From a0d6634387cf1d488578209361ea8ce9a8a538fe Mon Sep 17 00:00:00 2001 From: Alan Saul Date: Wed, 21 May 2014 11:30:52 +0100 Subject: [PATCH 01/39] Added a numpy version of univariate gaussian, untested and is significantly slower but may be useful soon. --- GPy/util/univariate_Gaussian.py | 31 +++++++++++++++++++++++++++++++ 1 file changed, 31 insertions(+) diff --git a/GPy/util/univariate_Gaussian.py b/GPy/util/univariate_Gaussian.py index 702ab25c..b5472e0a 100644 --- a/GPy/util/univariate_Gaussian.py +++ b/GPy/util/univariate_Gaussian.py @@ -40,6 +40,37 @@ def std_norm_cdf(x): weave.inline(code, arg_names=['x', 'cdf_x', 'N'], support_code=support_code) return cdf_x +def std_norm_cdf_np(x): + """ + Cumulative standard Gaussian distribution + Based on Abramowitz, M. and Stegun, I. (1970) + Around 3 times slower when x is a scalar otherwise quite a lot slower + """ + 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 inv_std_norm_cdf(x): """ Inverse cumulative standard Gaussian distribution From dd6f7c1f4c3f20d133efea073697fa782f50802e Mon Sep 17 00:00:00 2001 From: Neil Lawrence Date: Thu, 29 May 2014 16:57:01 +0100 Subject: [PATCH 02/39] Modified Spellman et al data load. --- GPy/installation.cfg | 2 +- GPy/util/datasets.py | 2 +- 2 files changed, 2 insertions(+), 2 deletions(-) diff --git a/GPy/installation.cfg b/GPy/installation.cfg index 867a15bf..901a7ef5 100644 --- a/GPy/installation.cfg +++ b/GPy/installation.cfg @@ -1,2 +1,2 @@ -# This is the local configuration file for GPy +# This is the local installation configuration file for GPy diff --git a/GPy/util/datasets.py b/GPy/util/datasets.py index 44c9a930..ea23b21c 100644 --- a/GPy/util/datasets.py +++ b/GPy/util/datasets.py @@ -385,7 +385,7 @@ def spellman_yeast(data_set='spellman_yeast'): Y = read_csv(filename, header=0, index_col=0, sep='\t') return data_details_return({'Y': Y}, data_set) -def spellman_yeast_cdc(data_set='spellman_yeast'): +def spellman_yeast_cdc15(data_set='spellman_yeast'): if not data_available(data_set): download_data(data_set) from pandas import read_csv From 6e30f3c6c37f6e00a3d03597d8abb945af28f49e Mon Sep 17 00:00:00 2001 From: Zhenwen Dai Date: Fri, 30 May 2014 18:56:23 +0100 Subject: [PATCH 03/39] [splitkern] support idx_p==0 --- GPy/kern/_src/independent_outputs.py | 2 ++ GPy/kern/_src/splitKern.py | 10 ++++++++++ 2 files changed, 12 insertions(+) diff --git a/GPy/kern/_src/independent_outputs.py b/GPy/kern/_src/independent_outputs.py index f07db692..21958267 100644 --- a/GPy/kern/_src/independent_outputs.py +++ b/GPy/kern/_src/independent_outputs.py @@ -20,6 +20,8 @@ def index_to_slices(index): 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) diff --git a/GPy/kern/_src/splitKern.py b/GPy/kern/_src/splitKern.py index dfaf5108..27e4f76b 100644 --- a/GPy/kern/_src/splitKern.py +++ b/GPy/kern/_src/splitKern.py @@ -20,6 +20,9 @@ class DiffGenomeKern(Kern): assert X2==None K = self.kern.K(X,X2) + if self.idx_p<=0 or self.idx_p>X.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 @@ -33,6 +36,9 @@ class DiffGenomeKern(Kern): 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 @@ -42,6 +48,10 @@ class DiffGenomeKern(Kern): 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 From 38ed60385aa0c9a2c1b54150e6efcf0fd5350620 Mon Sep 17 00:00:00 2001 From: Max Zwiessele Date: Tue, 3 Jun 2014 15:42:32 -0700 Subject: [PATCH 04/39] linalg had lowers missing for windows libraries to work correctly --- GPy/util/linalg.py | 5 +++-- 1 file changed, 3 insertions(+), 2 deletions(-) diff --git a/GPy/util/linalg.py b/GPy/util/linalg.py index 661a2b47..6a38a7c3 100644 --- a/GPy/util/linalg.py +++ b/GPy/util/linalg.py @@ -30,6 +30,7 @@ if config.getboolean('anaconda', 'installed') and config.getboolean('anaconda', dsyrk = mkl_rt.dsyrk dsyr = mkl_rt.dsyr _blas_available = True + print 'anaconda installed and mkl is loaded' except: _blas_available = False else: @@ -150,7 +151,7 @@ def dpotri(A, lower=1): assert lower==1, "scipy linalg behaviour is very weird. please use lower, fortran ordered arrays" A = force_F_ordered(A) - R, info = lapack.dpotri(A, lower=0) + R, info = lapack.dpotri(A, lower=1) symmetrify(R) return R, info @@ -217,7 +218,7 @@ def pdinv(A, *args): L = jitchol(A, *args) logdet = 2.*np.sum(np.log(np.diag(L))) Li = dtrtri(L) - Ai, _ = lapack.dpotri(L) + Ai, _ = lapack.dpotri(L, lower=1) # Ai = np.tril(Ai) + np.tril(Ai,-1).T symmetrify(Ai) From 730e229238062fa22b726e8c30c891d0819b3c6e Mon Sep 17 00:00:00 2001 From: Neil Lawrence Date: Wed, 4 Jun 2014 11:21:25 +0100 Subject: [PATCH 05/39] Minor edits to reading Lee data in datasets.py --- GPy/Youter.txt | 12 + .../parameterization/tmp/observable_array.py | 137 +++++ GPy/core/tmp/domains.py | 26 + GPy/core/tmp/fitc.py | 248 ++++++++ GPy/core/tmp/gp_base.py | 275 +++++++++ GPy/core/tmp/parameterized.py | 465 +++++++++++++++ GPy/core/tmp/priors.py | 217 +++++++ GPy/core/tmp/transformations.py | 143 +++++ GPy/examples/old_examples/GPLVM_demo.py | 28 + .../old_examples/GP_regression_demo.py | 51 ++ .../old_examples/GP_regression_kern_demo.py | 33 + GPy/examples/old_examples/oil_flow_demo.py | 53 ++ .../old_examples/sparse_GPLVM_demo.py | 31 + .../old_examples/sparse_GP_regression_demo.py | 70 +++ .../uncertain_input_GP_regression_demo.py | 31 + GPy/examples/old_examples/warped_GP_demo.py | 45 ++ GPy/kern/__init__.py~ | 14 + GPy/kern/_src/notes.txt | 5 + GPy/kern/_src/ode1_eq_lfm.py | 52 ++ GPy/kern/_src/old_symbolic.py | 445 ++++++++++++++ GPy/kern/_src/old_sympykern.py | 564 ++++++++++++++++++ GPy/kern/_src/poly_tmp.py | 134 +++++ GPy/kern/_src/symbolic2.py | 70 +++ GPy/kern/matlab_construct.py | 17 + GPy/kern/parts/eq.py | 318 ++++++++++ GPy/kern/parts/ode1.py | 428 +++++++++++++ GPy/kern/parts/sympykern_old.py | 461 ++++++++++++++ GPy/kern/ratquad.py | 179 ++++++ GPy/libpeerconnection.log | 0 GPy/likelihoods/negative_binomial.py~ | 31 + GPy/likelihoods/null_category.py | 53 ++ GPy/likelihoods/null_category.py~ | 46 ++ GPy/likelihoods/old_symbolic.py | 316 ++++++++++ GPy/likelihoods/symbolic.py~ | 234 ++++++++ GPy/likelihoods/symlikelihood.py~ | 318 ++++++++++ GPy/log_like_grad.txt | 1 + GPy/mappings/symbolic.py~ | 149 +++++ GPy/util/data_resources2.json | 1 + GPy/util/datasets.py | 10 +- GPy/util/libpeerconnection.log | 0 GPy/util/osu_accad/camper_04TXT.ZIP | 213 +++++++ GPy/util/osu_accad/connections.txt | 22 + GPy/util/osu_accad/dance_KB3_TXT.ZIP | Bin 0 -> 2077367 bytes GPy/util/osu_accad/dogwalkTXT.ZIP | Bin 0 -> 693086 bytes GPy/util/osu_accad/handspring1TXT.ZIP | Bin 0 -> 123509 bytes GPy/util/osu_accad/per20_TXT.ZIP | Bin 0 -> 2403103 bytes GPy/util/osu_accad/perTWO07_TXT.ZIP | Bin 0 -> 3205054 bytes GPy/util/osu_accad/perTWO13_TXT.ZIP | Bin 0 -> 695550 bytes GPy/util/osu_accad/perTWO14_TXT.ZIP | Bin 0 -> 897278 bytes GPy/util/osu_accad/perTWO15_TXT.ZIP | Bin 0 -> 2429360 bytes GPy/util/osu_accad/perTWO16_TXT.ZIP | Bin 0 -> 2909639 bytes GPy/util/osu_accad/quickwalkTXT.ZIP | Bin 0 -> 108118 bytes GPy/util/osu_accad/run1TXT.ZIP | Bin 0 -> 78645 bytes GPy/util/osu_accad/sprintTXT.ZIP | Bin 0 -> 96690 bytes GPy/util/osu_accad/swagger1TXT.ZIP | Bin 0 -> 196319 bytes GPy/util/osu_run1/Aug210107.txt | 266 +++++++++ GPy/util/osu_run1/connections.txt | 22 + GPy/util/osu_run1/run1TXT.ZIP | Bin 0 -> 78645 bytes GPy/util/osu_run1/sprintTXT.ZIP | Bin 0 -> 96690 bytes GPy/util/sinc.py | 34 ++ Untitled0.ipynb | 73 +++ svm_gui.py | 330 ++++++++++ test6.py | 95 +++ 63 files changed, 6761 insertions(+), 5 deletions(-) create mode 100644 GPy/Youter.txt create mode 100644 GPy/core/parameterization/tmp/observable_array.py create mode 100644 GPy/core/tmp/domains.py create mode 100644 GPy/core/tmp/fitc.py create mode 100644 GPy/core/tmp/gp_base.py create mode 100644 GPy/core/tmp/parameterized.py create mode 100644 GPy/core/tmp/priors.py create mode 100644 GPy/core/tmp/transformations.py create mode 100644 GPy/examples/old_examples/GPLVM_demo.py create mode 100644 GPy/examples/old_examples/GP_regression_demo.py create mode 100644 GPy/examples/old_examples/GP_regression_kern_demo.py create mode 100644 GPy/examples/old_examples/oil_flow_demo.py create mode 100644 GPy/examples/old_examples/sparse_GPLVM_demo.py create mode 100644 GPy/examples/old_examples/sparse_GP_regression_demo.py create mode 100644 GPy/examples/old_examples/uncertain_input_GP_regression_demo.py create mode 100644 GPy/examples/old_examples/warped_GP_demo.py create mode 100644 GPy/kern/__init__.py~ create mode 100644 GPy/kern/_src/notes.txt create mode 100644 GPy/kern/_src/ode1_eq_lfm.py create mode 100644 GPy/kern/_src/old_symbolic.py create mode 100644 GPy/kern/_src/old_sympykern.py create mode 100644 GPy/kern/_src/poly_tmp.py create mode 100644 GPy/kern/_src/symbolic2.py create mode 100644 GPy/kern/matlab_construct.py create mode 100644 GPy/kern/parts/eq.py create mode 100644 GPy/kern/parts/ode1.py create mode 100644 GPy/kern/parts/sympykern_old.py create mode 100644 GPy/kern/ratquad.py create mode 100644 GPy/libpeerconnection.log create mode 100644 GPy/likelihoods/negative_binomial.py~ create mode 100644 GPy/likelihoods/null_category.py create mode 100644 GPy/likelihoods/null_category.py~ create mode 100644 GPy/likelihoods/old_symbolic.py create mode 100644 GPy/likelihoods/symbolic.py~ create mode 100644 GPy/likelihoods/symlikelihood.py~ create mode 100644 GPy/log_like_grad.txt create mode 100644 GPy/mappings/symbolic.py~ create mode 100644 GPy/util/data_resources2.json create mode 100644 GPy/util/libpeerconnection.log create mode 100644 GPy/util/osu_accad/camper_04TXT.ZIP create mode 100644 GPy/util/osu_accad/connections.txt create mode 100644 GPy/util/osu_accad/dance_KB3_TXT.ZIP create mode 100644 GPy/util/osu_accad/dogwalkTXT.ZIP create mode 100644 GPy/util/osu_accad/handspring1TXT.ZIP create mode 100644 GPy/util/osu_accad/per20_TXT.ZIP create mode 100644 GPy/util/osu_accad/perTWO07_TXT.ZIP create mode 100644 GPy/util/osu_accad/perTWO13_TXT.ZIP create mode 100644 GPy/util/osu_accad/perTWO14_TXT.ZIP create mode 100644 GPy/util/osu_accad/perTWO15_TXT.ZIP create mode 100644 GPy/util/osu_accad/perTWO16_TXT.ZIP create mode 100644 GPy/util/osu_accad/quickwalkTXT.ZIP create mode 100644 GPy/util/osu_accad/run1TXT.ZIP create mode 100644 GPy/util/osu_accad/sprintTXT.ZIP create mode 100644 GPy/util/osu_accad/swagger1TXT.ZIP create mode 100644 GPy/util/osu_run1/Aug210107.txt create mode 100644 GPy/util/osu_run1/connections.txt create mode 100644 GPy/util/osu_run1/run1TXT.ZIP create mode 100644 GPy/util/osu_run1/sprintTXT.ZIP create mode 100644 GPy/util/sinc.py create mode 100644 Untitled0.ipynb create mode 100644 svm_gui.py create mode 100644 test6.py diff --git a/GPy/Youter.txt b/GPy/Youter.txt new file mode 100644 index 00000000..3b68a2c4 --- /dev/null +++ b/GPy/Youter.txt @@ -0,0 +1,12 @@ +models/generalized_FITC.py: self.Youter = np.dot(self.mu_tilde,self.mu_tilde.T) +models/generalized_FITC.py: B = -.5*np.sum(self.Qi*self.Youter) +models/GP_regression.py: # then it's more efficient to store Youter +models/GP_regression.py: self.Youter = np.dot(self.Y, self.Y.T) +models/GP_regression.py: self.Youter = None +models/GP_regression.py: Computes the model fit using Youter if it's available +models/GP_regression.py: if self.Youter is None: +models/GP_regression.py: return -0.5*np.sum(np.multiply(self.Ki, self.Youter)) +models/GP_regression.py: if self.Youter is None: +models/GP_regression.py: dL_dK = 0.5*(mdot(self.Ki, self.Youter, self.Ki) - self.D*self.Ki) +models/warped_GP.py: self.Youter = np.dot(self.Y, self.Y.T) +models/warped_GP.py: self.Youter = None diff --git a/GPy/core/parameterization/tmp/observable_array.py b/GPy/core/parameterization/tmp/observable_array.py new file mode 100644 index 00000000..fc9d6cf2 --- /dev/null +++ b/GPy/core/parameterization/tmp/observable_array.py @@ -0,0 +1,137 @@ +# Copyright (c) 2012, GPy authors (see AUTHORS.txt). +# Licensed under the BSD 3-clause license (see LICENSE.txt) + +__updated__ = '2014-03-31' + +import numpy as np +from parameter_core import Observable, Pickleable + +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): + 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 + #cls.__name__ = "ObsAr" # because of fixed printing of `array` in np printing + 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._observer_callables_ = getattr(obj, '_observer_callables_', None) + + def __array_wrap__(self, out_arr, context=None): + return out_arr.view(np.ndarray) + + def copy(self): + memo = {} + memo[id(self)] = self + 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 + s.__dict__.update(copy.deepcopy(self.__dict__, 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 \ No newline at end of file diff --git a/GPy/core/tmp/domains.py b/GPy/core/tmp/domains.py new file mode 100644 index 00000000..cefac6c2 --- /dev/null +++ b/GPy/core/tmp/domains.py @@ -0,0 +1,26 @@ +''' +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/tmp/fitc.py b/GPy/core/tmp/fitc.py new file mode 100644 index 00000000..97b4fb1d --- /dev/null +++ b/GPy/core/tmp/fitc.py @@ -0,0 +1,248 @@ +# 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/tmp/gp_base.py b/GPy/core/tmp/gp_base.py new file mode 100644 index 00000000..7d58c82c --- /dev/null +++ b/GPy/core/tmp/gp_base.py @@ -0,0 +1,275 @@ +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/tmp/parameterized.py b/GPy/core/tmp/parameterized.py new file mode 100644 index 00000000..35d2795c --- /dev/null +++ b/GPy/core/tmp/parameterized.py @@ -0,0 +1,465 @@ +# 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/tmp/priors.py b/GPy/core/tmp/priors.py new file mode 100644 index 00000000..43090ae3 --- /dev/null +++ b/GPy/core/tmp/priors.py @@ -0,0 +1,217 @@ +# 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/tmp/transformations.py b/GPy/core/tmp/transformations.py new file mode 100644 index 00000000..73a9837b --- /dev/null +++ b/GPy/core/tmp/transformations.py @@ -0,0 +1,143 @@ +# 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/examples/old_examples/GPLVM_demo.py b/GPy/examples/old_examples/GPLVM_demo.py new file mode 100644 index 00000000..651af6be --- /dev/null +++ b/GPy/examples/old_examples/GPLVM_demo.py @@ -0,0 +1,28 @@ +# 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 +import GPy +np.random.seed(1) +print "GPLVM with RBF kernel" + +N = 100 +Q = 1 +D = 2 +X = np.random.rand(N, Q) +k = GPy.kern.rbf(Q, 1.0, 2.0) + GPy.kern.white(Q, 0.00001) +K = k.K(X) +Y = np.random.multivariate_normal(np.zeros(N),K,D).T + +m = GPy.models.GPLVM(Y, Q) +m.constrain_positive('(rbf|bias|white)') + +pb.figure() +m.plot() +pb.title('PCA initialisation') +pb.figure() +m.optimize(messages = 1) +m.plot() +pb.title('After optimisation') diff --git a/GPy/examples/old_examples/GP_regression_demo.py b/GPy/examples/old_examples/GP_regression_demo.py new file mode 100644 index 00000000..0fe2fabd --- /dev/null +++ b/GPy/examples/old_examples/GP_regression_demo.py @@ -0,0 +1,51 @@ +# Copyright (c) 2012, GPy authors (see AUTHORS.txt). +# Licensed under the BSD 3-clause license (see LICENSE.txt) + + +""" +Simple Gaussian Processes regression with an RBF kernel +""" +import pylab as pb +import numpy as np +import GPy +pb.ion() +pb.close('all') + + +###################################### +## 1 dimensional example + +# sample inputs and outputs +X = np.random.uniform(-3.,3.,(20,1)) +Y = np.sin(X)+np.random.randn(20,1)*0.05 + +# create simple GP model +m = GPy.models.GP_regression(X,Y) + +# contrain all parameters to be positive +m.constrain_positive('') + +# optimize and plot +m.optimize('tnc', max_f_eval = 1000) +m.plot() +print(m) + +###################################### +## 2 dimensional example + +# sample inputs and outputs +X = np.random.uniform(-3.,3.,(40,2)) +Y = np.sin(X[:,0:1]) * np.sin(X[:,1:2])+np.random.randn(40,1)*0.05 + +# create simple GP model +m = GPy.models.GP_regression(X,Y) + +# contrain all parameters to be positive +m.constrain_positive('') +# optimize and plot +pb.figure() +m.optimize('tnc', max_f_eval = 1000) +m.plot() +print(m) + + diff --git a/GPy/examples/old_examples/GP_regression_kern_demo.py b/GPy/examples/old_examples/GP_regression_kern_demo.py new file mode 100644 index 00000000..8f0b9226 --- /dev/null +++ b/GPy/examples/old_examples/GP_regression_kern_demo.py @@ -0,0 +1,33 @@ +# Copyright (c) 2012, GPy authors (see AUTHORS.txt). +# Licensed under the BSD 3-clause license (see LICENSE.txt) + + +""" +Simple one-dimensional Gaussian Processes with assorted kernel functions +""" +import pylab as pb +import numpy as np +import GPy + +# sample inputs and outputs +D = 1 +X = np.random.randn(10,D)*2 +X = np.linspace(-1.5,1.5,5)[:,None] +X = np.append(X,[[5]],0) +Y = np.sin(np.pi*X/2) #+np.random.randn(X.shape[0],1)*0.05 + +models = [GPy.models.GP_regression(X,Y, k) for k in (GPy.kern.rbf(D), GPy.kern.Matern52(D), GPy.kern.Matern32(D), GPy.kern.exponential(D), GPy.kern.linear(D) + GPy.kern.white(D), GPy.kern.bias(D) + GPy.kern.white(D))] + +pb.figure(figsize=(12,8)) +for i,m in enumerate(models): + m.constrain_positive('') + m.optimize() + pb.subplot(3,2,i+1) + m.plot() + #pb.title(m.kern.parts[0].name) + +GPy.util.plot.align_subplots(3,2,(-3,6),(-2.5,2.5)) + +pb.show() + + diff --git a/GPy/examples/old_examples/oil_flow_demo.py b/GPy/examples/old_examples/oil_flow_demo.py new file mode 100644 index 00000000..eee74461 --- /dev/null +++ b/GPy/examples/old_examples/oil_flow_demo.py @@ -0,0 +1,53 @@ +# Copyright (c) 2012, GPy authors (see AUTHORS.txt). +# Licensed under the BSD 3-clause license (see LICENSE.txt) + + +import cPickle as pickle +import numpy as np +import pylab as pb +import GPy +import pylab as plt +np.random.seed(1) + +def plot_oil(X, theta, labels, label): + plt.figure() + X = X[:,np.argsort(theta)[:2]] + flow_type = (X[labels[:,0]==1]) + plt.plot(flow_type[:,0], flow_type[:,1], 'rx') + flow_type = (X[labels[:,1]==1]) + plt.plot(flow_type[:,0], flow_type[:,1], 'gx') + flow_type = (X[labels[:,2]==1]) + plt.plot(flow_type[:,0], flow_type[:,1], 'bx') + plt.title(label) + +data = pickle.load(open('../util/datasets/oil_flow_3classes.pickle', 'r')) + +Y = data['DataTrn'] +N, D = Y.shape +selected = np.random.permutation(N)[:200] +labels = data['DataTrnLbls'][selected] +Y = Y[selected] +N, D = Y.shape +Y -= Y.mean(axis=0) +Y /= Y.std(axis=0) + +Q = 2 +m1 = GPy.models.sparse_GPLVM(Y, Q, M = 15) +m1.constrain_positive('(rbf|bias|noise)') +m1.constrain_bounded('white', 1e-6, 1.0) + +plot_oil(m1.X, np.array([1,1]), labels, 'PCA initialization') +# m.optimize(messages = True) +m1.optimize('bfgs', messages = True) +plot_oil(m1.X, np.array([1,1]), labels, 'sparse GPLVM') +# pb.figure() +# m.plot() +# pb.title('PCA initialisation') +# pb.figure() +# m.optimize(messages = 1) +# m.plot() +# pb.title('After optimisation') +m = GPy.models.GPLVM(Y, Q) +m.constrain_positive('(white|rbf|bias|noise)') +m.optimize() +plot_oil(m.X, np.array([1,1]), labels, 'GPLVM') diff --git a/GPy/examples/old_examples/sparse_GPLVM_demo.py b/GPy/examples/old_examples/sparse_GPLVM_demo.py new file mode 100644 index 00000000..af125d6e --- /dev/null +++ b/GPy/examples/old_examples/sparse_GPLVM_demo.py @@ -0,0 +1,31 @@ +# 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 +import GPy +np.random.seed(1) +print "sparse GPLVM with RBF kernel" + +N = 100 +Q = 1 +D = 2 +#generate GPLVM-like data +X = np.random.rand(N, Q) +k = GPy.kern.rbf(Q, 1.0, 2.0) + GPy.kern.white(Q, 0.00001) +K = k.K(X) +Y = np.random.multivariate_normal(np.zeros(N),K,D).T + +m = GPy.models.sparse_GPLVM(Y, Q, M = 10) +m.constrain_positive('(rbf|bias|noise)') +m.constrain_bounded('white', 1e-3, 0.1) +# m.plot() + +pb.figure() +m.plot() +pb.title('PCA initialisation') +pb.figure() +m.optimize(messages = 1) +m.plot() +pb.title('After optimisation') diff --git a/GPy/examples/old_examples/sparse_GP_regression_demo.py b/GPy/examples/old_examples/sparse_GP_regression_demo.py new file mode 100644 index 00000000..13ff47e0 --- /dev/null +++ b/GPy/examples/old_examples/sparse_GP_regression_demo.py @@ -0,0 +1,70 @@ +# Copyright (c) 2012, GPy authors (see AUTHORS.txt). +# Licensed under the BSD 3-clause license (see LICENSE.txt) + + +import numpy as np +""" +Sparse Gaussian Processes regression with an RBF kernel +""" +import pylab as pb +import numpy as np +import GPy +np.random.seed(2) +pb.ion() +N = 500 + +###################################### +## 1 dimensional example + +# sample inputs and outputs +X = np.random.uniform(-3.,3.,(N,1)) +Y = np.sin(X)+np.random.randn(N,1)*0.05 + +# construct kernel +rbf = GPy.kern.rbf(1) +noise = GPy.kern.white(1) +kernel = rbf + noise + +# create simple GP model +m1 = GPy.models.sparse_GP_regression(X,Y,kernel, M = 10) + +# contrain all parameters to be positive +m1.constrain_positive('(variance|lengthscale|precision)') +#m1.constrain_positive('(variance|lengthscale)') +#m1.constrain_fixed('prec',10.) + + +#check gradient FIXME unit test please +m1.checkgrad() +# optimize and plot +m1.optimize('tnc', messages = 1) +m1.plot() +# print(m1) + +###################################### +## 2 dimensional example + +# # sample inputs and outputs +# X = np.random.uniform(-3.,3.,(N,2)) +# Y = np.sin(X[:,0:1]) * np.sin(X[:,1:2])+np.random.randn(N,1)*0.05 + +# # construct kernel +# rbf = GPy.kern.rbf(2) +# noise = GPy.kern.white(2) +# kernel = rbf + noise + +# # create simple GP model +# m2 = GPy.models.sparse_GP_regression(X,Y,kernel, M = 50) +# create simple GP model + +# # contrain all parameters to be positive (but not inducing inputs) +# m2.constrain_positive('(variance|lengthscale|precision)') + +# #check gradient FIXME unit test please +# m2.checkgrad() + +# # optimize and plot +# pb.figure() +# m2.optimize('tnc', messages = 1) +# m2.plot() +# print(m2) diff --git a/GPy/examples/old_examples/uncertain_input_GP_regression_demo.py b/GPy/examples/old_examples/uncertain_input_GP_regression_demo.py new file mode 100644 index 00000000..3d2c51f0 --- /dev/null +++ b/GPy/examples/old_examples/uncertain_input_GP_regression_demo.py @@ -0,0 +1,31 @@ +# 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 +pb.ion() +pb.close('all') + + +###################################### +## 1 dimensional example + +# sample inputs and outputs +S = np.ones((20,1)) +X = np.random.uniform(-3.,3.,(20,1)) +Y = np.sin(X)+np.random.randn(20,1)*0.05 + +k = GPy.kern.bias(1) + GPy.kern.white(1) + +# create simple GP model +m = GPy.models.uncertain_input_GP_regression(X,Y,S,kernel=k) + +# contrain all parameters to be positive +m.constrain_positive('(variance|prec)') + +# optimize and plot +m.optimize('tnc', max_f_eval = 1000, messages=1) +m.plot() +print(m) diff --git a/GPy/examples/old_examples/warped_GP_demo.py b/GPy/examples/old_examples/warped_GP_demo.py new file mode 100644 index 00000000..3b75694a --- /dev/null +++ b/GPy/examples/old_examples/warped_GP_demo.py @@ -0,0 +1,45 @@ +# Copyright (c) 2012, GPy authors (see AUTHORS.txt). +# Licensed under the BSD 3-clause license (see LICENSE.txt) + + +import numpy as np +import scipy as sp +import pdb, sys, pickle +import matplotlib.pylab as plt +import GPy +np.random.seed(1) + +N = 100 +# sample inputs and outputs +X = np.random.uniform(-np.pi,np.pi,(N,1)) +Y = np.sin(X)+np.random.randn(N,1)*0.05 +# Y += np.abs(Y.min()) + 0.5 +Z = np.exp(Y)# Y**(1/3.0) + +# rescaling targets? +Zmax = Z.max() +Zmin = Z.min() +Z = (Z-Zmin)/(Zmax-Zmin) - 0.5 + +m = GPy.models.warpedGP(X, Z, warping_terms = 2) +m.constrain_positive('(tanh_a|tanh_b|rbf|white|bias)') +m.randomize() +plt.figure() +plt.xlabel('predicted f(Z)') +plt.ylabel('actual f(Z)') +plt.plot(m.Y, Y, 'o', alpha = 0.5, label = 'before training') +m.optimize(messages = True) +plt.plot(m.Y, Y, 'o', alpha = 0.5, label = 'after training') +plt.legend(loc = 0) +m.plot_warping() +plt.figure() +plt.title('warped GP fit') +m.plot() + +m1 = GPy.models.GP_regression(X, Z) +m1.constrain_positive('(rbf|white|bias)') +m1.randomize() +m1.optimize(messages = True) +plt.figure() +plt.title('GP fit') +m1.plot() diff --git a/GPy/kern/__init__.py~ b/GPy/kern/__init__.py~ new file mode 100644 index 00000000..55b69bd7 --- /dev/null +++ b/GPy/kern/__init__.py~ @@ -0,0 +1,14 @@ +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.sympykern import Sympykern +from _src.stationary import Exponential, 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.ssrbf import SSRBF # TODO: ZD: did you remove this? +from _src.ODE_UY import ODE_UY + diff --git a/GPy/kern/_src/notes.txt b/GPy/kern/_src/notes.txt new file mode 100644 index 00000000..dd64fffd --- /dev/null +++ b/GPy/kern/_src/notes.txt @@ -0,0 +1,5 @@ +Combination covariances, with a particular flag (partition?) allow interogation of the individual covariance contribution. So if we have k_3 = k_1 + k_2 because f_3 = f_1 + f_2 then we allow a multi output covariance over f_1, f_2 and f_3 jointly. Then users can make observations of f_3 and f_1 and build a posterior over f_2 using multiple output encoding. When this flag is set an extra input is added to deal with it. We allow for a new 'combination covariance' of the form scale and add so that + +f_3 = f_1*a + f_2 + +Where a can also be negative. diff --git a/GPy/kern/_src/ode1_eq_lfm.py b/GPy/kern/_src/ode1_eq_lfm.py new file mode 100644 index 00000000..fffb3e3c --- /dev/null +++ b/GPy/kern/_src/ode1_eq_lfm.py @@ -0,0 +1,52 @@ +try: + import sympy as sym + sympy_available=True +except ImportError: + sympy_available=False + +import numpy as np +from GPy.util.symbolic import differfln +from symbolic import Symbolic +from sympy import Function, S, oo, I, cos, sin, asin, log, erf, pi, exp, sqrt, sign, gamma, polygamma + +class Ode1_eq_lfm(Symbolic): + """ + A symbolic covariance based on a first order differential equation being driven by a latent force that is an exponentiated quadratic. + + """ + def __init__(self, output_dim=1, param=None, name='Ode1_eq_lfm'): + + input_dim = 2 + x_0, z_0, decay_i, decay_j, lengthscale = sym.symbols('x_0, z_0, decay_i, decay_j, lengthscale', positive=True) + scale_i, scale_j = sym.symbols('scale_i, scale_j') + # note that covariance only valid for positive time. + + class sim_h(Function): + nargs = 5 + @classmethod + def eval(cls, 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 = differfln(arg_1, arg_2) + arg_1 = half_l_di + arg_2 = half_l_di - t/l + ln_part_2 = differfln(half_l_di, half_l_di - t/l) + + + return (exp(half_l_di*half_l_di + - d_i*(t-tprime) + + ln_part_1 + - log(d_i + d_j)) + - exp(half_l_di*half_l_di + - d_i*t - d_j*tprime + + ln_part_2 + - log(d_i + d_j))) + + + f = scale_i*scale_j*(sim_h(x_0, z_0, decay_i, decay_j, lengthscale) + + sim_h(z_0, x_0, decay_j, decay_i, lengthscale)) + # extra input dim is to signify the output dimension. + super(Ode1_eq_lfm, self).__init__(input_dim, k=f, output_dim=output_dim, name=name) + self.lengthscale.constrain_positive() + self.decay.constrain_positive() diff --git a/GPy/kern/_src/old_symbolic.py b/GPy/kern/_src/old_symbolic.py new file mode 100644 index 00000000..8f6d58c0 --- /dev/null +++ b/GPy/kern/_src/old_symbolic.py @@ -0,0 +1,445 @@ +# Check Matthew Rocklin's blog post. +try: + import sympy as sym + sympy_available=True + from sympy.utilities.lambdify import lambdify + from GPy.util.symbolic import stabilise +except ImportError: + sympy_available=False + +import numpy as np +from kern import Kern +from scipy.special import gammaln, gamma, erf, erfc, erfcx, polygamma +from GPy.util.functions import normcdf, normcdfln, logistic, logisticln, differfln +from ...core.parameterization import Param + +class Symbolic(Kern): + """ + A kernel object, where all the hard work is 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='symbolic', param=None, active_dims=None, operators=None, func_modules=[]): + + if k is None: + raise ValueError, "You must provide an argument for the covariance function." + + self.func_modules = func_modules + self.func_modules += [{'gamma':gamma, + 'gammaln':gammaln, + 'erf':erf, 'erfc':erfc, + 'erfcx':erfcx, + 'polygamma':polygamma, + 'differfln':differfln, + 'normcdf':normcdf, + 'normcdfln':normcdfln, + 'logistic':logistic, + 'logisticln':logisticln}, + 'numpy'] + + super(Symbolic, self).__init__(input_dim, active_dims, name) + + self._sym_k = k + + # pull the variable names out of the symbolic covariance function. + sym_vars = [e for e in k.atoms() if e.is_Symbol] + self._sym_x= sorted([e for e in sym_vars if e.name[0:2]=='x_'],key=lambda x:int(x.name[2:])) + self._sym_z= sorted([e for e in sym_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._sym_x)]) + assert all([z.name=='z_%i'%i for i,z in enumerate(self._sym_z)]) + assert len(self._sym_x)==len(self._sym_z) + x_dim=len(self._sym_x) + + self._sym_kdiag = k + for x, z in zip(self._sym_x, self._sym_z): + self._sym_kdiag = self._sym_kdiag.subs(z, x) + + # If it is a multi-output covariance, add an input for indexing the outputs. + self._real_input_dim = x_dim + # Check input dim is number of xs + 1 if output_dim is >1 + assert self.input_dim == x_dim + int(output_dim > 1) + self.output_dim = output_dim + + # extract parameter names from the covariance + thetas = sorted([e for e in sym_vars if not (e.name[0:2]=='x_' or e.name[0:2]=='z_')],key=lambda e:e.name) + + # Look for parameters with index (subscripts), they are associated with different outputs. + if self.output_dim>1: + self._sym_theta_i = sorted([e for e in thetas if (e.name[-2:]=='_i')], key=lambda e:e.name) + self._sym_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._sym_theta_i)==len(self._sym_theta_j) + assert all([theta_i.name[:-2]==theta_j.name[:-2] for theta_i, theta_j in zip(self._sym_theta_i, self._sym_theta_j)]) + + # Extract names of shared parameters (those without a subscript) + self._sym_theta = [theta for theta in thetas if theta not in self._sym_theta_i and theta not in self._sym_theta_j] + + self.num_split_params = len(self._sym_theta_i) + self._split_theta_names = ["%s"%theta.name[:-2] for theta in self._sym_theta_i] + # Add split parameters to the model. + for theta in self._split_theta_names: + # TODO: what if user has passed a parameter vector, how should that be stored and interpreted? + setattr(self, theta, Param(theta, np.ones(self.output_dim), None)) + self.add_parameter(getattr(self, theta)) + + + self.num_shared_params = len(self._sym_theta) + for theta_i, theta_j in zip(self._sym_theta_i, self._sym_theta_j): + self._sym_kdiag = self._sym_kdiag.subs(theta_j, theta_i) + + else: + self.num_split_params = 0 + self._split_theta_names = [] + self._sym_theta = thetas + self.num_shared_params = len(self._sym_theta) + + # Add parameters to the model. + for theta in self._sym_theta: + val = 1.0 + # TODO: what if user has passed a parameter vector, how should that be stored and interpreted? This is the old way before params class. + if param is not None: + if param.has_key(theta.name): + val = param[theta.name] + setattr(self, theta.name, Param(theta.name, val, None)) + self.add_parameters(getattr(self, theta.name)) + + # Differentiate with respect to parameters. + derivative_arguments = self._sym_x + self._sym_theta + if self.output_dim > 1: + derivative_arguments += self._sym_theta_i + + self.derivatives = {theta.name : stabilise(sym.diff(self._sym_k,theta)) for theta in derivative_arguments} + self.diag_derivatives = {theta.name : stabilise(sym.diff(self._sym_kdiag,theta)) for theta in derivative_arguments} + + # This gives the parameters for the arg list. + self.arg_list = self._sym_x + self._sym_z + self._sym_theta + self.diag_arg_list = self._sym_x + self._sym_theta + if self.output_dim > 1: + self.arg_list += self._sym_theta_i + self._sym_theta_j + self.diag_arg_list += self._sym_theta_i + + # Check if there are additional linear operators on the covariance. + self._sym_operators = operators + # TODO: Deal with linear operators + #if self._sym_operators: + # for operator in self._sym_operators: + + # psi_stats aren't yet implemented. + if False: + self.compute_psi_stats() + + # generate the code for the covariance functions + self._gen_code() + + def __add__(self,other): + return spkern(self._sym_k+other._sym_k) + + def _gen_code(self): + #fn_theano = theano_function([self.arg_lists], [self._sym_k + self.derivatives], dims={x: 1}, dtypes={x_0: 'float64', z_0: 'float64'}) + self._K_function = lambdify(self.arg_list, self._sym_k, self.func_modules) + self._K_derivatives_code = {key: lambdify(self.arg_list, self.derivatives[key], self.func_modules) for key in self.derivatives.keys()} + self._Kdiag_function = lambdify(self.diag_arg_list, self._sym_kdiag, self.func_modules) + self._Kdiag_derivatives_code = {key: lambdify(self.diag_arg_list, self.diag_derivatives[key], self.func_modules) for key in self.diag_derivatives.keys()} + + def K(self,X,X2=None): + self._K_computations(X, X2) + return self._K_function(**self._arguments) + + + def Kdiag(self,X): + self._K_computations(X) + return self._Kdiag_function(**self._diag_arguments) + + def _param_grad_helper(self,partial,X,Z,target): + pass + + + 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: + self._K_computations(X, X2) + gradients_X = np.zeros_like(X) + for i, x in enumerate(self._sym_x): + gf = self._K_derivatives_code[x.name] + gradients_X[:, i] = (gf(**self._arguments)*dL_dK).sum(1) + if X2 is None: + gradients_X *= 2 + return gradients_X + + def gradients_X_diag(self, dL_dK, X): + self._K_computations(X) + dX = np.zeros_like(X) + for i, x in enumerate(self._sym_x): + gf = self._Kdiag_derivatives_code[x.name] + dX[:, i] = gf(**self._diag_arguments)*dL_dK + return dX + + def update_gradients_full(self, dL_dK, X, X2=None): + # Need to extract parameters to local variables first + self._K_computations(X, X2) + for theta in self._sym_theta: + parameter = getattr(self, theta.name) + gf = self._K_derivatives_code[theta.name] + gradient = (gf(**self._arguments)*dL_dK).sum() + if X2 is not None: + gradient += (gf(**self._reverse_arguments)*dL_dK).sum() + setattr(parameter, 'gradient', gradient) + if self.output_dim>1: + for theta in self._sym_theta_i: + parameter = getattr(self, theta.name[:-2]) + gf = self._K_derivatives_code[theta.name] + A = gf(**self._arguments)*dL_dK + gradient = np.asarray([A[np.where(self._output_ind==i)].T.sum() + for i in np.arange(self.output_dim)]) + if X2 is None: + gradient *= 2 + else: + A = gf(**self._reverse_arguments)*dL_dK.T + gradient += np.asarray([A[np.where(self._output_ind2==i)].T.sum() + for i in np.arange(self.output_dim)]) + setattr(parameter, 'gradient', gradient) + + + def update_gradients_diag(self, dL_dKdiag, X): + self._K_computations(X) + for theta in self._sym_theta: + parameter = getattr(self, theta.name) + gf = self._Kdiag_derivatives_code[theta.name] + setattr(parameter, 'gradient', (gf(**self._diag_arguments)*dL_dKdiag).sum()) + if self.output_dim>1: + for theta in self._sym_theta_i: + parameter = getattr(self, theta.name[:-2]) + gf = self._Kdiag_derivatives_code[theta.name] + a = gf(**self._diag_arguments)*dL_dKdiag + setattr(parameter, 'gradient', + np.asarray([a[np.where(self._output_ind==i)].sum() + for i in np.arange(self.output_dim)])) + + def _K_computations(self, X, X2=None): + """Set up argument lists for the derivatives.""" + # Could check if this needs doing or not, there could + # definitely be some computational savings by checking for + # parameter updates here. + self._arguments = {} + self._diag_arguments = {} + for i, x in enumerate(self._sym_x): + self._arguments[x.name] = X[:, i][:, None] + self._diag_arguments[x.name] = X[:, i][:, None] + if self.output_dim > 1: + self._output_ind = np.asarray(X[:, -1], dtype='int') + for i, theta in enumerate(self._sym_theta_i): + self._arguments[theta.name] = np.asarray(getattr(self, theta.name[:-2])[self._output_ind])[:, None] + self._diag_arguments[theta.name] = self._arguments[theta.name] + for theta in self._sym_theta: + self._arguments[theta.name] = np.asarray(getattr(self, theta.name)) + self._diag_arguments[theta.name] = self._arguments[theta.name] + + if X2 is not None: + for i, z in enumerate(self._sym_z): + self._arguments[z.name] = X2[:, i][None, :] + if self.output_dim > 1: + self._output_ind2 = np.asarray(X2[:, -1], dtype='int') + for i, theta in enumerate(self._sym_theta_j): + self._arguments[theta.name] = np.asarray(getattr(self, theta.name[:-2])[self._output_ind2])[None, :] + else: + for z in self._sym_z: + self._arguments[z.name] = self._arguments['x_'+z.name[2:]].T + if self.output_dim > 1: + self._output_ind2 = self._output_ind + for theta in self._sym_theta_j: + self._arguments[theta.name] = self._arguments[theta.name[:-2] + '_i'].T + if X2 is not None: + # These arguments are needed in gradients when X2 is not equal to X. + self._reverse_arguments = self._arguments + for x, z in zip(self._sym_x, self._sym_z): + self._reverse_arguments[x.name] = self._arguments[z.name].T + self._reverse_arguments[z.name] = self._arguments[x.name].T + if self.output_dim > 1: + for theta_i, theta_j in zip(self._sym_theta_i, self._sym_theta_j): + self._reverse_arguments[theta_i.name] = self._arguments[theta_j.name].T + self._reverse_arguments[theta_j.name] = self._arguments[theta_i.name].T + +if False: + class Symcombine(CombinationKernel): + """ + Combine list of given sympy covariances together with the provided operations. + """ + def __init__(self, subkerns, operations, name='sympy_combine'): + super(Symcombine, self).__init__(subkerns, name) + for subkern, operation in zip(subkerns, operations): + self._sym_k += self._k_double_operate(subkern._sym_k, operation) + + #def _double_operate(self, k, operation): + + + @Cache_this(limit=2, force_kwargs=['which_parts']) + def K(self, X, X2=None, which_parts=None): + """ + Combine covariances with a linear operator. + """ + assert X.shape[1] == self.input_dim + 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): + assert X.shape[1] == self.input_dim + 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] + + 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 + + def psi0(self, Z, variational_posterior): + return reduce(np.add, (p.psi0(Z, variational_posterior) for p in self.parts)) + + def psi1(self, Z, variational_posterior): + return reduce(np.add, (p.psi1(Z, variational_posterior) for p in self.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) + psi2 += p1.variance * (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) + psi2 += p2.variance * (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 += (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(1) * 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(1) * 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_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(1) * p2.variance * 2. + else: + eff_dL_dpsi1 += dL_dpsi2.sum(1) * p2.psi1(Z, variational_posterior) * 2. + target += p1.gradients_Z_expectations(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_mu = np.zeros(variational_posterior.shape) + target_S = np.zeros(variational_posterior.shape) + 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(1) * p2.variance * 2. + else: + eff_dL_dpsi1 += dL_dpsi2.sum(1) * p2.psi1(Z, variational_posterior) * 2. + a, b = p1.gradients_qX_expectations(dL_dpsi0, eff_dL_dpsi1, dL_dpsi2, Z, variational_posterior) + target_mu += a + target_S += b + return target_mu, target_S + + def _getstate(self): + """ + Get the current state of the class, + here just all the indices, rest can get recomputed + """ + return super(Add, self)._getstate() + + def _setstate(self, state): + super(Add, self)._setstate(state) + + def add(self, other, name='sum'): + if isinstance(other, Add): + other_params = other._parameters_.copy() + for p in other_params: + other.remove_parameter(p) + self.add_parameters(*other_params) + else: self.add_parameter(other) + return self diff --git a/GPy/kern/_src/old_sympykern.py b/GPy/kern/_src/old_sympykern.py new file mode 100644 index 00000000..ab88fcef --- /dev/null +++ b/GPy/kern/_src/old_sympykern.py @@ -0,0 +1,564 @@ +# Check Matthew Rocklin's blog post. +try: + import sympy as sp + sympy_available=True + from sympy.utilities.autowrap import ufuncify +except ImportError: + sympy_available=False + exit() + +from sympy.core.cache import clear_cache +from sympy.utilities.codegen import codegen + +try: + from scipy import weave + weave_available = True +except ImportError: + weave_available = False + +import os +current_dir = os.path.dirname(os.path.abspath(os.path.dirname(__file__))) +import sys +import numpy as np +import re +import tempfile +import pdb +import ast + +from kernpart import Kernpart +from ...core.parameterization import Param +from ...core.parameterization.transformations import Logexp +# TODO have this set up in a set up file! +user_code_storage = tempfile.gettempdir() + +class spkern(Kern): + """ + 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: + name='sympykern' + if k is None: + raise ValueError, "You must provide an argument for the covariance function." + super(spkern, self).__init__(input_dim, name) + + self._sp_k = k + + # pull the variable names out of the symbolic covariance function. + 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) + x_dim=len(self._sp_x) + + # If it is a multi-output covariance, add an input for indexing the outputs. + self._real_input_dim = x_dim + # Check input dim is number of xs + 1 if output_dim is >1 + assert self.input_dim == x_dim + int(output_dim > 1) + self.output_dim = output_dim + + # extract parameter names from the covariance + 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 (subscripts), they are associated with different outputs. + 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 (those without a subscript) + 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, Param(theta, np.ones(self.output_dim), None)) + self.add_parameters(getattr(self, theta)) + + #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 + + # Add parameters to the model. + 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) + setattr(self, theta.name, Param(theta.name, val, None)) + self.add_parameters(getattr(self, theta.name)) + #deal with param + #self._set_params(self._get_params()) + + # Differentiate with respect to parameters. + 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] + + # differentiate with respect to input variables. + self._sp_dk_dx = [sp.diff(k,xi).simplify() for xi in self._sp_x] + + # psi_stats aren't yet implemented. + if False: + self.compute_psi_stats() + + self._code = {} + + # generate the code for the covariance functions + self._gen_code() + + if weave_available: + if False: + extra_compile_args = ['-ftree-vectorize', '-mssse3', '-ftree-vectorizer-verbose=5'] + else: + extra_compile_args = [] + + self.weave_kwargs = { + 'support_code': None, #self._function_code, + 'include_dirs':[user_code_storage, os.path.join(current_dir,'parts/')], + 'headers':['"sympy_helpers.h"', '"'+self.name+'.h"'], + 'sources':[os.path.join(current_dir,"parts/sympy_helpers.cpp"), os.path.join(user_code_storage, self.name+'.cpp')], + 'extra_compile_args':extra_compile_args, + 'extra_link_args':['-lgomp'], + 'verbose':True} + self.parameters_changed() # initializes caches + + + def __add__(self,other): + return spkern(self._sp_k+other._sp_k) + + def _gen_code(self): + + 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)] + # generate c functions from sympy objects + if weave_available: + code_type = "C" + else: + code_type = "PYTHON" + # Need to add the sympy_helpers header in here. + (foo_c,self._function_code), (foo_h,self._function_header) = \ + codegen(code_list, + code_type, + self.name, + argument_sequence=argument_sequence) + + + # Use weave to compute the underlying functions. + if weave_available: + # put the header file where we can find it + f = file(os.path.join(user_code_storage, self.name + '.h'),'w') + f.write(self._function_header) + f.close() + + + if weave_available: + # Substitute any known derivatives which sympy doesn't compute + self._function_code = re.sub('DiracDelta\(.+?,.+?\)','0.0',self._function_code) + # put the cpp file in user code storage (defaults to temp file location) + f = file(os.path.join(user_code_storage, self.name + '.cpp'),'w') + else: + # put the python file in user code storage + f = file(os.path.join(user_code_storage, self.name + '.py'),'w') + f.write(self._function_code) + f.close() + + if weave_available: + # arg_list will store the arguments required for the C code. + input_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 reverse argument list is also required + if self.output_dim>1: + reverse_input_arg_list = list(input_arg_list) + reverse_input_arg_list.reverse() + + # This gives the parameters for the arg list. + param_arg_list = [shared_params.name for shared_params in self._sp_theta] + arg_list = input_arg_list + param_arg_list + + precompute_list=[] + if self.output_dim > 1: + reverse_arg_list= reverse_input_arg_list + list(param_arg_list) + # For multiple outputs, also need the split parameters. + 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) + + # Now we use the arguments in code that computes the separate parts. + + # Any precomputations will be done here eventually. + self._precompute = \ + """ + // Precompute code would go here. It will be called when parameters are updated. + """ + + # Here's the code to do the looping for K + self._code['K'] =\ + """ + // _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 input_dim = X_array->dimensions[1]; + //#pragma omp parallel for + for (i=0;i1: + for i, theta in enumerate(self._sp_theta_i): + grad_func_list = [' '*26 + 'TARGET1(ii) += PARTIAL2(i, j)*dk_d%s(%s);'%(theta.name, arg_string)] + grad_func_list += [' '*26 + 'TARGET1(jj) += PARTIAL2(i, j)*dk_d%s(%s);'%(theta.name, reverse_arg_string)] + grad_func_list = c_define_output_indices+grad_func_list + + grad_func_string = '\n'.join(grad_func_list) + self._code['dK_d' + theta.name] =\ + """ + 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;idimensions[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) += partial[i*num_inducing+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._code['dK_dX'] = \ + """ + // _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 _generate_inline(self, code, X, target=None, Z=None, partial=None): + output_dim = self.output_dim + # Need to extract parameters to local variables first + for shared_params in self._sp_theta: + locals()[shared_params.name] = getattr(self, shared_params.name) + + for split_params in self._split_theta_names: + locals()[split_params] = np.asarray(getattr(self, split_params)) + arg_names = self._get_arg_names(target, Z, partial) + + if weave_available: + return weave.inline(code=code, arg_names=arg_names,**self.weave_kwargs) + else: + raise RuntimeError('Weave not available and other variants of sympy covariance not yet implemented') + + def K(self,X,Z,target): + if Z is None: + self._generate_inline(self._code['K_X'], X, target) + else: + self._generate_inline(self._code['K'], X, target, Z) + + + def Kdiag(self,X,target): + self._generate_inline(self._code['Kdiag'], X, target) + + def _param_grad_helper(self,partial,X,Z,target): + if Z is None: + self._generate_inline(self._code['dK_dtheta_X'], X, target, Z, partial) + else: + self._generate_inline(self._code['dK_dtheta'], X, target, Z, partial) + + def dKdiag_dtheta(self,partial,X,target): + self._generate_inline(self._code['dKdiag_dtheta'], X, target, Z=None, partial=partial).namelocals()[shared_params.name] = getattr(self, shared_params.name) + + def gradients_X(self,partial,X,Z,target): + if Z is None: + self._generate_inline(self._code['dK_dX_X'], X, target, Z, partial) + else: + self._generate_inline(self._code['dK_dX'], X, target, Z, partial) + + def dKdiag_dX(self,partial,X,target): + self._generate_inline(self._code['dKdiag_dX'], X, target, Z, 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 parameters_changed(self): + # Reset the caches + self._cache, self._cache2 = np.empty(shape=(2, 1)) + self._cache3, self._cache4, self._cache5 = np.empty(shape=(3, 1)) + + def update_gradients_full(self, dL_dK, X): + # Need to extract parameters to local variables first + self._K_computations(X, None) + for shared_params in self._sp_theta: + parameter = getattr(self, shared_params.name) + code = self._code['dK_d' + shared_params.name] + setattr(parameter, 'gradient', self._generate_inline(code, X, target=None, Z=None, partial=dL_dK)) + + for split_params in self._split_theta_names: + parameter = getattr(self, split_params.name) + code = self._code['dK_d' + split_params.name] + setattr(parameter, 'gradient', self._generate_inline(code, X, target=None, Z=None, partial=dL_dK)) + + + # def update_gradients_sparse(self, dL_dKmm, dL_dKnm, dL_dKdiag, X, Z): + # #contributions from Kdiag + # self.variance.gradient = np.sum(dL_dKdiag) + + # #from Knm + # self._K_computations(X, Z) + # self.variance.gradient += np.sum(dL_dKnm * self._K_dvar) + # if self.ARD: + # self.lengthscale.gradient = self._dL_dlengthscales_via_K(dL_dKnm, X, Z) + + # else: + # self.lengthscale.gradient = (self.variance / self.lengthscale) * np.sum(self._K_dvar * self._K_dist2 * dL_dKnm) + + # #from Kmm + # self._K_computations(Z, None) + # self.variance.gradient += np.sum(dL_dKmm * self._K_dvar) + # if self.ARD: + # self.lengthscale.gradient += self._dL_dlengthscales_via_K(dL_dKmm, Z, None) + # else: + # self.lengthscale.gradient += (self.variance / self.lengthscale) * np.sum(self._K_dvar * self._K_dist2 * dL_dKmm) + + + #---------------------------------------# + # Precomputations # + #---------------------------------------# + + def _K_computations(self, X, Z): + if Z is None: + self._generate_inline(self._precompute, X) + else: + self._generate_inline(self._precompute, X, Z=Z) diff --git a/GPy/kern/_src/poly_tmp.py b/GPy/kern/_src/poly_tmp.py new file mode 100644 index 00000000..703b0d70 --- /dev/null +++ b/GPy/kern/_src/poly_tmp.py @@ -0,0 +1,134 @@ +# Copyright (c) 2013, GPy authors (see AUTHORS.txt). +# Licensed under the BSD 3-clause license (see LICENSE.txt) + +from kernpart import Kernpart +import numpy as np +four_over_tau = 2./np.pi + +class POLY(Kernpart): + """ + + Polynomial kernel parameter initialisation. Included for completeness, but generally not recommended, is the polynomial kernel: + + .. math:: + k(x, y) = \sigma^2\*(\sigma_w^2 x'y+\sigma_b^b)^d + + The kernel parameters are :math:`\sigma^2` (variance), :math:`\sigma^2_w` + (weight_variance), :math:`\sigma^2_b` (bias_variance) and d + (degree). Only gradients of the first three are provided for + kernel optimisation, it is assumed that polynomial degree would + be set by hand. + + The kernel is not recommended as it is badly behaved when the + :math:`\sigma^2_w\*x'\*y + \sigma^2_b` has a magnitude greater than one. For completeness + there is an automatic relevance determination version of this + kernel provided (NOTE YET IMPLEMENTED!). + :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 degree: the degree of the polynomial. + :type degree: int + :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 + + """ + + def __init__(self, input_dim, variance=1., weight_variance=None, bias_variance=1., degree=2, ARD=False): + self.input_dim = input_dim + self.ARD = ARD + if not ARD: + self.num_params=3 + if weight_variance is not None: + weight_variance = np.asarray(weight_variance) + assert weight_variance.size == 1, "Only one weight variance needed for non-ARD kernel" + else: + weight_variance = 1.*np.ones(1) + else: + self.num_params = self.input_dim + 2 + if weight_variance is not None: + weight_variance = np.asarray(weight_variance) + assert weight_variance.size == self.input_dim, "bad number of weight variances" + else: + weight_variance = np.ones(self.input_dim) + raise NotImplementedError + self.degree=degree + self.name='poly_deg' + str(self.degree) + self._set_params(np.hstack((variance, weight_variance.flatten(), bias_variance))) + + def _get_params(self): + return np.hstack((self.variance, self.weight_variance.flatten(), self.bias_variance)) + + def _set_params(self, x): + assert x.size == (self.num_params) + self.variance = x[0] + self.weight_variance = x[1:-1] + self.weight_std = np.sqrt(self.weight_variance) + self.bias_variance = x[-1] + + def _get_param_names(self): + if self.num_params == 3: + return ['variance', 'weight_variance', 'bias_variance'] + else: + return ['variance'] + ['weight_variance_%i' % i for i in range(self.lengthscale.size)] + ['bias_variance'] + + def K(self, X, X2, target): + """Return covariance between X and X2.""" + self._K_computations(X, X2) + target += self.variance*self._K_dvar + + def Kdiag(self, X, target): + """Compute the diagonal of the covariance matrix for X.""" + self._K_diag_computations(X) + target+= self.variance*self._K_diag_dvar + + def dK_dtheta(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) + base_cov_grad = base*dL_dK + + + + target[0] += np.sum(self._K_dvar*dL_dK) + target[1] += (self._K_inner_prod*base_cov_grad).sum() + target[2] += base_cov_grad.sum() + + + def dK_dX(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 + if X2 is None: + target += 2*self.weight_variance*self.degree*self.variance*(((X[None,:, :])) *(arg**(self.degree-1))[:, :, None]*dL_dK[:, :, None]).sum(1) + else: + target += self.weight_variance*self.degree*self.variance*(((X2[None,:, :])) *(arg**(self.degree-1))[:, :, None]*dL_dK[:, :, None]).sum(1) + + def dKdiag_dX(self, dL_dKdiag, X, target): + """Gradient of diagonal of covariance with respect to X""" + self._K_diag_computations(X) + arg = self._K_diag_poly_arg + target += 2.*self.weight_variance*self.degree*self.variance*X*dL_dKdiag[:, None]*(arg**(self.degree-1))[:, None] + + + def _K_computations(self, X, X2): + if self.ARD: + pass + else: + if X2 is None: + self._K_inner_prod = np.dot(X,X.T) + else: + self._K_inner_prod = np.dot(X,X2.T) + self._K_poly_arg = self._K_inner_prod*self.weight_variance + self.bias_variance + self._K_dvar = self._K_poly_arg**self.degree + + def _K_diag_computations(self, X): + if self.ARD: + pass + else: + self._K_diag_poly_arg = (X*X).sum(1)*self.weight_variance + self.bias_variance + self._K_diag_dvar = self._K_diag_poly_arg**self.degree diff --git a/GPy/kern/_src/symbolic2.py b/GPy/kern/_src/symbolic2.py new file mode 100644 index 00000000..a991d2c9 --- /dev/null +++ b/GPy/kern/_src/symbolic2.py @@ -0,0 +1,70 @@ +# 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 ... + self.eval_update_gradients('k', dL_dK, X=X) + else: + self.eval_update_gradients('k', dL_dK, X=X, Z=X2) + + + def update_gradients_diag(self, dL_dKdiag, X): + self.eval_update_gradients('kdiag', dL_dKdiag, X) + diff --git a/GPy/kern/matlab_construct.py b/GPy/kern/matlab_construct.py new file mode 100644 index 00000000..7b0d02c4 --- /dev/null +++ b/GPy/kern/matlab_construct.py @@ -0,0 +1,17 @@ +# Copyright (c) 2013, GPy authors (see AUTHORS.txt). +# Licensed under the BSD 3-clause license (see LICENSE.txt) + +# Construct covariance functions from matlab saves. +import numpy as np +from kern import kern +import parts +import scipy.io + +def read_matlab(mat_data) + mat_data = scipy.io.loadmat(os.path.join(data_path, data_set, 'frey_rawface.mat')) + if mat_data['type']=='cmpnd': + # cmpnd kernel + types = [] + for i in range(mat_data['comp'][0][0]): + types.append(mat_data['comp'][0][0][i] + diff --git a/GPy/kern/parts/eq.py b/GPy/kern/parts/eq.py new file mode 100644 index 00000000..5c808f8a --- /dev/null +++ b/GPy/kern/parts/eq.py @@ -0,0 +1,318 @@ +# 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 + +class EQ(Kernpart_stationary): + """ + Exponentiated Quadratic covariance function als known as radial basis function, squared-exponential 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): + Kernpart_stationary.__init__(self, input_dim, lengthscale, ARD) + self.name = 'rbf' + self._set_params(np.hstack((variance, self.lengthscale.flatten()))) + + # a set of optional args to pass to weave + self.weave_options = {'headers' : [''], + 'extra_compile_args': ['-fopenmp -O3'], # -march=native'], + 'extra_link_args' : ['-lgomp']} + + + + 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] + Kernpart_stationary._set_params(self, x[1:]) + + 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 + #include + """ + weave.inline(code, support_code=support_code, libraries=['gomp'], + 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/ode1.py b/GPy/kern/parts/ode1.py new file mode 100644 index 00000000..4d7a5d7f --- /dev/null +++ b/GPy/kern/parts/ode1.py @@ -0,0 +1,428 @@ +# 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 +from GPy.util import ln_diff_erfs +import pdb +from scipy import weave + +class Ode1(Kernpart): + """ + Covariance function for first order differential equation driven by an exponetiated quadratic covariance. + + This kernel has the form + .. math:: + + :param num_outputs: number of outputs driven by latent function. + :type num_outputs: int + + .. Note: see first order differential equation examples in GPy.examples.regression for some usage. + """ + def __init__(self,num_outputs, W=None, rank=1, delay=None, kappa=None): + self.rank = rank + self.input_dim = 1 + self.name = 'ode1' + self.num_outputs = num_outputs + self.num_params = self.num_outputs*(1. + self.rank) + 1 + if kappa is not None: + self.num_params+=num_outputs + if delay is not None: + self.num_params+=num_outputs + self.rank = rank + if W is None: + self.W = 0.5*np.random.randn(self.num_outputs,self.rank)/np.sqrt(self.rank) + else: + assert W.shape==(self.num_outputs,self.rank) + self.W = W + + if kappa is not None: + assert kappa.shape==(self.num_outputs,) + self.kappa = kappa + + if delay is not None: + assert delay.shape==(self.num_outputs,) + self.delay = delay + self._set_params(self._get_params()) + + def _get_params(self): + param_list = [self.W.flatten()] + if self.kappa is not None: + param_list.append(self.kappa) + param_list.append(self.decay) + if self.delay is not None: + param_list.append(self.delay) + param_list.append(self.length_scale) + return np.hstack(param_list) + + def _set_params(self,x): + assert x.size == self.num_params + end = self.num_outputs*self.rank + self.W = x[:end].reshape(self.num_outputs,self.rank) + start = end + self.B = np.dot(self.W,self.W.T) + if self.kappa is not None: + end+=self.num_outputs + self.kappa = x[start:end] + self.B += np.diag(self.kappa) + start=end + end+=num_outputs + self.decay = x[start:end] + start=end + if self.delay is not None: + end+=num_outputs + self.delay = x[start:end] + start=end + end+=1 + self.length_scale = x[start] + self.sigma = np.sqrt(2)*self.length_scale + + + def _get_param_names(self): + param_names = sum([['W%i_%i'%(i,j) for j in range(self.rank)] for i in range(self.num_outputs)],[]) + if self.kappa is not None: + param_names += ['kappa_%i'%i for i in range(self.num_outputs)] + param_names += ['decay_%i'%i for i in range(self.num_outputs)] + if self.delay is not None: + param_names += ['delay_%i'%i for i in range(self.num_outputs)] + param_names+= ['length_scale'] + return param_names + + def K(self,X,X2,target): + + if X.shape[1] > 2: + raise ValueError('Input matrix for ode1 covariance should have at most two columns, one containing times, the other output indices') + + self._K_computations() + target += self._scales*self._dK_dvar + + if self.gaussian_initial: + # Add covariance associated with initial condition. + t1_mat = self._t[self._rorder, None] + t2_mat = self._t2[None, self._rorder2] + target+=self.initial_variance * np.exp(- self.decay * (t1_mat + t2_mat)) + + + + def Kdiag(self,index,target): + #target += np.diag(self.B)[np.asarray(index,dtype=np.int).flatten()] + pass + + def dK_dtheta(self,dL_dK,index,index2,target): + pass + + def dKdiag_dtheta(self,dL_dKdiag,index,target): + pass + + def dK_dX(self,dL_dK,X,X2,target): + pass + + def _extract_t_indices(X, X2=None): + """Extract times and output indices from the input matrix X. Times are ordered according to their index for convenience of computation, this ordering is stored in self._order and self.order2. These orderings are then mapped back to the original ordering (in X) using self._rorder and self._rorder2. """ + + # TODO: some fast checking here to see if this needs recomputing? + self._t = X[:, 0] + if X.shape[1]==1: + # No index passed, assume single output of ode model. + self._index = np.ones_like(X[:, 1],dtype=np.int) + self._index = np.asarray(X[:, 1],dtype=np.int) + # Sort indices so that outputs are in blocks for computational + # convenience. + self._order = self._index.argsort() + self._index = self._index[self._order] + self._t = self._t[self._order] + self._rorder = self._order.argsort() # rorder is for reversing the order + + if X2 is None: + self._t2 = None + self._index2 = None + self._rorder2 = self._rorder + else: + if X2.shape[1] > 2: + raise ValueError('Input matrix for ode1 covariance should have at most two columns, one containing times, the other output indices') + self._t2 = X2[:, 0] + if X.shape[1]==1: + # No index passed, assume single output of ode model. + self._index2 = np.ones_like(X2[:, 1],dtype=np.int) + self._index2 = np.asarray(X2[:, 1],dtype=np.int) + self._order2 = self._index2.argsort() + slef._index2 = self._index2[self._order2] + self._t2 = self._t2[self._order2] + self._rorder2 = self._order2.argsort() # rorder2 is for reversing order + + def _K_computations(X, X2): + """Perform main body of computations for the ode1 covariance function.""" + # First extract times and indices. + self._extract_t_indices(X, X2) + + self._K_compute_eq() + self._K_compute_eq_x_ode() + if X2 is None: + self._K_ode_eq = self._K_ode_eq.T + else: + self._K_compute_eq_x_ode(transpose=True) + self._K_compute_ode() + + # Reorder values of blocks for placing back into _K_dvar. + self._K_dvar[self._rorder, :] = np.vstack(( + np.hstack((self._K_eq, self._Keq_ode)) + np.hstack((self._K_ode_eq, self.K_ode))))[:, self._rorder2] + + + def _K_compute_eq(): + """Compute covariance for latent covariance.""" + t_eq = self._t[self._index==0] + if t_eq.shape[0]==0: + self._K_eq = np.zeros((0, 0)) + return + + if self._t2 is None: + self._dist2 = np.square(t_eq[:, None] - t_eq[None, :]) + else: + t2_eq = self._t2[self._index2==0] + if t2_eq.shape[0]==0: + self._K_eq_eq = np.zeros((0, 0)) + return + self._dist2 = np.square(t_eq[:, None] - t2_eq[None, :]) + + self._K_eq = np.exp(-self._dist2/(2*self.length_scale*self.length_scale)) + if self.is_normalise: + self._K_eq/=(np.sqrt(2*np.pi)*self.length_scale) + + def _K_compute_ode_eq(transpose=False): + """Compute the cross covariances between latent exponentiated quadratic and observed ordinary differential equations. + + :param transpose: if set to false the exponentiated quadratic is on the rows of the matrix and is computed according to self._t, if set to true it is on the columns and is computed according to self._t2 (default=False). + :type transpose: bool""" + + if transpose: + t_ode = self._t2[self._index>0] + index_ode = self._index2[self._index>0]-1 + if t_ode.shape[0]==0: + self._K_ode = np.zeros((0, 0)) + return + + if self._t2 is not None: + t2_ode = self._t2[self._index2>0] + index2_ode = self._index2[self._index2>0]-1 + if t2_eq.shape[0]==0: + self._K_ode = np.zeros((0, 0)) + return + else: + + # Matrix giving scales of each output + self._scale = np.zeros((t_ode.shape[0], t_eq.shape[0])) + code=""" + for(int i=0;i0] + index_ode = self._index[self._index>0]-1 + if t_ode.shape[0]==0: + self._K_ode = np.zeros((0, 0)) + return + + if self._t2 is not None: + t2_ode = self._t2[self._index2>0] + index2_ode = self._index2[self._index2>0]-1 + if t2_eq.shape[0]==0: + self._K_ode = np.zeros((0, 0)) + return + + if self._index2 is None: + # Matrix giving scales of each output + self._scale = np.zeros((t_ode.shape[0], t_ode.shape[0])) + code=""" + for(int i=0;i 1 or t2.shape[1] > 1: + raise error('Input can only have one column') + + # Vector of decays and delays associated with each output. + Decay = np.zeros(t.shape[0]) + Delay = np.zeros(t.shape[0]) + Decay2 = np.zeros(t2.shape[0]) + Delay2 = np.zeros(t2.shape[0]) + code=""" + for(int i=0;i 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(), os.path.join(current_dir,'parts/')], + 'headers':['"sympy_helpers.h"'], + 'sources':[os.path.join(current_dir,"parts/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",'kernel_code',argument_sequence=argument_sequence) + #put the header file where we can find it + f = file(os.path.join(tempfile.gettempdir(),'kernel_code.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/ratquad.py b/GPy/kern/ratquad.py new file mode 100644 index 00000000..90bff8e9 --- /dev/null +++ b/GPy/kern/ratquad.py @@ -0,0 +1,179 @@ +# 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 rbf(kernpart): + """ + Rational quadratic kernel. + .. math:: + + k(r) = \sigma^2 \left(\frac{(\ell^{-2} + r^2)}{2*\alpha}\right)^{-\alpha} \qquad \qquad \\text{ where } r = \sqrt{\frac{\sum_{i=1}^d (x_i-x^\prime_i)^2}{\ell^2}} + + where \ell is the lengthscale, \alpha the smoothness, \sigma^2 the variance and d the dimensionality of the input. + + :param D: the number of input dimensions + :type D: int + :param variance: the variance of the kernel + :type variance: float + :param lengthscale: the lengthscale of the kernel (l) + :type lengthscale: float + :param smoothness: the smoothness parameter of the kernel + :type lengthscale: float + + .. Note: for rational quadratic with different lengthscale on each dimension, see ratquad_ARD + """ + + def __init__(self,D,variance=1.,lengthscale=1.,smoothness)=1.: + self.D = D + self.Nparam = 3 + self.name = 'ratquad' + self._set_params(np.hstack((variance,lengthscale,smoothness))) + + #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 _get_params(self): + return np.hstack((self.variance,self.lengthscale,self.smoothness)) + + def _set_params(self,x): + self.variance, self.lengthscale, self.smoothness = 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 _get_param_names(self): + return ['variance','lengthscale','smoothness'] + + def K(self,X,X2,target): + if X2 is None: + X2 = X + self._K_computations(X,X2) + np.add(self.variance*self._K_dvar, target,target) + + def Kdiag(self,X,target): + np.add(target,self.variance,target) + + def dK_dtheta(self,partial,X,X2,target): + self._K_computations(X,X2) + target[0] += np.sum(self._K_dvar*partial) + target[1] += np.sum(self._K_dvar*self.variance*self._K_dist2/self.lengthscale*partial) + target[2] += + def dKdiag_dtheta(self,partial,X,target): + #NB: derivative of diagonal elements wrt lengthscale is 0 + target[0] += np.sum(partial) + + def dK_dX(self,partial,X,X2,target): + self._K_computations(X,X2) + if X2 is None: + _K_dist = 2*X[:, None, :] - X[None, :, :] + else: + _K_dist = X[:,None,:]-X2[None,:,:] + dK_dX = np.transpose(-self.variance*self._K_dvar[:,:,np.newaxis]*_K_dist/self.lengthscale2,(1,0,2)) + target += np.sum(dK_dX*partial.T[:,:,None],0) + + def dKdiag_dX(self,partial,X,target): + pass + + def _K_computations(self,X,X2): + if not (np.all(X==self._X) and np.all(X2==self._X2)): + self._X = X + self._X2 = X2 + if X2 is None: X2 = X + XXT = np.dot(X,X2.T) + if X is X2: + self._K_dist2 = (-2.*XXT + np.diag(XXT)[:,np.newaxis] + np.diag(XXT)[np.newaxis,:])/self.lengthscale2 + else: + self._K_dist2 = (-2.*XXT + np.sum(np.square(X),1)[:,np.newaxis] + np.sum(np.square(X2),1)[np.newaxis,:])/self.lengthscale2 + self._K_dvar = (0.5./self.smoothness*(1./self.lengthscale2 + self._K_dist2))**(-self.smoothness) + + def psi0(self,Z,mu,S,target): + target += self.variance + + def dpsi0_dtheta(self,partial,Z,mu,S,target): + target[0] += 1. + + def dpsi0_dmuS(self,Z,mu,S,target_mu,target_S): + pass + + def psi1(self,Z,mu,S,target): + self._psi_computations(Z,mu,S) + target += self._psi1 + + def dpsi1_dtheta(self,partial,Z,mu,S,target): + self._psi_computations(Z,mu,S) + denom_deriv = S[:,None,:]/(self.lengthscale**3+self.lengthscale*S[:,None,:]) + d_length = self._psi1[:,:,None]*(self.lengthscale*np.square(self._psi1_dist/(self.lengthscale2+S[:,None,:])) + denom_deriv) + target[0] += np.sum(partial*self._psi1/self.variance) + target[1] += np.sum(d_length*partial[:,:,None]) + + def dpsi1_dZ(self,partial,Z,mu,S,target): + self._psi_computations(Z,mu,S) + target += np.sum(partial[:,:,None]*-self._psi1[:,:,None]*self._psi1_dist/self.lengthscale2/self._psi1_denom,0) + + def dpsi1_dmuS(self,partial,Z,mu,S,target_mu,target_S): + self._psi_computations(Z,mu,S) + tmp = self._psi1[:,:,None]/self.lengthscale2/self._psi1_denom + target_mu += np.sum(partial*tmp*self._psi1_dist,1) + target_S += np.sum(partial*0.5*tmp*(self._psi1_dist_sq-1),1) + + def psi2(self,Z,mu,S,target): + self._psi_computations(Z,mu,S) + target += self._psi2.sum(0) #TODO: psi2 should be NxMxM (for het. noise) + + def dpsi2_dtheta(self,partial,Z,mu,S,target): + """Shape N,M,M,Ntheta""" + self._psi_computations(Z,mu,S) + d_var = np.sum(2.*self._psi2/self.variance,0) + d_length = self._psi2[:,:,:,None]*(0.5*self._psi2_Zdist_sq*self._psi2_denom + 2.*self._psi2_mudist_sq + 2.*S[:,None,None,:]/self.lengthscale2)/(self.lengthscale*self._psi2_denom) + d_length = d_length.sum(0) + target[0] += np.sum(partial*d_var) + target[1] += np.sum(d_length*partial) + + def dpsi2_dZ(self,partial,Z,mu,S,target): + """Returns shape N,M,M,Q""" + self._psi_computations(Z,mu,S) + dZ = self._psi2[:,:,:,None]/self.lengthscale2*(-0.5*self._psi2_Zdist + self._psi2_mudist/self._psi2_denom) + target += np.sum(partial[None,:,:,None]*dZ,0).sum(1) + + def dpsi2_dmuS(self,Z,mu,S,target_mu,target_S): + """Think N,M,M,Q """ + self._psi_computations(Z,mu,S) + tmp = self._psi2[:,:,:,None]/self.lengthscale2/self._psi2_denom + target_mu += (partial*-tmp*2.*self._psi2_mudist).sum(1).sum(1) + target_S += (partial*tmp*(2.*self._psi2_mudist_sq-1)).sum(1).sum(1) + + def _psi_computations(self,Z,mu,S): + #here are the "statistics" for psi1 and psi2 + if not np.all(Z==self._Z): + #Z has changed, compute Z specific stuff + self._psi2_Zhat = 0.5*(Z[:,None,:] +Z[None,:,:]) # M,M,Q + self._psi2_Zdist = Z[:,None,:]-Z[None,:,:] # M,M,Q + self._psi2_Zdist_sq = np.square(self._psi2_Zdist)/self.lengthscale2 # M,M,Q + self._Z = Z + + if not (np.all(Z==self._Z) and np.all(mu==self._mu) and np.all(S==self._S)): + #something's changed. recompute EVERYTHING + + #TODO: make more efficient for large Q (using NDL's dot product trick) + #psi1 + self._psi1_denom = S[:,None,:]/self.lengthscale2 + 1. + self._psi1_dist = Z[None,:,:]-mu[:,None,:] + self._psi1_dist_sq = np.square(self._psi1_dist)/self.lengthscale2/self._psi1_denom + self._psi1_exponent = -0.5*np.sum(self._psi1_dist_sq+np.log(self._psi1_denom),-1) + self._psi1 = self.variance*np.exp(self._psi1_exponent) + + #psi2 + self._psi2_denom = 2.*S[:,None,None,:]/self.lengthscale2+1. # N,M,M,Q + self._psi2_mudist = mu[:,None,None,:]-self._psi2_Zhat #N,M,M,Q + self._psi2_mudist_sq = np.square(self._psi2_mudist)/(self.lengthscale2*self._psi2_denom) + self._psi2_exponent = np.sum(-self._psi2_Zdist_sq/4. -self._psi2_mudist_sq -0.5*np.log(self._psi2_denom),-1) #N,M,M + self._psi2 = np.square(self.variance)*np.exp(self._psi2_exponent) # N,M,M + + self._Z, self._mu, self._S = Z, mu,S + diff --git a/GPy/libpeerconnection.log b/GPy/libpeerconnection.log new file mode 100644 index 00000000..e69de29b diff --git a/GPy/likelihoods/negative_binomial.py~ b/GPy/likelihoods/negative_binomial.py~ new file mode 100644 index 00000000..4ca5514b --- /dev/null +++ b/GPy/likelihoods/negative_binomial.py~ @@ -0,0 +1,31 @@ +# Copyright (c) 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 Negative_binomial(Symbolic): + """ + Negative binomial + + .. math:: + p(y_{i}|\pi(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 diff --git a/GPy/likelihoods/null_category.py b/GPy/likelihoods/null_category.py new file mode 100644 index 00000000..00fb9c53 --- /dev/null +++ b/GPy/likelihoods/null_category.py @@ -0,0 +1,53 @@ +# Copyright (c) 2014 The GPy authors (see AUTHORS.txt) +# Licensed under the BSD 3-clause license (see LICENSE.txt) + + +try: + import sympy as sym + sympy_available=True + from sympy.utilities.lambdify import lambdify + from GPy.util.symbolic import gammaln, normcdfln, normcdf + from sympy.functions.elementary.piecewise import Piecewise +except ImportError: + sympy_available=False + +import numpy as np +from ..util.univariate_Gaussian import std_norm_pdf, std_norm_cdf +import link_functions +from symbolic import Symbolic +from scipy import stats + +if sympy_available: + class Null_category(Symbolic): + """ + Null category noise model. + + .. math:: + + .. Note:: + Y takes -1, 0 or 1. + + .. See also:: + symbolic.py, for the parent class + """ + def __init__(self, gp_link=None): + if gp_link is None: + gp_link = link_functions.Identity() + # width of the null category. + width = sym.Symbol('width', positive=True, real=True) + # prior probability of positive class + p = sym.Symbol('p', positive=True, real=True) + y = sym.Symbol('y', binary=True) + f = sym.Symbol('f', positive=True, real=True) + + log_pdf_missing = sym.log((1-p)*normcdf(-f-width/2) + +p*normcdf(f+width/2)) + log_pdf = (y-1)*normcdfln(-f-width/2)+y*normcdfln(f+width/2) + super(Null_category, self).__init__(log_pdf=log_pdf, missing_log_pdf=log_pdf_missing, gp_link=gp_link, name='Null_category') + + self.p=0.5 + self.p.constrain_bounded(0., 1.) + self.width = 1. + self.width.constrain_fixed() + self.log_concave = False + diff --git a/GPy/likelihoods/null_category.py~ b/GPy/likelihoods/null_category.py~ new file mode 100644 index 00000000..5bc5b727 --- /dev/null +++ b/GPy/likelihoods/null_category.py~ @@ -0,0 +1,46 @@ +# Copyright (c) 2014 The GPy authors (see AUTHORS.txt) +# Licensed under the BSD 3-clause license (see LICENSE.txt) + + +try: + import sympy as sym + sympy_available=True + from sympy.utilities.lambdify import lambdify + from GPy.util.symbolic import gammaln, ln_cum_gaussian, cum_gaussian +except ImportError: + sympy_available=False + +import numpy as np +from ..util.univariate_Gaussian import std_norm_pdf, std_norm_cdf +import link_functions +from symbolic import Symbolic +from scipy import stats + +if sympy_available: + class Negative_binomial(Symbolic): + """ + Negative binomial + + .. math:: + p(y_{i}|\pi(f_{i})) = \left(\frac{r}{r+f_i}\right)^r \frac{\Gamma(r+y_i)}{y!\Gamma(r)}\left(\frac{f_i}{r+f_i}\right)^{y_i} + + .. Note:: + Y takes non zero integer values.. + link function should have a positive domain, e.g. log (default). + + .. See also:: + symbolic.py, for the parent class + """ + def __init__(self, gp_link=None): + if gp_link is None: + gp_link = link_functions.Log() + + dispersion = sym.Symbol('dispersion', positive=True, real=True) + y = sym.Symbol('y', nonnegative=True, integer=True) + f = sym.Symbol('f', positive=True, real=True) + log_pdf=dispersion*sym.log(dispersion) - (dispersion+y)*sym.log(dispersion+f) + gammaln(y+dispersion) - gammaln(y+1) - gammaln(dispersion) + y*sym.log(f) + super(Negative_binomial, self).__init__(log_pdf=log_pdf, gp_link=gp_link, name='Negative_binomial') + + # TODO: Check this. + self.log_concave = False + diff --git a/GPy/likelihoods/old_symbolic.py b/GPy/likelihoods/old_symbolic.py new file mode 100644 index 00000000..feac9e9d --- /dev/null +++ b/GPy/likelihoods/old_symbolic.py @@ -0,0 +1,316 @@ +# Copyright (c) 2014 GPy Authors +# Licensed under the BSD 3-clause license (see LICENSE.txt) + +try: + import sympy as sym + sympy_available=True + from sympy.utilities.lambdify import lambdify +except ImportError: + sympy_available=False + +import numpy as np +import link_functions +from scipy import stats, integrate +from scipy.special import gammaln, gamma, erf, erfc, erfcx, polygamma +from GPy.util.functions import normcdf, normcdfln, logistic, logisticln +from likelihood import Likelihood +from ..core.parameterization import Param + + +if sympy_available: + class Symbolic(Likelihood): + """ + Symbolic likelihood. + + Likelihood where the form of the likelihood is provided by a sympy expression. + + """ + def __init__(self, log_pdf=None, logZ=None, missing_log_pdf=None, gp_link=None, name='symbolic', log_concave=False, param=None, func_modules=[]): + + if gp_link is None: + gp_link = link_functions.Identity() + + if log_pdf is None: + raise ValueError, "You must provide an argument for the log pdf." + + self.func_modules = func_modules + self.func_modules += [{'gamma':gamma, + 'gammaln':gammaln, + 'erf':erf, 'erfc':erfc, + 'erfcx':erfcx, + 'polygamma':polygamma, + 'normcdf':normcdf, + 'normcdfln':normcdfln, + 'logistic':logistic, + 'logisticln':logisticln}, + 'numpy'] + + super(Symbolic, self).__init__(gp_link, name=name) + self.missing_data = False + self._sym_log_pdf = log_pdf + if missing_log_pdf: + self.missing_data = True + self._sym_missing_log_pdf = missing_log_pdf + + # pull the variable names out of the symbolic pdf + sym_vars = [e for e in self._sym_log_pdf.atoms() if e.is_Symbol] + self._sym_f = [e for e in sym_vars if e.name=='f'] + if not self._sym_f: + raise ValueError('No variable f in log pdf.') + self._sym_y = [e for e in sym_vars if e.name=='y'] + if not self._sym_y: + raise ValueError('No variable y in log pdf.') + self._sym_theta = sorted([e for e in sym_vars if not (e.name=='f' or e.name=='y')],key=lambda e:e.name) + + theta_names = [theta.name for theta in self._sym_theta] + if self.missing_data: + # pull the variable names out of missing data + sym_vars = [e for e in self._sym_missing_log_pdf.atoms() if e.is_Symbol] + sym_f = [e for e in sym_vars if e.name=='f'] + if not sym_f: + raise ValueError('No variable f in missing data log pdf.') + sym_y = [e for e in sym_vars if e.name=='y'] + if sym_y: + raise ValueError('Data is present in missing data portion of likelihood.') + # additional missing data parameters + missing_theta = sorted([e for e in sym_vars if not (e.name=='f' or e.name=='missing' or e.name in theta_names)],key=lambda e:e.name) + self._sym_theta += missing_theta + self._sym_theta = sorted(self._sym_theta, key=lambda e:e.name) + + # These are all the arguments need to compute likelihoods. + self.arg_list = self._sym_y + self._sym_f + self._sym_theta + + # these are arguments for computing derivatives. + derivative_arguments = self._sym_f + self._sym_theta + + # Do symbolic work to compute derivatives. + self._log_pdf_derivatives = {theta.name : stabilise(sym.diff(self._sym_log_pdf,theta)) for theta in derivative_arguments} + self._log_pdf_second_derivatives = {theta.name : stabilise(sym.diff(self._log_pdf_derivatives['f'],theta)) for theta in derivative_arguments} + self._log_pdf_third_derivatives = {theta.name : stabilise(sym.diff(self._log_pdf_second_derivatives['f'],theta)) for theta in derivative_arguments} + + if self.missing_data: + # Do symbolic work to compute derivatives. + self._missing_log_pdf_derivatives = {theta.name : stabilise(sym.diff(self._sym_missing_log_pdf,theta)) for theta in derivative_arguments} + self._missing_log_pdf_second_derivatives = {theta.name : stabilise(sym.diff(self._missing_log_pdf_derivatives['f'],theta)) for theta in derivative_arguments} + self._missing_log_pdf_third_derivatives = {theta.name : stabilise(sym.diff(self._missing_log_pdf_second_derivatives['f'],theta)) for theta in derivative_arguments} + + + # Add parameters to the model. + for theta in self._sym_theta: + val = 1.0 + # TODO: need to decide how to handle user passing values for the se parameter vectors. + if param is not None: + if param.has_key(theta.name): + val = param[theta.name] + setattr(self, theta.name, Param(theta.name, val, None)) + self.add_parameters(getattr(self, theta.name)) + + + # TODO: Is there an easy way to check whether the pdf is log + # concave? For the moment, need user to specify. + self.log_concave = log_concave + + # initialise code arguments + self._arguments = {} + + # generate the code for the pdf and derivatives + self._gen_code() + + def list_functions(self): + """Return a list of all symbolic functions in the model and their names.""" + def _gen_code(self): + """Generate the code from the symbolic parts that will be used for likleihod computation.""" + # TODO: Check here whether theano is available and set up + # functions accordingly. + symbolic_functions = [self._sym_log_pdf] + deriv_list = [self._log_pdf_derivatives, self._log_pdf_second_derivatives, self._log_pdf_third_derivatives] + symbolic_functions += [deriv[key] for key in sorted(deriv.keys()) for deriv in deriv_list] + if self.missing_data: + symbolic_functions+=[self._sym_missing_log_pdf] + deriv_list = [self._missing_log_pdf_derivatives, self._missing_log_pdf_second_derivatives, self._missing_log_pdf_third_derivatives] + symbolic_functions += [deriv[key] for key in sorted(deriv.keys()) for deriv in deriv_list] + # self._log_pdf_function = lambdify(self.arg_list, self._sym_log_pdf, self.func_modules) + + # # compute code for derivatives + # self._derivative_code = {key: lambdify(self.arg_list, self._log_pdf_derivatives[key], self.func_modules) for key in self._log_pdf_derivatives.keys()} + # self._second_derivative_code = {key: lambdify(self.arg_list, self._log_pdf_second_derivatives[key], self.func_modules) for key in self._log_pdf_second_derivatives.keys()} + # self._third_derivative_code = {key: lambdify(self.arg_list, self._log_pdf_third_derivatives[key], self.func_modules) for key in self._log_pdf_third_derivatives.keys()} + + # if self.missing_data: + # self._missing_derivative_code = {key: lambdify(self.arg_list, self._missing_log_pdf_derivatives[key], self.func_modules) for key in self._missing_log_pdf_derivatives.keys()} + # self._missing_second_derivative_code = {key: lambdify(self.arg_list, self._missing_log_pdf_second_derivatives[key], self.func_modules) for key in self._missing_log_pdf_second_derivatives.keys()} + # self._missing_third_derivative_code = {key: lambdify(self.arg_list, self._missing_log_pdf_third_derivatives[key], self.func_modules) for key in self._missing_log_pdf_third_derivatives.keys()} + + # TODO: compute EP code parts based on logZ. We need dlogZ/dmu, d2logZ/dmu2 and dlogZ/dtheta + + def parameters_changed(self): + pass + + def update_gradients(self, grads): + """ + Pull out the gradients, be careful as the order must match the order + in which the parameters are added + """ + # The way the Laplace approximation is run requires the + # covariance function to compute the true gradient (because it + # is dependent on the mode). This means we actually compute + # the gradient outside this object. This function would + # normally ask the object to update its gradients internally, + # but here it provides them externally, because they are + # computed in the inference code. TODO: Thought: How does this + # effect EP? Shouldn't this be done by a separate + # Laplace-approximation specific call? + for grad, theta in zip(grads, self._sym_theta): + parameter = getattr(self, theta.name) + setattr(parameter, 'gradient', grad) + + def _arguments_update(self, f, y): + """Set up argument lists for the derivatives.""" + # If we do make use of Theano, then at this point we would + # need to do a lot of precomputation to ensure that the + # likelihoods and gradients are computed together, then check + # for parameter changes before updating. + for i, fvar in enumerate(self._sym_f): + self._arguments[fvar.name] = f + for i, yvar in enumerate(self._sym_y): + self._arguments[yvar.name] = y + for theta in self._sym_theta: + self._arguments[theta.name] = np.asarray(getattr(self, theta.name)) + + def pdf_link(self, inv_link_f, y, Y_metadata=None): + """ + Likelihood function given inverse link of f. + + :param inv_link_f: inverse link of latent variables. + :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 + """ + return np.exp(self.logpdf_link(inv_link_f, y, Y_metadata=None)) + + def logpdf_link(self, inv_link_f, y, Y_metadata=None): + """ + Log Likelihood Function given inverse link of latent variables. + + :param inv_inv_link_f: latent variables (inverse link of f) + :type inv_inv_link_f: Nx1 array + :param y: data + :type y: Nx1 array + :param Y_metadata: Y_metadata + :returns: likelihood evaluated for this point + :rtype: float + + """ + assert np.atleast_1d(inv_link_f).shape == np.atleast_1d(y).shape + self._arguments_update(inv_link_f, y) + if self.missing_data: + ll = np.where(np.isnan(y), self._missing_log_pdf_function(**self._missing_arguments), self._log_pdf_function(**self._arguments)) + else: + ll = np.where(np.isnan(y), 0., self._log_pdf_function(**self._arguments)) + return np.sum(ll) + + def dlogpdf_dlink(self, inv_link_f, y, Y_metadata=None): + """ + Gradient of log likelihood with respect to the inverse link function. + + :param inv_inv_link_f: latent variables (inverse link of f) + :type inv_inv_link_f: Nx1 array + :param y: data + :type y: Nx1 array + :param Y_metadata: Y_metadata + :returns: gradient of likelihood with respect to each point. + :rtype: Nx1 array + + """ + assert np.atleast_1d(inv_link_f).shape == np.atleast_1d(y).shape + self._arguments_update(inv_link_f, y) + if self.missing_data: + return np.where(np.isnan(y), self._missing_derivative_code['f'](**self._missing_argments), self._derivative_code['f'](**self._argments)) + else: + return np.where(np.isnan(y), 0., self._derivative_code['f'](**self._arguments)) + + def d2logpdf_dlink2(self, inv_link_f, y, Y_metadata=None): + """ + Hessian of log likelihood given inverse link of latent variables with respect to that inverse link. + i.e. second derivative logpdf at y given inv_link(f_i) and inv_link(f_j) w.r.t inv_link(f_i) and inv_link(f_j). + + + :param inv_link_f: inverse link of the latent variables. + :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:: + Returns 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 + self._arguments_update(inv_link_f, y) + if self.missing_data: + return np.where(np.isnan(y), self._missing_second_derivative_code['f'](**self._missing_argments), self._second_derivative_code['f'](**self._argments)) + else: + return np.where(np.isnan(y), 0., self._second_derivative_code['f'](**self._arguments)) + + def d3logpdf_dlink3(self, inv_link_f, y, Y_metadata=None): + assert np.atleast_1d(inv_link_f).shape == np.atleast_1d(y).shape + self._arguments_update(inv_link_f, y) + if self.missing_data: + return np.where(np.isnan(y), self._missing_third_derivative_code['f'](**self._missing_argments), self._third_derivative_code['f'](**self._argments)) + else: + return np.where(np.isnan(y), 0., self._third_derivative_code['f'](**self._arguments)) + + def dlogpdf_link_dtheta(self, inv_link_f, y, Y_metadata=None): + assert np.atleast_1d(inv_link_f).shape == np.atleast_1d(y).shape + self._arguments_update(inv_link_f, y) + g = np.zeros((np.atleast_1d(y).shape[0], len(self._sym_theta))) + for i, theta in enumerate(self._sym_theta): + if self.missing_data: + g[:, i:i+1] = np.where(np.isnan(y), self._missing_derivative_code[theta.name](**self._arguments), self._derivative_code[theta.name](**self._arguments)) + else: + g[:, i:i+1] = np.where(np.isnan(y), 0., self._derivative_code[theta.name](**self._arguments)) + return g.sum(0) + + def dlogpdf_dlink_dtheta(self, inv_link_f, y, Y_metadata=None): + assert np.atleast_1d(inv_link_f).shape == np.atleast_1d(y).shape + self._arguments_update(inv_link_f, y) + g = np.zeros((np.atleast_1d(y).shape[0], len(self._sym_theta))) + for i, theta in enumerate(self._sym_theta): + if self.missing_data: + g[:, i:i+1] = np.where(np.isnan(y), self._missing_second_derivative_code[theta.name](**self._arguments), self._second_derivative_code[theta.name](**self._arguments)) + else: + g[:, i:i+1] = np.where(np.isnan(y), 0., self._second_derivative_code[theta.name](**self._arguments)) + return g + + def d2logpdf_dlink2_dtheta(self, inv_link_f, y, Y_metadata=None): + assert np.atleast_1d(inv_link_f).shape == np.atleast_1d(y).shape + self._arguments_update(inv_link_f, y) + g = np.zeros((np.atleast_1d(y).shape[0], len(self._sym_theta))) + for i, theta in enumerate(self._sym_theta): + if self.missing_data: + g[:, i:i+1] = np.where(np.isnan(y), self._missing_third_derivative_code[theta.name](**self._arguments), self._third_derivative_code[theta.name](**self._arguments)) + else: + g[:, i:i+1] = np.where(np.isnan(y), 0., self._third_derivative_code[theta.name](**self._arguments)) + return g + + def predictive_mean(self, mu, sigma, Y_metadata=None): + raise NotImplementedError + + def predictive_variance(self, mu,variance, predictive_mean=None, Y_metadata=None): + raise NotImplementedError + + def conditional_mean(self, gp): + raise NotImplementedError + + def conditional_variance(self, gp): + raise NotImplementedError + + def samples(self, gp, Y_metadata=None): + raise NotImplementedError diff --git a/GPy/likelihoods/symbolic.py~ b/GPy/likelihoods/symbolic.py~ new file mode 100644 index 00000000..e45aafa5 --- /dev/null +++ b/GPy/likelihoods/symbolic.py~ @@ -0,0 +1,234 @@ +# Copyright (c) 2014 GPy Authors +# Licensed under the BSD 3-clause license (see LICENSE.txt) + +import numpy as np +import sympy as sp +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 Symbolic(Likelihood): + """ + Symbolic likelihood. + + Likelihood where the form of the likelihood is provided by a sympy expression. + + """ + def __init__(self, likelihood=None, log_likelihood=None, gp_link=None, name='symbolic', log_concave=False): + if gp_link is None: + gp_link = link_functions.Identity() + + if likelihood is None and log_likelihood is None: + raise ValueError, "You must provide an argument for the likelihood or the log likelihood." + + super(Symbolic, self).__init__(gp_link, name=name) + + if likelihood is None: + self._sp_likelihood = sp.exp(log_likelihood).simplify() + self._sp_log_likelihood = log_likelihood + + if log_likelihood is None: + self._sp_likelihood = likelihood + self._sp_log_likelihood = sp.log(likelihood).simplify() + + # extract parameter names from the covariance + # pull the variable names out of the symbolic covariance function. + sp_vars = [e for e in self._sp_likelihood.atoms() if e.is_Symbol] + # f subscript allows the likelihood of y to be dependent on multiple functions of f. The index of these functions would need to be specified in y_meta. + self._sp_f = sorted([e for e in sp_vars if e.name[0:2]=='f_'],key=lambda x:int(x.name[2:])) + self._sp_y = sorted([e for e in sp_vars if e.name=='y'],key=lambda x:int(x.name[2:])) + self._sp_theta = sorted([e for e in sp_vars if not (e.name[0:2]=='f_' or e.name=='y')],key=lambda e:e.name) + + self.arg_list = self._sp_y + self._sp_f + self._sp_theta + # this gives us the arguments for first derivative + first_derivative_arguments = self._sp_f + self._sp_theta + second_derivative_arguments = {} + for arg in first_derivative_arguments: + if arg.name[0:2] == 'f_': + # take all second derivatives with respect to everything + second_derivative_arguments[arg.name] = first_derivative_arguments + second_derivative_arguments = self._sp_f + self._sp_theta + third_derivative_arguments = self._sp_f + self._sp_theta + self._likelihood_derivatives = {theta.name : sp.diff(self._sp_likelihood,theta).simplify() for theta in derivative_arguments} + self._log_likelihood_derivatives = {theta.name : sp.diff(self._sp_log_likelihood,theta).simplify() for theta in derivative_arguments} + + # Add parameters to the model. + for theta in self._sp_theta: + val = 1.0 + # TODO: what if user has passed a parameter vector, how should that be stored and interpreted? This is the old way before params class. + if param is not None: + if param.has_key(theta): + val = param[theta] + setattr(self, theta.name, Param(theta.name, val, None)) + self.add_parameters(getattr(self, theta.name)) + + + # By default it won't be log concave. It would be nice to check for this somehow though! + self.log_concave = log_concave + + # initialise code arguments + self._arguments = {} + + # generate the code for the likelihood and derivatives + self._gen_code() + + def _gen_code(self): + # Potentially run theano here as an option. + self._likelihood_function = lambdify(self.arg_list, self._sp_likelihood, 'numpy') + self._log_likelihood_function = lambdify(self.arg_list, self._sp_log_likelihood, 'numpy') + # for derivatives we need gradient of the likelihood, gradient of log likelihood + for key in self.derivatives.keys(): + setattr(self, '_log_likelihood_diff_' + key, lambdify(self.arg_list, self.derivatives[key], 'numpy')) + + + pass + + def parameters_changed(self): + pass + + def update_gradients(self, grads): + """ + Pull out the gradients, be careful as the order must match the order + in which the parameters are added + """ + for grad, theta in zip(grads, self._sp_theta): + parameter = getattr(self, theta.name) + setattr(parameter, 'gradient', grad) + + def _arguments_update(self, f, y): + """Set up argument lists for the derivatives.""" + # Could check if this needs doing or not, there could + # definitely be some computational savings by checking for + # parameter updates here. + for i, f in enumerate(self._sp_f): + self._arguments[f.name] = f[:, i][:, None] + for i, y in enumerate(self._sp_y): + self._arguments[y.name] = y[:, i][:, None] + + for theta in self._sp_theta: + self._arguments[theta.name] = np.asarray(getattr(self, theta.name)) + + def pdf_link(self, inv_link_f, y, Y_metadata=None): + """ + Likelihood function given inverse link of f. + + :param inv_link_f: inverse link of latent variables. + :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 + self._arguments_update(inv_link_f, y) + l = self._likelihood_function(**self._arguments) + return np.prod(l) + + def logpdf_link(self, inv_link_f, y, Y_metadata=None): + """ + Log Likelihood Function given inverse link of latent variables. + + :param inv_inv_link_f: latent variables (inverse link of f) + :type inv_inv_link_f: Nx1 array + :param y: data + :type y: Nx1 array + :param Y_metadata: Y_metadata + :returns: likelihood evaluated for this point + :rtype: float + + """ + assert np.atleast_1d(inv_link_f).shape == np.atleast_1d(y).shape + self._arguments_update(inv_link_f, y) + ll = self._log_likelihood_function(**self._arguments) + return np.sum(ll) + + def dlogpdf_dlink(self, inv_link_f, y, Y_metadata=None): + """ + Gradient of log likelihood with respect to the inverse link function. + + :param inv_inv_link_f: latent variables (inverse link of f) + :type inv_inv_link_f: Nx1 array + :param y: data + :type y: Nx1 array + :param Y_metadata: Y_metadata + :returns: gradient of likelihood with respect to each point. + :rtype: Nx1 array + + """ + + assert np.atleast_1d(inv_link_f).shape == np.atleast_1d(y).shape + self._arguments_update(inv_link_f, y) + return self._log_likelihood_diff['f_0'](**self._arguments) + + 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 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 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 predictive_mean(self, mu, sigma, Y_metadata=None): + return self.gp_link.transf(mu) # only true in link is monotoci, 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 #not defined for small degress fo freedom + 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() + pass diff --git a/GPy/likelihoods/symlikelihood.py~ b/GPy/likelihoods/symlikelihood.py~ new file mode 100644 index 00000000..49db9365 --- /dev/null +++ b/GPy/likelihoods/symlikelihood.py~ @@ -0,0 +1,318 @@ +# Copyright (c) 2012, 2013 Ricardo Andrade +# Licensed under the BSD 3-clause license (see LICENSE.txt) + +import numpy as np +import sympy as sp +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 Symbolic(Likelihood): + """ + Symbolic likelihood. + + Likelihood where the form of the likelihood is provided by a sympy expression. + + """ + def __init__(self, likelihood=None, log_likelihood=None, gp_link=None, name='symbolic', log_concave=False): + if gp_link is None: + gp_link = link_functions.Identity() + + if likelihood is None and log_likelihood is None: + raise ValueError, "You must provide an argument for the likelihood or the log likelihood." + + super(Symbolic, self).__init__(gp_link, name=name) + + if likelihood is None: + self._sp_likelihood = sp.exp(log_likelihood).simplify() + self._sp_log_likelihood = log_likelihood + + if log_likelihood is None: + self._sp_likelihood = likelihood + self._sp_log_likelihood = sp.log(likelihood).simplify() + + # extract parameter names from the covariance + # pull the variable names out of the symbolic covariance function. + sp_vars = [e for e in self._sp_likelihood.atoms() if e.is_Symbol] + self._sp_f = sorted([e for e in sp_vars if e.name[0:2]=='f_'],key=lambda x:int(x.name[2:])) + self._sp_y = sorted([e for e in sp_vars if e.name[0:2]=='y_'],key=lambda x:int(x.name[2:])) + self._sp_theta = sorted([e for e in sp_vars if not (e.name[0:2]=='f_' or e.name[0:2]=='y_')],key=lambda e:e.name) + + self.arg_list = self._sp_y + self._sp_f + self._sp_theta + first_derivative_arguments = self._sp_f + self._sp_theta + second_derivative_arguments = self._sp_f + self._sp_theta + third_derivative_arguments = self._sp_f + self._sp_theta + self._likelihood_derivatives = {theta.name : sp.diff(self._sp_likelihood,theta).simplify() for theta in derivative_arguments} + self._log_likelihood_derivatives = {theta.name : sp.diff(self._sp_log_likelihood,theta).simplify() for theta in derivative_arguments} + + # Add parameters to the model. + for theta in self._sp_theta: + val = 1.0 + # TODO: what if user has passed a parameter vector, how should that be stored and interpreted? This is the old way before params class. + if param is not None: + if param.has_key(theta): + val = param[theta] + setattr(self, theta.name, Param(theta.name, val, None)) + self.add_parameters(getattr(self, theta.name)) + + + # By default it won't be log concave. It would be nice to check for this somehow though! + self.log_concave = log_concave + + # initialise code arguments + self._arguments = {} + + # generate the code for the covariance functions + self._gen_code() + + def _gen_code(self): + # Potentially run theano here as an option. + self._likelihood_function = lambdify(self.arg_list, self._sp_likelihood, 'numpy') + self._log_likelihood_function = lambdify(self.arg_list, self._sp_log_likelihood, 'numpy') + for key in self.derivatives.keys(): + setattr(self, '_likelihood_diff_' + key, lambdify(self.arg_list, self.derivatives[key], 'numpy')) + + + pass + + def parameters_changed(self): + pass + + 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] + pass + + def _arguments_update(self, f, y): + """Set up argument lists for the derivatives.""" + # Could check if this needs doing or not, there could + # definitely be some computational savings by checking for + # parameter updates here. + for i, f in enumerate(self._sp_f): + self._arguments[f.name] = f[:, i][:, None] + for i, y in enumerate(self._sp_y): + self._arguments[f.name] = y[:, i][:, None] + + for theta in self._sp_theta: + self._arguments[theta.name] = np.asarray(getattr(self, theta.name)) + + def pdf_link(self, 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 link_f: latent variables link(f) + :type 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(link_f).shape == np.atleast_1d(y).shape + self._arguments_update(link_f, y) + l = self._likelihood_function(**self._arguments) + return np.prod(l) + + def logpdf_link(self, 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 link_f: latent variables (link(f)) + :type 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(link_f).shape == np.atleast_1d(y).shape + self._arguments_update(link_f, y) + ll = self._log_likelihood_function(**self._arguments) + return np.sum(ll) + + 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) + + .. 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 link_f: latent variables (f) + :type 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(link_f).shape == np.atleast_1d(y).shape + e = y - link_f + grad = ((self.v + 1) * e) / (self.v * self.sigma2 + (e**2)) + 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) 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 link_f: latent variables link(f) + :type 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(link_f).shape == np.atleast_1d(y).shape + e = y - 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, 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 link_f: latent variables link(f) + :type 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(link_f).shape == np.atleast_1d(y).shape + e = y - 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, 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 link_f: latent variables link(f) + :type 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(link_f).shape == np.atleast_1d(y).shape + e = y - 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, 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 link_f: latent variables link_f + :type 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(link_f).shape == np.atleast_1d(y).shape + e = y - 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, 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 link_f: latent variables link(f) + :type 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(link_f).shape == np.atleast_1d(y).shape + e = y - 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): + return self.gp_link.transf(mu) # only true in link is monotoci, 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 #not defined for small degress fo freedom + 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() + pass diff --git a/GPy/log_like_grad.txt b/GPy/log_like_grad.txt new file mode 100644 index 00000000..f5a28ef4 --- /dev/null +++ b/GPy/log_like_grad.txt @@ -0,0 +1 @@ +core/model.py: def get(self,name): diff --git a/GPy/mappings/symbolic.py~ b/GPy/mappings/symbolic.py~ new file mode 100644 index 00000000..6c399408 --- /dev/null +++ b/GPy/mappings/symbolic.py~ @@ -0,0 +1,149 @@ +# Copyright (c) 2014 GPy Authors +# Licensed under the BSD 3-clause license (see LICENSE.txt) + +try: + import sympy as sym + sympy_available=True + from sympy.utilities.lambdify import lambdify + from GPy.util.symbolic import stabilise +except ImportError: + sympy_available=False + +from ..core.mapping import Mapping, Bijective_mapping +import numpy as np +from scipy.special import gammaln, gamma, erf, erfc, erfcx, polygamma +from GPy.util.functions import normcdf, normcdfln, logistic, logisticln +from ..core.parameterization import Param + + +if sympy_available: + class Symbolic(Mapping): + """ + Symbolic likelihood. + + Likelihood where the form of the likelihood is provided by a sympy expression. + + """ + def __init__(self, f=None, logZ=None, name='symbolic', param=None, func_modules=[]): + + + if f is None: + raise ValueError, "You must provide an argument for the function." + + self.func_modules = func_modules + self.func_modules += [{'gamma':gamma, + 'gammaln':gammaln, + 'erf':erf, 'erfc':erfc, + 'erfcx':erfcx, + 'polygamma':polygamma, + 'normcdf':normcdf, + 'normcdfln':normcdfln, + 'logistic':logistic, + 'logisticln':logisticln}, + 'numpy'] + + super(Symbolic, self).__init__(gp_link, name=name) + self.symbolic['function'] = f + + # pull the variable names out of the symbolic pdf + sym_vars = [e for e in f.atoms() if e.is_Symbol] + self.symbolic['x'] = [e for e in sym_vars if e.name[:2]=='x_'] + if not self.symbolic['f']: + raise ValueError('No variable x in f().') + self.symbolic['theta'] = sorted([e for e in sym_vars if not e.name[:2]=='x_'],key=lambda e:e.name) + + theta_names = [theta.name for theta in self.symbolic['theta'] + + # These are all the arguments need to compute the mapping. + self.arg_list = self.symbolic['x'] + self.symbolic['theta'] + + # these are arguments for computing derivatives. + derivative_arguments = self.arg_list + + # Do symbolic work to compute derivatives. + self.symbolic['derivatives'] = {theta.name : stabilise(sym.diff(f,theta)) for theta in derivative_arguments} + + # Add parameters to the model. + for theta in self._sym_theta: + val = 1.0 + # TODO: need to decide how to handle user passing values for the se parameter vectors. + if param is not None: + if param.has_key(theta.name): + val = param[theta.name] + setattr(self, theta.name, Param(theta.name, val, None)) + self.add_parameters(getattr(self, theta.name)) + + # initialise code arguments + self._arguments = {} + + # generate the code for the pdf and derivatives + self._gen_code() + + def _gen_code(self): + """Generate the code from the symbolic parts that will be used for likleihod computation.""" + + self.code = GPy.util.function.gen_code(self.symbolic) + + def parameters_changed(self): + # do all the precomputation codes. + for variable, code in self.code['precompute'].items(): + self.setattr(variable, eval(code, self.namespace)) + + def update_gradients(self, grads): + """ + """ + for param, code in self.code['derivatives'].items(): + self.getattr(param).setattr('gradient', + eval(code, self.namespace)) + pass + + def _arguments_update(self, x): + """Set up argument lists for the derivatives.""" + # If we do make use of Theano, then at this point we would + # need to do a lot of precomputation to ensure that the + # likelihoods and gradients are computed together, then check + # for parameter changes before updating. + for i, fvar in enumerate(self._sym_x): + self._arguments[fvar.name] = x[:, i] + for theta in self._sym_theta: + self._arguments[theta.name] = np.asarray(getattr(self, theta.name)) + + def f(self, x): + """ + Likelihood function given inverse link of f. + + :param inv_link_f: inverse link of latent variables. + :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 + """ + self._arguments_update(inv_link_f, y) + return self._f_function(x) + + + def df_dX(self, X): + """ + Gradient of log likelihood with respect to the inverse link function. + + :param inv_inv_link_f: latent variables (inverse link of f) + :type inv_inv_link_f: Nx1 array + :param y: data + :type y: Nx1 array + :param Y_metadata: Y_metadata + :returns: gradient of likelihood with respect to each point. + :rtype: Nx1 array + + """ + self._arguments_update(X) + return self._derivative_code['X'](**self._arguments) + + def df_dtheta(self, X): + self._arguments_update(X) + g = np.zeros((np.atleast_1d(X).shape[0], len(self._sym_theta))) + for i, theta in enumerate(self._sym_theta): + g[:, i:i+1] = self._derivative_code[theta.name](**self._arguments) + return g.sum(0) + diff --git a/GPy/util/data_resources2.json b/GPy/util/data_resources2.json new file mode 100644 index 00000000..a5a9ee46 --- /dev/null +++ b/GPy/util/data_resources2.json @@ -0,0 +1 @@ +{"olivetti_glasses": {"files": [["has_glasses.np"], ["olivettifaces.mat"]], "license": null, "citation": "Information recorded in olivetti_faces entry. Should be used from there.", "details": "Information recorded in olivetti_faces entry. Should be used from there.", "urls": ["http://staffwww.dcs.shef.ac.uk/people/N.Lawrence/dataset_mirror/olivetti_faces/", "http://www.cs.nyu.edu/~roweis/data/"], "size": 4261047}, "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}, "google_trends": {"files": [[]], "license": null, "citation": "", "details": "Google trends results.", "urls": ["http://www.google.com/trends/"], "size": 0}, "mauna_loa": {"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.", "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)", "urls": ["ftp://aftp.cmdl.noaa.gov/products/trends/co2/"], "size": 46779}, "osu_run1": {"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/).", "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.", "urls": ["http://accad.osu.edu/research/mocap/data/", "http://staffwww.dcs.shef.ac.uk/people/N.Lawrence/dataset_mirror/stick/"], "size": 338103}, "swiss_roll": {"files": [["swiss_roll_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": "Swiss roll data made available by Tenenbaum, de Silva and Langford to demonstrate isomap, available from http://isomap.stanford.edu/datasets.html.", "urls": ["http://isomap.stanford.edu/"], "size": 800256}, "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}, "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}, "singlecell": {"files": [["singlecell.csv"]], "license": "ScienceDirect: http://www.elsevier.com/locate/termsandconditions?utm_source=sciencedirect&utm_medium=link&utm_campaign=terms", "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 Singlecell experiment in Mouse, measuring 48 gene expressions in 1-64 cell states. The labels have been created as in Guo et al. [2010]", "urls": ["http://staffwww.dcs.sheffield.ac.uk/people/M.Zwiessele/data/singlecell/"], "size": 233.1}, "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}, "creep_rupture": {"files": [["creeprupt.tar"]], "license": null, "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.", "urls": ["http://www.msm.cam.ac.uk/map/data/tar/"], "size": 602797}, "olivetti_faces": {"files": [["att_faces.zip"], ["olivettifaces.mat"]], "license": null, "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. ", "urls": ["http://staffwww.dcs.shef.ac.uk/people/N.Lawrence/dataset_mirror/olivetti_faces/", "http://www.cs.nyu.edu/~roweis/data/"], "size": 8561331}, "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. Consists of WiFi access point strengths taken during a circuit of the Paul Allen building at the University of Washington.", "urls": ["http://staffwww.dcs.shef.ac.uk/people/N.Lawrence/dataset_mirror/robot_wireless/"], "size": 284390}, "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.\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.", "urls": ["http://mocap.cs.cmu.edu/subjects"], "size": null}, "football_data": {"files": [["E0.csv", "E1.csv", "E2.csv", "E3.csv"]], "license": null, "citation": "", "details": "Results of English football matches since 1993/94 season.", "urls": ["http://www.football-data.co.uk/mmz4281/"], "size": 1}, "decampos_characters": {"files": [["characters.npy", "digits.npy"]], "license": null, "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.", "urls": ["http://staffwww.dcs.shef.ac.uk/people/N.Lawrence/dataset_mirror/decampos_digits/"], "size": 2031872}, "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}, "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}, "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. 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).", "urls": ["http://staffwww.dcs.shef.ac.uk/people/N.Lawrence/dataset_mirror/epomeo_gpx/"], "size": 2031872}, "ankur_pose_data": {"files": [["ankurDataPoseSilhouette.mat"]], "license": null, "citation": "3D Human Pose from Silhouettes by Relevance Vector Regression (In CVPR'04). A. Agarwal and B. Triggs.", "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.", "urls": ["http://staffwww.dcs.shef.ac.uk/people/N.Lawrence/dataset_mirror/ankur_pose_data/"], "size": 1}, "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}, "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}, "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": "\n 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 ", "urls": ["http://hapmap.ncbi.nlm.nih.gov/downloads/genotypes/latest_phaseIII_ncbi_b36/plink_format/"], "size": 3458246739}, "boxjenkins_airline": {"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.", "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.", "urls": ["http://staffwww.dcs.shef.ac.uk/people/N.Lawrence/dataset_mirror/boxjenkins_airline/"], "size": 46779}, "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}, "xw_pen": {"files": [["xw_pen_15.csv"]], "license": null, "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.", "urls": ["http://staffwww.dcs.shef.ac.uk/people/N.Lawrence/dataset_mirror/xw_pen/"], "size": 3410}} \ No newline at end of file diff --git a/GPy/util/datasets.py b/GPy/util/datasets.py index ea23b21c..2f43a3e8 100644 --- a/GPy/util/datasets.py +++ b/GPy/util/datasets.py @@ -405,11 +405,11 @@ def lee_yeast_ChIP(data_set='lee_yeast_ChIP'): import zipfile dir_path = os.path.join(data_path, data_set) filename = os.path.join(dir_path, 'binding_by_gene.tsv') - X = read_csv(filename, header=1, index_col=0, sep='\t') - transcription_factors = [col for col in X.columns if col[:7] != 'Unnamed'] - annotations = X[['Unnamed: 1', 'Unnamed: 2', 'Unnamed: 3']] - X = X[transcription_factors] - return data_details_return({'annotations' : annotations, 'X' : X, 'transcription_factors': transcription_factors}, data_set) + 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): diff --git a/GPy/util/libpeerconnection.log b/GPy/util/libpeerconnection.log new file mode 100644 index 00000000..e69de29b diff --git a/GPy/util/osu_accad/camper_04TXT.ZIP b/GPy/util/osu_accad/camper_04TXT.ZIP new file mode 100644 index 00000000..66b43e08 --- /dev/null +++ b/GPy/util/osu_accad/camper_04TXT.ZIP @@ -0,0 +1,213 @@ + + + + + +ACCAD | Page Not Found + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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+ + + + + + \ No newline at end of file diff --git a/GPy/util/osu_accad/connections.txt b/GPy/util/osu_accad/connections.txt new file mode 100644 index 00000000..e1886100 --- /dev/null +++ b/GPy/util/osu_accad/connections.txt @@ -0,0 +1,22 @@ +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/osu_accad/dance_KB3_TXT.ZIP b/GPy/util/osu_accad/dance_KB3_TXT.ZIP new file mode 100644 index 0000000000000000000000000000000000000000..01cdcedc9780f068a2851c264b9e8b05c0979701 GIT binary patch literal 2077367 zcmc$^RZtvG@GeRSkYFJ|aCf)GH8?E05Zs+zT!JNNaCci++!l9-;J#>Zhv0!g2oAyS z?|;vg*YkEBW~#bpditxGnx2}kTOITo?E?x5%3BnFn_uh(#;VqQ4Kyf`hejv_|7k%M zZcwPRtc9byg%dA7w}+QUYL04xK$mCkl3?#+D)-;4;;+d?Bmjt!j8PQf8Jaxy>o3H} 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