mirror of
https://github.com/SheffieldML/GPy.git
synced 2026-05-13 05:52:38 +02:00
Broken whilst unlinking GP and sparse_GP, kern not being imported
This commit is contained in:
Alan Saul
parent
26b4cd6c4f
commit
1302c46ace
16 changed files with 328 additions and 318 deletions
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@ -5,7 +5,7 @@ import numpy as np
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import pylab as pb
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import sys, pdb
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from GPLVM import GPLVM
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from sparse_GP import sparse_GP
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from ..core import sparse_GP
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from GPy.util.linalg import pdinv
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from ..likelihoods import Gaussian
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from .. import kern
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@ -65,6 +65,7 @@ class Bayesian_GPLVM(sparse_GP, GPLVM):
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self._savedABCD = []
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sparse_GP.__init__(self, X, likelihood, kernel, Z=Z, X_variance=X_variance, **kwargs)
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self._set_params(self._get_params())
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@property
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def oldps(self):
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@ -96,7 +97,7 @@ class Bayesian_GPLVM(sparse_GP, GPLVM):
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def _clipped(self, x):
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return x # np.clip(x, -1e300, 1e300)
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def _set_params(self, x, save_old=True, save_count=0):
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# try:
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x = self._clipped(x)
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@ -7,7 +7,7 @@ from ..util.linalg import mdot, jitchol, chol_inv, tdot, symmetrify,pdinv
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from ..util.plot import gpplot
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from .. import kern
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from scipy import stats, linalg
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from sparse_GP import sparse_GP
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from ..core import sparse_GP
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def backsub_both_sides(L,X):
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""" Return L^-T * X * L^-1, assumuing X is symmetrical and L is lower cholesky"""
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@ -16,6 +16,9 @@ def backsub_both_sides(L,X):
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class FITC(sparse_GP):
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def __init__(self, X, likelihood, kernel, Z, X_variance=None, normalize_X=False):
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super(FITC, self).__init__(X, likelihood, kernel, normalize_X=normalize_X)
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def update_likelihood_approximation(self):
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"""
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Approximates a non-gaussian likelihood using Expectation Propagation
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288
GPy/models/GP.py
288
GPy/models/GP.py
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@ -1,288 +0,0 @@
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# Copyright (c) 2012, GPy authors (see AUTHORS.txt).
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# Licensed under the BSD 3-clause license (see LICENSE.txt)
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import numpy as np
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from scipy import linalg
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import pylab as pb
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from .. import kern
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from ..core import model
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from ..util.linalg import pdinv, mdot, tdot
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from ..util.plot import gpplot, x_frame1D, x_frame2D, Tango
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from ..likelihoods import EP
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class GP(model):
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"""
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Gaussian Process model for regression and EP
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:param X: input observations
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:param kernel: a GPy kernel, defaults to rbf+white
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:parm likelihood: a GPy likelihood
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:param normalize_X: whether to normalize the input data before computing (predictions will be in original scales)
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:type normalize_X: False|True
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:rtype: model object
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:param epsilon_ep: convergence criterion for the Expectation Propagation algorithm, defaults to 0.1
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:param powerep: power-EP parameters [$\eta$,$\delta$], defaults to [1.,1.]
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:type powerep: list
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.. Note:: Multiple independent outputs are allowed using columns of Y
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"""
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def __init__(self, X, likelihood, kernel, normalize_X=False):
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# parse arguments
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self.X = X
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assert len(self.X.shape) == 2
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self.N, self.Q = self.X.shape
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assert isinstance(kernel, kern.kern)
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self.kern = kernel
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self.likelihood = likelihood
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assert self.X.shape[0] == self.likelihood.data.shape[0]
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self.N, self.D = self.likelihood.data.shape
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# here's some simple normalization for the inputs
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if normalize_X:
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self._Xmean = X.mean(0)[None, :]
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self._Xstd = X.std(0)[None, :]
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self.X = (X.copy() - self._Xmean) / self._Xstd
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if hasattr(self, 'Z'):
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self.Z = (self.Z - self._Xmean) / self._Xstd
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else:
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self._Xmean = np.zeros((1, self.X.shape[1]))
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self._Xstd = np.ones((1, self.X.shape[1]))
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if not hasattr(self,'has_uncertain_inputs'):
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self.has_uncertain_inputs = False
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model.__init__(self)
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def dL_dZ(self):
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"""
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TODO: one day we might like to learn Z by gradient methods?
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"""
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#FIXME: this doesn;t live here.
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return np.zeros_like(self.Z)
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def _set_params(self, p):
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self.kern._set_params_transformed(p[:self.kern.Nparam_transformed()])
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self.likelihood._set_params(p[self.kern.Nparam_transformed():])
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self.K = self.kern.K(self.X)
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self.K += self.likelihood.covariance_matrix
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self.Ki, self.L, self.Li, self.K_logdet = pdinv(self.K)
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# the gradient of the likelihood wrt the covariance matrix
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if self.likelihood.YYT is None:
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#alpha = np.dot(self.Ki, self.likelihood.Y)
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alpha,_ = linalg.lapack.flapack.dpotrs(self.L, self.likelihood.Y,lower=1)
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self.dL_dK = 0.5 * (tdot(alpha) - self.D * self.Ki)
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else:
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#tmp = mdot(self.Ki, self.likelihood.YYT, self.Ki)
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tmp, _ = linalg.lapack.flapack.dpotrs(self.L, np.asfortranarray(self.likelihood.YYT), lower=1)
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tmp, _ = linalg.lapack.flapack.dpotrs(self.L, np.asfortranarray(tmp.T), lower=1)
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self.dL_dK = 0.5 * (tmp - self.D * self.Ki)
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def _get_params(self):
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return np.hstack((self.kern._get_params_transformed(), self.likelihood._get_params()))
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def _get_param_names(self):
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return self.kern._get_param_names_transformed() + self.likelihood._get_param_names()
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def update_likelihood_approximation(self):
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"""
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Approximates a non-gaussian likelihood using Expectation Propagation
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For a Gaussian likelihood, no iteration is required:
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this function does nothing
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"""
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self.likelihood.fit_full(self.kern.K(self.X))
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self._set_params(self._get_params()) # update the GP
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def _model_fit_term(self):
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"""
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Computes the model fit using YYT if it's available
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"""
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if self.likelihood.YYT is None:
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tmp, _ = linalg.lapack.flapack.dtrtrs(self.L, np.asfortranarray(self.likelihood.Y), lower=1)
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return -0.5 * np.sum(np.square(tmp))
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#return -0.5 * np.sum(np.square(np.dot(self.Li, self.likelihood.Y)))
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else:
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return -0.5 * np.sum(np.multiply(self.Ki, self.likelihood.YYT))
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def log_likelihood(self):
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"""
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The log marginal likelihood of the GP.
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For an EP model, can be written as the log likelihood of a regression
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model for a new variable Y* = v_tilde/tau_tilde, with a covariance
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matrix K* = K + diag(1./tau_tilde) plus a normalization term.
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"""
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return -0.5 * self.D * self.K_logdet + self._model_fit_term() + self.likelihood.Z
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def _log_likelihood_gradients(self):
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"""
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The gradient of all parameters.
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Note, we use the chain rule: dL_dtheta = dL_dK * d_K_dtheta
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"""
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return np.hstack((self.kern.dK_dtheta(dL_dK=self.dL_dK, X=self.X), self.likelihood._gradients(partial=np.diag(self.dL_dK))))
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def _raw_predict(self, _Xnew, which_parts='all', full_cov=False,stop=False):
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"""
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Internal helper function for making predictions, does not account
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for normalization or likelihood
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"""
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Kx = self.kern.K(_Xnew,self.X,which_parts=which_parts).T
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#KiKx = np.dot(self.Ki, Kx)
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KiKx, _ = linalg.lapack.flapack.dpotrs(self.L, np.asfortranarray(Kx), lower=1)
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mu = np.dot(KiKx.T, self.likelihood.Y)
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if full_cov:
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Kxx = self.kern.K(_Xnew, which_parts=which_parts)
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var = Kxx - np.dot(KiKx.T, Kx)
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else:
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Kxx = self.kern.Kdiag(_Xnew, which_parts=which_parts)
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var = Kxx - np.sum(np.multiply(KiKx, Kx), 0)
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var = var[:, None]
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if stop:
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debug_this
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return mu, var
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def predict(self, Xnew, which_parts='all', full_cov=False):
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"""
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Predict the function(s) at the new point(s) Xnew.
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Arguments
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---------
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:param Xnew: The points at which to make a prediction
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:type Xnew: np.ndarray, Nnew x self.Q
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:param which_parts: specifies which outputs kernel(s) to use in prediction
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:type which_parts: ('all', list of bools)
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:param full_cov: whether to return the folll covariance matrix, or just the diagonal
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:type full_cov: bool
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:rtype: posterior mean, a Numpy array, Nnew x self.D
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:rtype: posterior variance, a Numpy array, Nnew x 1 if full_cov=False, Nnew x Nnew otherwise
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:rtype: lower and upper boundaries of the 95% confidence intervals, Numpy arrays, Nnew x self.D
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If full_cov and self.D > 1, the return shape of var is Nnew x Nnew x self.D. If self.D == 1, the return shape is Nnew x Nnew.
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This is to allow for different normalizations of the output dimensions.
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"""
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# normalize X values
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Xnew = (Xnew.copy() - self._Xmean) / self._Xstd
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mu, var = self._raw_predict(Xnew, full_cov=full_cov, which_parts=which_parts)
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# now push through likelihood
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mean, var, _025pm, _975pm = self.likelihood.predictive_values(mu, var, full_cov)
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return mean, var, _025pm, _975pm
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def plot_f(self, samples=0, plot_limits=None, which_data='all', which_parts='all', resolution=None, full_cov=False):
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"""
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Plot the GP's view of the world, where the data is normalized and the
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likelihood is Gaussian.
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:param samples: the number of a posteriori samples to plot
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:param which_data: which if the training data to plot (default all)
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:type which_data: 'all' or a slice object to slice self.X, self.Y
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:param plot_limits: The limits of the plot. If 1D [xmin,xmax], if 2D [[xmin,ymin],[xmax,ymax]]. Defaluts to data limits
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:param which_parts: which of the kernel functions to plot (additively)
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:type which_parts: 'all', or list of bools
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:param resolution: the number of intervals to sample the GP on. Defaults to 200 in 1D and 50 (a 50x50 grid) in 2D
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Plot the posterior of the GP.
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- In one dimension, the function is plotted with a shaded region identifying two standard deviations.
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- In two dimsensions, a contour-plot shows the mean predicted function
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- In higher dimensions, we've no implemented this yet !TODO!
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Can plot only part of the data and part of the posterior functions
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using which_data and which_functions
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"""
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if which_data == 'all':
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which_data = slice(None)
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if self.X.shape[1] == 1:
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Xnew, xmin, xmax = x_frame1D(self.X, plot_limits=plot_limits)
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if samples == 0:
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m, v = self._raw_predict(Xnew, which_parts=which_parts)
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gpplot(Xnew, m, m - 2 * np.sqrt(v), m + 2 * np.sqrt(v))
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pb.plot(self.X[which_data], self.likelihood.Y[which_data], 'kx', mew=1.5)
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else:
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m, v = self._raw_predict(Xnew, which_parts=which_parts, full_cov=True)
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Ysim = np.random.multivariate_normal(m.flatten(), v, samples)
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gpplot(Xnew, m, m - 2 * np.sqrt(np.diag(v)[:, None]), m + 2 * np.sqrt(np.diag(v))[:, None])
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for i in range(samples):
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pb.plot(Xnew, Ysim[i, :], Tango.colorsHex['darkBlue'], linewidth=0.25)
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pb.plot(self.X[which_data], self.likelihood.Y[which_data], 'kx', mew=1.5)
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pb.xlim(xmin, xmax)
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ymin, ymax = min(np.append(self.likelihood.Y, m - 2 * np.sqrt(np.diag(v)[:, None]))), max(np.append(self.likelihood.Y, m + 2 * np.sqrt(np.diag(v)[:, None])))
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ymin, ymax = ymin - 0.1 * (ymax - ymin), ymax + 0.1 * (ymax - ymin)
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pb.ylim(ymin, ymax)
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if hasattr(self, 'Z'):
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pb.plot(self.Z, self.Z * 0 + pb.ylim()[0], 'r|', mew=1.5, markersize=12)
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elif self.X.shape[1] == 2:
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resolution = resolution or 50
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Xnew, xmin, xmax, xx, yy = x_frame2D(self.X, plot_limits, resolution)
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m, v = self._raw_predict(Xnew, which_parts=which_parts)
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m = m.reshape(resolution, resolution).T
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pb.contour(xx, yy, m, vmin=m.min(), vmax=m.max(), cmap=pb.cm.jet)
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pb.scatter(Xorig[:, 0], Xorig[:, 1], 40, Yorig, linewidth=0, cmap=pb.cm.jet, vmin=m.min(), vmax=m.max())
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pb.xlim(xmin[0], xmax[0])
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pb.ylim(xmin[1], xmax[1])
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else:
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raise NotImplementedError, "Cannot define a frame with more than two input dimensions"
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def plot(self, samples=0, plot_limits=None, which_data='all', which_parts='all', resolution=None, levels=20):
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"""
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TODO: Docstrings!
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:param levels: for 2D plotting, the number of contour levels to use
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"""
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# TODO include samples
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if which_data == 'all':
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which_data = slice(None)
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if self.X.shape[1] == 1:
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Xu = self.X * self._Xstd + self._Xmean # NOTE self.X are the normalized values now
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Xnew, xmin, xmax = x_frame1D(Xu, plot_limits=plot_limits)
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m, var, lower, upper = self.predict(Xnew, which_parts=which_parts)
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for d in range(m.shape[1]):
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gpplot(Xnew, m[:,d], lower[:,d], upper[:,d])
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pb.plot(Xu[which_data], self.likelihood.data[which_data,d], 'kx', mew=1.5)
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if self.has_uncertain_inputs:
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pb.errorbar(Xu[which_data, 0], self.likelihood.data[which_data, 0],
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xerr=2 * np.sqrt(self.X_variance[which_data, 0]),
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ecolor='k', fmt=None, elinewidth=.5, alpha=.5)
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ymin, ymax = min(np.append(self.likelihood.data, lower)), max(np.append(self.likelihood.data, upper))
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ymin, ymax = ymin - 0.1 * (ymax - ymin), ymax + 0.1 * (ymax - ymin)
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pb.xlim(xmin, xmax)
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pb.ylim(ymin, ymax)
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if hasattr(self, 'Z'):
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Zu = self.Z * self._Xstd + self._Xmean
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pb.plot(Zu, Zu * 0 + pb.ylim()[0], 'r|', mew=1.5, markersize=12)
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# pb.errorbar(self.X[:,0], pb.ylim()[0]+np.zeros(self.N), xerr=2*np.sqrt(self.X_variance.flatten()))
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elif self.X.shape[1] == 2: # FIXME
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resolution = resolution or 50
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Xnew, xx, yy, xmin, xmax = x_frame2D(self.X, plot_limits, resolution)
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x, y = np.linspace(xmin[0], xmax[0], resolution), np.linspace(xmin[1], xmax[1], resolution)
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m, var, lower, upper = self.predict(Xnew, which_parts=which_parts)
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m = m.reshape(resolution, resolution).T
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pb.contour(x, y, m, levels, vmin=m.min(), vmax=m.max(), cmap=pb.cm.jet)
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Yf = self.likelihood.Y.flatten()
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pb.scatter(self.X[:, 0], self.X[:, 1], 40, Yf, cmap=pb.cm.jet, vmin=m.min(), vmax=m.max(), linewidth=0.)
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pb.xlim(xmin[0], xmax[0])
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pb.ylim(xmin[1], xmax[1])
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if hasattr(self, 'Z'):
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pb.plot(self.Z[:, 0], self.Z[:, 1], 'wo')
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else:
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raise NotImplementedError, "Cannot define a frame with more than two input dimensions"
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@ -8,7 +8,7 @@ import sys, pdb
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from .. import kern
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from ..core import model
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from ..util.linalg import pdinv, PCA
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from GP import GP
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from ..core import GP
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from ..likelihoods import Gaussian
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from .. import util
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from GPy.util import plot_latent
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@ -32,7 +32,8 @@ class GPLVM(GP):
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if kernel is None:
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kernel = kern.rbf(Q, ARD=Q>1) + kern.bias(Q, np.exp(-2)) + kern.white(Q, np.exp(-2))
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likelihood = Gaussian(Y, normalize=normalize_Y)
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GP.__init__(self, X, likelihood, kernel, **kwargs)
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super(GPLVM, self).__init__(self, X, likelihood, kernel, **kwargs)
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self._set_params(self._get_params())
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def initialise_latent(self, init, Q, Y):
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if init == 'PCA':
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@ -63,4 +64,4 @@ class GPLVM(GP):
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pb.plot(mu[:,0], mu[:,1],'k',linewidth=1.5)
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def plot_latent(self, *args, **kwargs):
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util.plot_latent.plot_latent(self, *args, **kwargs)
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util.plot_latent.plot_latent(self, *args, **kwargs)
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@ -3,7 +3,7 @@
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import numpy as np
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from GP import GP
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from ..core import GP
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from .. import likelihoods
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from .. import kern
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@ -31,4 +31,5 @@ class GP_regression(GP):
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likelihood = likelihoods.Gaussian(Y,normalize=normalize_Y)
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GP.__init__(self, X, likelihood, kernel, normalize_X=normalize_X)
|
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super(GP_regression, self).__init__(self, X, likelihood, kernel, normalize_X=normalize_X)
|
||||
self._set_params(self._get_params())
|
||||
|
|
|
|||
|
|
@ -2,9 +2,9 @@
|
|||
# Licensed under the BSD 3-clause license (see LICENSE.txt)
|
||||
|
||||
|
||||
from GP import GP
|
||||
#from GP import GP
|
||||
#from sparse_GP import sparse_GP
|
||||
from GP_regression import GP_regression
|
||||
from sparse_GP import sparse_GP
|
||||
from sparse_GP_regression import sparse_GP_regression
|
||||
from GPLVM import GPLVM
|
||||
from warped_GP import warpedGP
|
||||
|
|
|
|||
|
|
@ -7,7 +7,7 @@ from ..util.linalg import mdot, jitchol, chol_inv, pdinv, trace_dot
|
|||
from ..util.plot import gpplot
|
||||
from .. import kern
|
||||
from scipy import stats, linalg
|
||||
from sparse_GP import sparse_GP
|
||||
from ..core import sparse_GP
|
||||
|
||||
def backsub_both_sides(L,X):
|
||||
""" Return L^-T * X * L^-1, assumuing X is symmetrical and L is lower cholesky"""
|
||||
|
|
@ -36,12 +36,12 @@ class generalized_FITC(sparse_GP):
|
|||
"""
|
||||
|
||||
def __init__(self, X, likelihood, kernel, Z, X_variance=None, normalize_X=False):
|
||||
|
||||
self.Z = Z
|
||||
self.M = self.Z.shape[0]
|
||||
self.true_precision = likelihood.precision
|
||||
|
||||
sparse_GP.__init__(self, X, likelihood, kernel=kernel, Z=self.Z, X_variance=None, normalize_X=False)
|
||||
super(generalized_FITC, self).__init__(self, X, likelihood, kernel=kernel, Z=self.Z, X_variance=None, normalize_X=False)
|
||||
self._set_params(self._get_params())
|
||||
|
||||
def _set_params(self, p):
|
||||
self.Z = p[:self.M*self.Q].reshape(self.M, self.Q)
|
||||
|
|
|
|||
|
|
@ -5,7 +5,7 @@ Created on 10 Apr 2013
|
|||
'''
|
||||
from GPy.core import model
|
||||
from GPy.models.Bayesian_GPLVM import Bayesian_GPLVM
|
||||
from GPy.models.sparse_GP import sparse_GP
|
||||
from GPy.core import sparse_GP
|
||||
from GPy.util.linalg import PCA
|
||||
from scipy import linalg
|
||||
import numpy
|
||||
|
|
@ -23,7 +23,7 @@ class MRD(model):
|
|||
:type likelihood_list: [GPy.likelihood] | [Y1..Yy]
|
||||
:param names: names for different gplvm models
|
||||
:type names: [str]
|
||||
:param Q: latent dimensionality (will raise
|
||||
:param Q: latent dimensionality (will raise
|
||||
:type Q: int
|
||||
:param initx: initialisation method for the latent space
|
||||
:type initx: 'PCA'|'random'
|
||||
|
|
@ -77,6 +77,7 @@ class MRD(model):
|
|||
self.MQ = self.M * self.Q
|
||||
|
||||
model.__init__(self) # @UndefinedVariable
|
||||
self._set_params(self._get_params())
|
||||
|
||||
@property
|
||||
def X(self):
|
||||
|
|
@ -153,7 +154,7 @@ class MRD(model):
|
|||
def _get_params(self):
|
||||
"""
|
||||
return parameter list containing private and shared parameters as follows:
|
||||
|
||||
|
||||
=================================================================
|
||||
| mu | S | Z || theta1 | theta2 | .. | thetaN |
|
||||
=================================================================
|
||||
|
|
|
|||
|
|
@ -1,284 +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, tdot, symmetrify, backsub_both_sides, chol_inv
|
||||
from ..util.plot import gpplot
|
||||
from .. import kern
|
||||
from GP import GP
|
||||
from scipy import linalg
|
||||
from ..likelihoods import Gaussian
|
||||
|
||||
class sparse_GP(GP):
|
||||
"""
|
||||
Variational sparse GP model
|
||||
|
||||
:param X: inputs
|
||||
:type X: np.ndarray (N x Q)
|
||||
: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 (N x Q) | None
|
||||
:param Z: inducing inputs (optional, see note)
|
||||
:type Z: np.ndarray (M x Q) | None
|
||||
:param M : Number of inducing points (optional, default 10. Ignored if Z is not None)
|
||||
:type M: 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):
|
||||
self.Z = Z
|
||||
self.M = Z.shape[0]
|
||||
self.likelihood = likelihood
|
||||
|
||||
if X_variance is None:
|
||||
self.has_uncertain_inputs = False
|
||||
else:
|
||||
assert X_variance.shape == X.shape
|
||||
self.has_uncertain_inputs = True
|
||||
self.X_variance = X_variance
|
||||
|
||||
GP.__init__(self, X, likelihood, kernel=kernel, normalize_X=normalize_X)
|
||||
|
||||
# normalize X uncertainty also
|
||||
if self.has_uncertain_inputs:
|
||||
self.X_variance /= np.square(self._Xstd)
|
||||
|
||||
|
||||
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).T
|
||||
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.Z, self.X)
|
||||
self.psi2 = None
|
||||
|
||||
def _computations(self):
|
||||
|
||||
# factor 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.N, 1, 1))).sum(0)
|
||||
else:
|
||||
psi2_beta = self.psi2.sum(0) * self.likelihood.precision
|
||||
evals, evecs = 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 * (np.sqrt(self.likelihood.precision.flatten().reshape(1, self.N)))
|
||||
else:
|
||||
tmp = self.psi1 * (np.sqrt(self.likelihood.precision))
|
||||
tmp, _ = linalg.lapack.flapack.dtrtrs(self.Lm, np.asfortranarray(tmp), lower=1)
|
||||
self.A = tdot(tmp)
|
||||
|
||||
|
||||
# factor B
|
||||
self.B = np.eye(self.M) + self.A
|
||||
self.LB = jitchol(self.B)
|
||||
|
||||
# TODO: make a switch for either first compute psi1V, or VV.T
|
||||
self.psi1V = np.dot(self.psi1, self.likelihood.V)
|
||||
|
||||
# back substutue C into psi1V
|
||||
tmp, info1 = linalg.lapack.flapack.dtrtrs(self.Lm, np.asfortranarray(self.psi1V), lower=1, trans=0)
|
||||
self._LBi_Lmi_psi1V, _ = linalg.lapack.flapack.dtrtrs(self.LB, np.asfortranarray(tmp), lower=1, trans=0)
|
||||
tmp, info2 = linalg.lapack.flapack.dpotrs(self.LB, tmp, lower=1)
|
||||
self.Cpsi1V, info3 = linalg.lapack.flapack.dtrtrs(self.Lm, tmp, lower=1, trans=1)
|
||||
|
||||
# Compute dL_dKmm
|
||||
tmp = tdot(self._LBi_Lmi_psi1V)
|
||||
self.DBi_plus_BiPBi = backsub_both_sides(self.LB, self.D * np.eye(self.M) + tmp)
|
||||
tmp = -0.5 * self.DBi_plus_BiPBi
|
||||
tmp += -0.5 * self.B * self.D
|
||||
tmp += self.D * np.eye(self.M)
|
||||
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.D * (self.likelihood.precision * np.ones([self.N, 1])).flatten()
|
||||
self.dL_dpsi1 = np.dot(self.Cpsi1V, self.likelihood.V.T)
|
||||
dL_dpsi2_beta = 0.5 * backsub_both_sides(self.Lm, self.D * np.eye(self.M) - 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(1, self.N))
|
||||
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.N, axis=0)
|
||||
else:
|
||||
# subsume back into psi1 (==Kmn)
|
||||
self.dL_dpsi1 += 2.*np.dot(dL_dpsi2, self.psi1)
|
||||
self.dL_dpsi2 = None
|
||||
|
||||
|
||||
# the partial derivative vector for the likelihood
|
||||
if self.likelihood.Nparams == 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
|
||||
self.partial_for_likelihood = -0.5 * self.N * self.D * self.likelihood.precision + 0.5 * self.likelihood.trYYT * self.likelihood.precision ** 2
|
||||
self.partial_for_likelihood += 0.5 * self.D * (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) - np.sum(np.square(self._LBi_Lmi_psi1V)))
|
||||
|
||||
|
||||
|
||||
def log_likelihood(self):
|
||||
""" Compute the (lower bound on the) log marginal likelihood """
|
||||
if self.likelihood.is_heteroscedastic:
|
||||
A = -0.5 * self.N * self.D * 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.D * (np.sum(self.likelihood.precision.flatten() * self.psi0) - np.trace(self.A))
|
||||
else:
|
||||
A = -0.5 * self.N * self.D * (np.log(2.*np.pi) - np.log(self.likelihood.precision)) - 0.5 * self.likelihood.precision * self.likelihood.trYYT
|
||||
B = -0.5 * self.D * (np.sum(self.likelihood.precision * self.psi0) - np.trace(self.A))
|
||||
C = -self.D * (np.sum(np.log(np.diag(self.LB)))) # + 0.5 * self.M * np.log(sf2))
|
||||
D = 0.5 * np.sum(np.square(self._LBi_Lmi_psi1V))
|
||||
return A + B + C + D + self.likelihood.Z
|
||||
|
||||
def _set_params(self, p):
|
||||
self.Z = p[:self.M * self.Q].reshape(self.M, self.Q)
|
||||
self.kern._set_params(p[self.Z.size:self.Z.size + self.kern.Nparam])
|
||||
self.likelihood._set_params(p[self.Z.size + self.kern.Nparam:])
|
||||
self._compute_kernel_matrices()
|
||||
self._computations()
|
||||
|
||||
def _get_params(self):
|
||||
return np.hstack([self.Z.flatten(), GP._get_params(self)])
|
||||
|
||||
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])], []) + GP._get_param_names(self)
|
||||
|
||||
def update_likelihood_approximation(self):
|
||||
"""
|
||||
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() # TODO check consistency with pseudo_EP
|
||||
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, diag_tr_psi2Kmmi) # 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)
|
||||
# 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.T, 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.Z, self.X)
|
||||
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 = 2.*self.kern.dK_dX(self.dL_dKmm, self.Z) # factor of two becase of vertical and horizontal 'stripes' in dKmm_dZ
|
||||
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, 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"""
|
||||
|
||||
Bi, _ = linalg.lapack.flapack.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.M) - Bi)
|
||||
|
||||
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 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
|
||||
else:
|
||||
Kxx = self.kern.Kdiag(Xnew, which_parts=which_parts)
|
||||
var = Kxx - np.sum(Kx * np.dot(Kmmi_LmiBLmi, Kx), 0)
|
||||
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)
|
||||
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)
|
||||
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):
|
||||
"""
|
||||
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.Q
|
||||
:param X_variance_new: The uncertainty in the prediction points
|
||||
:type X_variance_new: np.ndarray, Nnew x self.Q
|
||||
: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 folll covariance matrix, or just the diagonal
|
||||
:type full_cov: bool
|
||||
:rtype: posterior mean, a Numpy array, Nnew x self.D
|
||||
: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.D
|
||||
|
||||
|
||||
If full_cov and self.D > 1, the return shape of var is Nnew x Nnew x self.D. If self.D == 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._Xmean) / self._Xstd
|
||||
if X_variance_new is not None:
|
||||
X_variance_new = X_variance_new / self._Xstd ** 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)
|
||||
|
||||
return mean, var, _025pm, _975pm
|
||||
|
||||
|
|
@ -8,7 +8,7 @@ import sys, pdb
|
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# from .. import kern
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# from ..core import model
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# from ..util.linalg import pdinv, PCA
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from GPLVM import GPLVM
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from ..core import GPLVM
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from sparse_GP_regression import sparse_GP_regression
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class sparse_GPLVM(sparse_GP_regression, GPLVM):
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|
|
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@ -3,7 +3,7 @@
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|
||||
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import numpy as np
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from sparse_GP import sparse_GP
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from ..core import sparse_GP
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from .. import likelihoods
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from .. import kern
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||||
from ..likelihoods import likelihood
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|
|
@ -43,4 +43,5 @@ class sparse_GP_regression(sparse_GP):
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#likelihood defaults to Gaussian
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likelihood = likelihoods.Gaussian(Y,normalize=normalize_Y)
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||||
|
||||
sparse_GP.__init__(self, X, likelihood, kernel, Z, normalize_X=normalize_X)
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||||
super(sparse_GP_regression, self).__init__(self, X, likelihood, kernel, Z, normalize_X=normalize_X)
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self._set_params(self._get_params())
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||||
|
|
|
|||
|
|
@ -9,7 +9,7 @@ from ..util.linalg import pdinv
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|||
from ..util.plot import gpplot
|
||||
from ..util.warping_functions import *
|
||||
from GP_regression import GP_regression
|
||||
from GP import GP
|
||||
from ..core import GP
|
||||
from .. import likelihoods
|
||||
from .. import kern
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||||
|
||||
|
|
@ -29,7 +29,8 @@ class warpedGP(GP):
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|||
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)
|
||||
super(warpedGP, self).__init__(self, X, likelihood, kernel, normalize_X=normalize_X)
|
||||
self._set_params(self._get_params())
|
||||
|
||||
def _scale_data(self, Y):
|
||||
self._Ymax = Y.max()
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue