set a slice of the +`inducing_inputs`:: + + >>> m.inducing_inputs[2:, 0] = [1,3,5] + >>> print m.inducing_indputs + Index | sparse_gp.inducing_inputs | Constraint | Prior | Tied to + [0 0] | -4 | | | N/A + [1 0] | -2 | | | N/A + [2 0] | 1 | | | N/A + [3 0] | 3 | | | N/A + [4 0] | 5 | | | N/A + +Or you use the parameters as normal numpy arrays for calculations:: + + >>> precision = 1./m.Gaussian_noise.variance + array([ 3.33333333]) + +Getting the model's log likelihood ============================================= Appart form the printing the model, the marginal log-likelihood can be obtained by using the function -``log_likelihood()``. Also, the log-likelihood gradients -wrt. each parameter can be obtained with the funcion -``_log_likelihood_gradients()``. :: +``log_likelihood()``.:: - m.log_likelihood() - -791.15371409346153 + >>> m.log_likelihood() + array([-152.83377316]) - m._log_likelihood_gradients() - array([ 7.08278455e-03, 1.37118783e+01, 2.66948031e+00, - 3.50184014e+00, 7.08278455e-03, -1.43501702e+02, - 6.10662266e+01, -2.18472649e+02, 2.14663691e+02]) +If you want to ensure the log likelihood as a float, call `float()` +around it:: -Removing the model's constraints + >>> float(m.log_likelihood()) + -152.83377316356177 + +Getting the model parameter's gradients +============================ +The gradients of a model can shed light on understanding the +(possibly hard) optimization process. The gradients of each parameter +handle can be accessed through their `gradient` field.:: + + >>> print m.gradient + [ 5.51170031 9.71735112 -4.20282106 -3.45667035 -1.58828165 + -2.11549358 12.40292787 -627.75467803] + >>> print m.rbf.gradient + [ -2.11549358 12.40292787] + >>> m.optimize() + >>> print m.gradient + [ -5.98046560e-04 -3.64576085e-04 1.98005930e-04 3.43381219e-04 + -6.85685104e-04 -1.28800748e-05 1.08552429e-03 2.74058081e-01] + +Adjusting the model's constraints ================================ When we initially call the example, it was optimized and hence the log-likelihood gradients were close to zero. However, since @@ -130,88 +240,102 @@ we have been changing the parameters, the gradients are far from zero now. Next we are going to show how to optimize the model setting different restrictions on the parameters. -Once a constrain has been set on a parameter, it is possible to remove it -with the command ``unconstrain()``, and -just as the previous matching commands, it also accepts regular expression. -In this case we will remove all the constraints: :: +Once a constraint has been set on a parameter, it is possible to remove +it with the command ``unconstrain()``, which can be called on any +parameter handle of the model. The methods `constrain()` and +`unconstrain()` return the indices which were actually unconstrained, +relative to the parameter handle the method was called on. This is +particularly handy for reporting which parameters where reconstrained, +when reconstraining a parameter, which was already constrained:: - m.unconstrain('') + >>> m.rbf.variance.unconstrain() + array([0]) + >>>m.unconstrain() + array([6, 7]) -Constraining and optimising the model -===================================== -A requisite needed for some parameters, such as variances, -is to be positive. This is constraint is easily set -with the function ``constrain_positive()``. Regular expressions -are also accepted. :: +If you want to unconstrain only a specific constraint, you can pass it +as an argument of ``unconstrain(Transformation)`` (:py:class:`~GPy.constraints.Transformation`), or call +the respective method, such as ``unconstrain_fixed()`` (or +``unfix()``) to only unfix fixed parameters.:: - m.constrain_positive('.*var') + >>> m.inducing_input[0].fix() + >>> m.unfix() + >>> m.rbf.constrain_positive() + >>> print m + Name : sparse gp + Log-likelihood : 620.741066698 + Number of Parameters : 8 + Parameters: + sparse_gp. | Value | Constraint | Prior | Tied to + inducing inputs | (5, 1) | | | + rbf.variance | 1.48329711218 | +ve | | + rbf.lengthscale | 2.5430947048 | +ve | | + Gaussian_noise.variance | 0.00229714444128 | | | -For convenience, GPy also provides a catch all function -which ensures that anything which appears to require -positivity is constrianed appropriately:: +As you can see, ``unfix()`` only unfixed the inducing_input, and did +not change the positive constraint of the kernel. - m.ensure_default_constraints() +The parameter handles come with default constraints, so you will +rarely be needing to adjust the constraints of a model. In the rare +cases of needing to adjust the constraints of a model, or in need of +fixing some parameters, you can do so with the functions +``constrain_{positive|negative|bounded|fixed}()``.:: -Fixing parameters -================= -Parameters values can be fixed using ``constrain_fixed()``. -For example we can define the first inducing input to be -fixed on zero: :: + m['.*var'].constrain_positive() - m.constrain_fixed('iip_0',0) - -Bounding parameters -=================== -Defining bounding constraints is an easily task in GPy too, -it only requires to use the function ``constrain_bounded()``. -For example, lets bound inducing inputs 2 and 3 to have -values between -4 and -1: :: +Available Constraints +============== + +* :py:meth:`~GPy.constraints.Logexp` +* :py:meth:`~GPy.constraints.Exponent` +* :py:meth:`~GPy.constraints.Square` +* :py:meth:`~GPy.constraints.Logistic` +* :py:meth:`~GPy.constraints.LogexpNeg` +* :py:meth:`~GPy.constraints.NegativeExponent` +* :py:meth:`~GPy.constraints.NegativeLogexp` - m.constrain_bounded('iip_(1|2)',-4,-1) Tying Parameters -================ -The values of two or more parameters can be tied together, -so that they share the same value during optimization. -The function to do so is ``tie_params()``. For the example -we are using, it doesn't make sense to tie parameters together, -however for the sake of the example we will tie the white noise -and the variance together. See `A kernel overview `_. -for a proper use of the tying capabilities.:: +============ +Not yet implemented for GPy version 0.6.0 - m.tie_params('.*e_var') Optimizing the model ==================== + Once we have finished defining the constraints, we can now optimize the model with the function ``optimize``.:: - m.optimize() + m.Gaussian_noise.constrain_positive() + m.rbf.constrain_positive() + m.optimize() -We can print again the model and check the new results. -The table now shows that ``iip_0_0`` is fixed, ``iip_1_0`` -and ``iip_2_0`` are bounded and the kernel parameters are constrained to -be positive. In addition the table now indicates that -white_variance and noise_variance are tied together.:: +By deafult, GPy uses the lbfgsb optimizer. + +Some optional parameters may be discussed here. - Log-likelihood: 9.967e+01 +* ``optimizer``: which optimizer to use, currently there are ``lbfgsb, fmin_tnc, + scg, simplex`` or any unique identifier uniquely identifying an + optimizer. Thus, you can say ``m.optimize('bfgs') for using the + ``lbfgsb`` optimizer +* ``messages``: if the optimizer is verbose. Each optimizer has its + own way of printing, so do not be confused by differing messages of + different optimizers +* ``max_iters``: Maximum number of iterations to take. Some optimizers + see iterations as function calls, others as iterations of the + algorithm. Please be advised to look into ``scipy.optimize`` for + more instructions, if the number of iterations matter, so you can + give the right parameters to ``optimize()`` +* ``gtol``: only for some optimizers. Will determine the convergence + criterion, as the tolerance of gradient to finish the optimization. - Name | Value | Constraints | Ties | Prior - ------------------------------------------------------------------ - iip_0_0 | 0.0000 | Fixed | | - iip_1_0 | -2.8834 | (-4, -1) | | - iip_2_0 | -1.9152 | (-4, -1) | | - iip_3_0 | 1.5034 | | | - iip_4_0 | -1.0162 | | | - rbf_variance | 0.0158 | (+ve) | | - rbf_lengthscale | 0.9760 | (+ve) | | - white_variance | 0.0049 | (+ve) | (0) | - noise_variance | 0.0049 | (+ve) | (0) | +Further Reading +=============== - -Further Reading -=============== -All of the mechansiams for dealing with parameters are baked right into GPy.core.model, from which all of the classes in GPy.models inherrit. To learn how to construct your own model, you might want to read :ref:`creating_new_models`. - -By deafult, GPy uses the scg optimizer. To use other optimisers, and to control the setting of those optimisers, as well as other funky features like automated restarts and diagnostics, you can read the optimization tutorial ??link??. +All of the mechansiams for dealing +with parameters are baked right into GPy.core.model, from which all of +the classes in GPy.models inherrit. To learn how to construct your own +model, you might want to read :ref:`creating_new_models`. If you want +to learn how to create kernels, please refer to +:ref:`creating_new_kernels` diff --git a/doc/tuto_parameterized.rst b/doc/tuto_parameterized.rst new file mode 100644 index 00000000..507ec109 --- /dev/null +++ b/doc/tuto_parameterized.rst @@ -0,0 +1,23 @@ +.. _parameterized: + +******************* +Parameterization handling +******************* + +Parameterization in GPy is done through so called parameter handles. The parameter handles are handles to parameters of a model of any kind. A parameter handle can be constrained, fixed, randomized and others. All parameters in GPy have a name, with which they can be accessed in the model. The most common way of accesssing a parameter programmatically though, is by variable name. + +Parameter handles +============== + +A parameter handle in GPy is a handle on a parameter, as the name suggests. A parameter can be constrained, fixed, randomized and more (See e.g. `working with models`). This gives the freedom to the model to handle parameter distribution and model updates as efficiently as possible. All parameter handles share a common memory space, which is just a flat numpy array, stored in the highest parent of a model hierarchy. +In the following we will introduce and elucidate the different parameter handles which exist in GPy. + +:py:class:`~GPy.core.parameterization.parameterized.Parameterized` +========== + +A parameterized object itself holds parameter handles and is just a summarization of the parameters below. It can use those parameters to change the internal state of the model and GPy ensures those parameters to allways hold the right value when in an optimization routine or any other update. + +:py:class:`~GPy.core.parameterization.param.Param` +=========== + +The lowest level of parameter is a numpy array. This Param class inherits all functionality of a numpy array and can simply be used as if it where a numpy array. These parameters can be accessed in the same way as a numpy array is indexed. diff --git a/setup.py b/setup.py index b6b78f18..c4963bcc 100644 --- a/setup.py +++ b/setup.py @@ -4,13 +4,12 @@ import os from setuptools import setup +# Version number +version = '0.6.0' def read(fname): return open(os.path.join(os.path.dirname(__file__), fname)).read() -# Version number -version = read('GPy/version') - setup(name = 'GPy', version = version, author = read('AUTHORS.txt'), @@ -19,17 +18,34 @@ setup(name = 'GPy', license = "BSD 3-clause", keywords = "machine-learning gaussian-processes kernels", url = "http://sheffieldml.github.com/GPy/", - packages = ['GPy', 'GPy.core', 'GPy.kern', 'GPy.util', 'GPy.models_modules', 'GPy.inference', 'GPy.examples', 'GPy.likelihoods', 'GPy.testing', 'GPy.util.latent_space_visualizations', 'GPy.util.latent_space_visualizations.controllers', 'GPy.likelihoods.noise_models', 'GPy.kern.parts', 'GPy.mappings'], + packages = ["GPy.models", + "GPy.inference.optimization", + "GPy.inference.mcmc", + "GPy.inference", + "GPy.inference.latent_function_inference", + "GPy.likelihoods", "GPy.mappings", + "GPy.examples", "GPy.core.parameterization", + "GPy.core", "GPy.testing", + "GPy", "GPy.util", "GPy.kern", + "GPy.kern._src.psi_comp", "GPy.kern._src", + "GPy.plotting.matplot_dep.latent_space_visualizations.controllers", + "GPy.plotting.matplot_dep.latent_space_visualizations", + "GPy.plotting.matplot_dep", "GPy.plotting"], package_dir={'GPy': 'GPy'}, - package_data = {'GPy': ['GPy/examples', 'gpy_config.cfg', 'util/data_resources.json', 'version']}, + package_data = {'GPy': ['defaults.cfg', 'installation.cfg', + 'util/data_resources.json', + 'util/football_teams.json']}, + include_package_data = True, py_modules = ['GPy.__init__'], + test_suite = 'GPy.testing', long_description=read('README.md'), - install_requires=['scipy >= 0.12','matplotlib >= 1.2', 'nose'], - extras_require = { - 'docs':['Sphinx', 'ipython'], - }, - classifiers=[ - "License :: OSI Approved :: BSD License"], - #ext_modules = [Extension(name = 'GPy.kern.lfmUpsilonf2py', - # sources = ['GPy/kern/src/lfmUpsilonf2py.f90'])], + install_requires=['numpy>=1.7', 'scipy>=0.12'], + extras_require = {'docs':['matplotlib >=1.3','Sphinx','IPython']}, + classifiers=['License :: OSI Approved :: BSD License', + 'Natural Language :: English', + 'Operating System :: MacOS :: MacOS X', + 'Operating System :: Microsoft :: Windows', + 'Operating System :: POSIX :: Linux', + 'Programming Language :: Python :: 2.7', + 'Topic :: Scientific/Engineering :: Artificial Intelligence'] )