Source code for GPy.models.gp_kronecker_gaussian_regression

# Copyright (c) 2014, James Hensman, Alan Saul
# Licensed under the BSD 3-clause license (see LICENSE.txt)

import numpy as np
from ..core import Model
from paramz import ObsAr
from .. import likelihoods

[docs]class GPKroneckerGaussianRegression(Model): """ Kronecker GP regression Take two kernels computed on separate spaces K1(X1), K2(X2), and a data matrix Y which is f size (N1, N2). The effective covaraince is np.kron(K2, K1) The effective data is vec(Y) = Y.flatten(order='F') The noise must be iid Gaussian. See [stegle_et_al_2011]_. .. rubric:: References .. [stegle_et_al_2011] Stegle, O.; Lippert, C.; Mooij, J.M.; Lawrence, N.D.; Borgwardt, K.:Efficient inference in matrix-variate Gaussian models with \iid observation noise. In: Advances in Neural Information Processing Systems, 2011, Pages 630-638 """ def __init__(self, X1, X2, Y, kern1, kern2, noise_var=1., name='KGPR'): super(GPKroneckerGaussianRegression, self).__init__(name=name) # accept the construction arguments self.X1 = ObsAr(X1) self.X2 = ObsAr(X2) self.Y = Y self.kern1, self.kern2 = kern1, kern2 self.link_parameter(self.kern1) self.link_parameter(self.kern2) self.likelihood = likelihoods.Gaussian() self.likelihood.variance = noise_var self.link_parameter(self.likelihood) self.num_data1, self.input_dim1 = self.X1.shape self.num_data2, self.input_dim2 = self.X2.shape assert kern1.input_dim == self.input_dim1 assert kern2.input_dim == self.input_dim2 assert Y.shape == (self.num_data1, self.num_data2)
[docs] def log_likelihood(self): return self._log_marginal_likelihood
[docs] def parameters_changed(self): (N1, D1), (N2, D2) = self.X1.shape, self.X2.shape K1, K2 = self.kern1.K(self.X1), self.kern2.K(self.X2) # eigendecompositon S1, U1 = np.linalg.eigh(K1) S2, U2 = np.linalg.eigh(K2) W = np.kron(S2, S1) + self.likelihood.variance Y_ = # store these quantities: needed for prediction Wi = 1./W Ytilde = Y_.flatten(order='F')*Wi self._log_marginal_likelihood = -0.5*self.num_data1*self.num_data2*np.log(2*np.pi)\ -0.5*np.sum(np.log(W))\ -0.5*'F'), Ytilde) # gradients for data fit part Yt_reshaped = Ytilde.reshape(N1, N2, order='F') tmp = dL_dK1 = .5*(tmp*S2).dot(tmp.T) tmp = dL_dK2 = .5*(tmp*S1).dot(tmp.T) # gradients for logdet Wi_reshaped = Wi.reshape(N1, N2, order='F') tmp =, S2) dL_dK1 += -0.5*(U1*tmp).dot(U1.T) tmp =, S1) dL_dK2 += -0.5*(U2*tmp).dot(U2.T) self.kern1.update_gradients_full(dL_dK1, self.X1) self.kern2.update_gradients_full(dL_dK2, self.X2) # gradients for noise variance dL_dsigma2 = -0.5*Wi.sum() + 0.5*np.sum(np.square(Ytilde)) self.likelihood.variance.gradient = dL_dsigma2 # store these quantities for prediction: self.Wi, self.Ytilde, self.U1, self.U2 = Wi, Ytilde, U1, U2
[docs] def predict(self, X1new, X2new): """ Return the predictive mean and variance at a series of new points X1new, X2new Only returns the diagonal of the predictive variance, for now. :param X1new: The points at which to make a prediction :type X1new: np.ndarray, Nnew x self.input_dim1 :param X2new: The points at which to make a prediction :type X2new: np.ndarray, Nnew x self.input_dim2 """ k1xf = self.kern1.K(X1new, self.X1) k2xf = self.kern2.K(X2new, self.X2) A = B = mu =, self.num_data2, order='F')).dot(B.T).flatten(order='F') k1xx = self.kern1.Kdiag(X1new) k2xx = self.kern2.Kdiag(X2new) BA = np.kron(B, A) var = np.kron(k2xx, k1xx) - np.sum(BA**2*self.Wi, 1) + self.likelihood.variance return mu[:, None], var[:, None]