mirror of
https://github.com/SheffieldML/GPy.git
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Merge branch 'devel' of github.com:SheffieldML/GPy into devel
This commit is contained in:
Nicolas
commit
fe9dcfae9d
3 changed files with 0 additions and 476 deletions
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@ -157,11 +157,6 @@ def FITC_crescent_data(num_inducing=10, seed=default_seed):
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:type num_inducing: int
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"""
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data = GPy.util.datasets.crescent_data(seed=seed)
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Y = data['Y']
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Y[Y.flatten()==-1]=0
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data = GPy.util.datasets.crescent_data(seed=seed)
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Y = data['Y']
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Y[Y.flatten()==-1]=0
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@ -1,252 +0,0 @@
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# Copyright (c) 2012, GPy authors (see AUTHORS.txt).
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# Licensed under the BSD 3-clause license (see LICENSE.txt)
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import numpy as np
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import pylab as pb
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from ..util.linalg import mdot, jitchol, chol_inv, tdot, symmetrify, pdinv
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from ..util.plot import gpplot
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from .. import kern
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from scipy import stats, linalg
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from GPy.core.sparse_gp import SparseGP
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def backsub_both_sides(L, X):
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""" Return L^-T * X * L^-1, assumuing X is symmetrical and L is lower cholesky"""
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tmp, _ = linalg.lapack.flapack.dtrtrs(L, np.asfortranarray(X), lower=1, trans=1)
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return linalg.lapack.flapack.dtrtrs(L, np.asfortranarray(tmp.T), lower=1, trans=1)[0].T
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class FITC(SparseGP):
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def __init__(self, X, likelihood, kernel, Z, X_variance=None, normalize_X=False):
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super(FITC, self).__init__(X, likelihood, kernel, normalize_X=normalize_X)
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def update_likelihood_approximation(self):
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"""
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Approximates a non-gaussian likelihood using Expectation Propagation
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For a Gaussian (or direct: TODO) likelihood, no iteration is required:
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this function does nothing
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Diag(Knn - Qnn) is added to the noise term to use the tools already implemented in SparseGP.
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The true precison is now 'true_precision' not 'precision'.
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"""
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if self.has_uncertain_inputs:
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raise NotImplementedError, "FITC approximation not implemented for uncertain inputs"
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else:
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self.likelihood.fit_FITC(self.Kmm, self.psi1, self.psi0)
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self._set_params(self._get_params()) # update the GP
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def _computations(self):
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# factor Kmm
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self.Lm = jitchol(self.Kmm)
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self.Lmi, info = linalg.lapack.flapack.dtrtrs(self.Lm, np.eye(self.num_inducing), lower=1)
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Lmipsi1 = np.dot(self.Lmi, self.psi1)
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self.Qnn = np.dot(Lmipsi1.T, Lmipsi1).copy()
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self.Diag0 = self.psi0 - np.diag(self.Qnn)
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self.beta_star = self.likelihood.precision / (1. + self.likelihood.precision * self.Diag0[:, None]) # Includes Diag0 in the precision
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self.V_star = self.beta_star * self.likelihood.Y
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# The rather complex computations of self.A
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if self.has_uncertain_inputs:
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raise NotImplementedError
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else:
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if self.likelihood.is_heteroscedastic:
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assert self.likelihood.input_dim == 1
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tmp = self.psi1 * (np.sqrt(self.beta_star.flatten().reshape(1, self.num_data)))
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tmp, _ = linalg.lapack.flapack.dtrtrs(self.Lm, np.asfortranarray(tmp), lower=1)
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self.A = tdot(tmp)
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# factor B
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self.B = np.eye(self.num_inducing) + self.A
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self.LB = jitchol(self.B)
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self.LBi = chol_inv(self.LB)
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self.psi1V = np.dot(self.psi1, self.V_star)
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Lmi_psi1V, info = linalg.lapack.flapack.dtrtrs(self.Lm, np.asfortranarray(self.psi1V), lower=1, trans=0)
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self._LBi_Lmi_psi1V, _ = linalg.lapack.flapack.dtrtrs(self.LB, np.asfortranarray(Lmi_psi1V), lower=1, trans=0)
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Kmmipsi1 = np.dot(self.Lmi.T, Lmipsi1)
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b_psi1_Ki = self.beta_star * Kmmipsi1.T
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Ki_pbp_Ki = np.dot(Kmmipsi1, b_psi1_Ki)
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Kmmi = np.dot(self.Lmi.T, self.Lmi)
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LBiLmi = np.dot(self.LBi, self.Lmi)
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LBL_inv = np.dot(LBiLmi.T, LBiLmi)
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VVT = np.outer(self.V_star, self.V_star)
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VV_p_Ki = np.dot(VVT, Kmmipsi1.T)
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Ki_pVVp_Ki = np.dot(Kmmipsi1, VV_p_Ki)
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psi1beta = self.psi1 * self.beta_star.T
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H = self.Kmm + mdot(self.psi1, psi1beta.T)
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LH = jitchol(H)
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LHi = chol_inv(LH)
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Hi = np.dot(LHi.T, LHi)
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betapsi1TLmiLBi = np.dot(psi1beta.T, LBiLmi.T)
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alpha = np.array([np.dot(a.T, a) for a in betapsi1TLmiLBi])[:, None]
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gamma_1 = mdot(VVT, self.psi1.T, Hi)
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pHip = mdot(self.psi1.T, Hi, self.psi1)
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gamma_2 = mdot(self.beta_star * pHip, self.V_star)
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gamma_3 = self.V_star * gamma_2
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self._dL_dpsi0 = -0.5 * self.beta_star # dA_dpsi0: logdet(self.beta_star)
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self._dL_dpsi0 += .5 * self.V_star ** 2 # dA_psi0: yT*beta_star*y
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self._dL_dpsi0 += .5 * alpha # dC_dpsi0
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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
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self._dL_dpsi1 = b_psi1_Ki.copy() # dA_dpsi1: logdet(self.beta_star)
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self._dL_dpsi1 += -np.dot(psi1beta.T, LBL_inv) # dC_dpsi1
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self._dL_dpsi1 += gamma_1 - mdot(psi1beta.T, Hi, self.psi1, gamma_1) # dD_dpsi1
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self._dL_dKmm = -0.5 * np.dot(Kmmipsi1, b_psi1_Ki) # dA_dKmm: logdet(self.beta_star)
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self._dL_dKmm += .5 * (LBL_inv - Kmmi) + mdot(LBL_inv, psi1beta, Kmmipsi1.T) # dC_dKmm
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self._dL_dKmm += -.5 * mdot(Hi, self.psi1, gamma_1) # dD_dKmm
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self._dpsi1_dtheta = 0
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self._dpsi1_dX = 0
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self._dKmm_dtheta = 0
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self._dKmm_dX = 0
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self._dpsi1_dX_jkj = 0
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self._dpsi1_dtheta_jkj = 0
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for i, V_n, alpha_n, gamma_n, gamma_k in zip(range(self.num_data), self.V_star, alpha, gamma_2, gamma_3):
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K_pp_K = np.dot(Kmmipsi1[:, i:(i + 1)], Kmmipsi1[:, i:(i + 1)].T)
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# Diag_dpsi1 = Diag_dA_dpsi1: yT*beta_star*y + Diag_dC_dpsi1 +Diag_dD_dpsi1
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_dpsi1 = (-V_n ** 2 - alpha_n + 2.*gamma_k - gamma_n ** 2) * Kmmipsi1.T[i:(i + 1), :]
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# Diag_dKmm = Diag_dA_dKmm: yT*beta_star*y +Diag_dC_dKmm +Diag_dD_dKmm
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_dKmm = .5 * (V_n ** 2 + alpha_n + gamma_n ** 2 - 2.*gamma_k) * K_pp_K # Diag_dD_dKmm
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self._dpsi1_dtheta += self.kern.dK_dtheta(_dpsi1, self.X[i:i + 1, :], self.Z)
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self._dKmm_dtheta += self.kern.dK_dtheta(_dKmm, self.Z)
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self._dKmm_dX += 2.*self.kern.dK_dX(_dKmm , self.Z)
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self._dpsi1_dX += self.kern.dK_dX(_dpsi1.T, self.Z, self.X[i:i + 1, :])
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# the partial derivative vector for the likelihood
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if self.likelihood.Nparams == 0:
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# save computation here.
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self.partial_for_likelihood = None
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elif self.likelihood.is_heteroscedastic:
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raise NotImplementedError, "heteroscedatic derivates not implemented"
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else:
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# likelihood is not heterscedatic
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dbstar_dnoise = self.likelihood.precision * (self.beta_star ** 2 * self.Diag0[:, None] - self.beta_star)
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Lmi_psi1 = mdot(self.Lmi, self.psi1)
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LBiLmipsi1 = np.dot(self.LBi, Lmi_psi1)
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aux_0 = np.dot(self._LBi_Lmi_psi1V.T, LBiLmipsi1)
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aux_1 = self.likelihood.Y.T * np.dot(self._LBi_Lmi_psi1V.T, LBiLmipsi1)
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aux_2 = np.dot(LBiLmipsi1.T, self._LBi_Lmi_psi1V)
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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)
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dC_dnoise = -0.5 * np.sum(mdot(self.LBi.T, self.LBi, Lmi_psi1) * Lmi_psi1 * dbstar_dnoise.T)
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dC_dnoise = -0.5 * np.sum(mdot(self.LBi.T, self.LBi, Lmi_psi1) * Lmi_psi1 * dbstar_dnoise.T)
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dD_dnoise_1 = mdot(self.V_star * LBiLmipsi1.T, LBiLmipsi1 * dbstar_dnoise.T * self.likelihood.Y.T)
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alpha = mdot(LBiLmipsi1, self.V_star)
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alpha_ = mdot(LBiLmipsi1.T, alpha)
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dD_dnoise_2 = -0.5 * self.input_dim * np.sum(alpha_ ** 2 * dbstar_dnoise)
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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)
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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)
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dD_dnoise = dD_dnoise_1 + dD_dnoise_2
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self.partial_for_likelihood = dA_dnoise + dC_dnoise + dD_dnoise
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def log_likelihood(self):
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""" Compute the (lower bound on the) log marginal likelihood """
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A = -0.5 * self.num_data * self.input_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)
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C = -self.input_dim * (np.sum(np.log(np.diag(self.LB))))
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D = 0.5 * np.sum(np.square(self._LBi_Lmi_psi1V))
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return A + C + D
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def _log_likelihood_gradients(self):
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pass
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return np.hstack((self.dL_dZ().flatten(), self.dL_dtheta(), self.likelihood._gradients(partial=self.partial_for_likelihood)))
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def dL_dtheta(self):
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if self.has_uncertain_inputs:
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raise NotImplementedError, "FITC approximation not implemented for uncertain inputs"
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else:
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dL_dtheta = self.kern.dKdiag_dtheta(self._dL_dpsi0, self.X)
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dL_dtheta += self.kern.dK_dtheta(self._dL_dpsi1, self.X, self.Z)
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dL_dtheta += self.kern.dK_dtheta(self._dL_dKmm, X=self.Z)
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dL_dtheta += self._dKmm_dtheta
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dL_dtheta += self._dpsi1_dtheta
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return dL_dtheta
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def dL_dZ(self):
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if self.has_uncertain_inputs:
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raise NotImplementedError, "FITC approximation not implemented for uncertain inputs"
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else:
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dL_dZ = self.kern.dK_dX(self._dL_dpsi1.T, self.Z, self.X)
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dL_dZ += 2. * self.kern.dK_dX(self._dL_dKmm, X=self.Z)
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dL_dZ += self._dpsi1_dX
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dL_dZ += self._dKmm_dX
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return dL_dZ
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def _raw_predict(self, Xnew, which_parts, full_cov=False):
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if self.likelihood.is_heteroscedastic:
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Iplus_Dprod_i = 1. / (1. + self.Diag0 * self.likelihood.precision.flatten())
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self.Diag = self.Diag0 * Iplus_Dprod_i
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self.P = Iplus_Dprod_i[:, None] * self.psi1.T
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self.RPT0 = np.dot(self.Lmi, self.psi1)
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self.L = np.linalg.cholesky(np.eye(self.num_inducing) + np.dot(self.RPT0, ((1. - Iplus_Dprod_i) / self.Diag0)[:, None] * self.RPT0.T))
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self.R, info = linalg.flapack.dtrtrs(self.L, self.Lmi, lower=1)
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self.RPT = np.dot(self.R, self.P.T)
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self.Sigma = np.diag(self.Diag) + np.dot(self.RPT.T, self.RPT)
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self.w = self.Diag * self.likelihood.v_tilde
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self.Gamma = np.dot(self.R.T, np.dot(self.RPT, self.likelihood.v_tilde))
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self.mu = self.w + np.dot(self.P, self.Gamma)
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"""
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Make a prediction for the generalized FITC model
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Arguments
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---------
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X : Input prediction data - Nx1 numpy array (floats)
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"""
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# q(u|f) = N(u| R0i*mu_u*f, R0i*C*R0i.T)
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# Ci = I + (RPT0)Di(RPT0).T
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# C = I - [RPT0] * (input_dim+[RPT0].T*[RPT0])^-1*[RPT0].T
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# = I - [RPT0] * (input_dim + self.Qnn)^-1 * [RPT0].T
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# = I - [RPT0] * (U*U.T)^-1 * [RPT0].T
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# = I - V.T * V
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U = np.linalg.cholesky(np.diag(self.Diag0) + self.Qnn)
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V, info = linalg.flapack.dtrtrs(U, self.RPT0.T, lower=1)
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C = np.eye(self.num_inducing) - np.dot(V.T, V)
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mu_u = np.dot(C, self.RPT0) * (1. / self.Diag0[None, :])
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# self.C = C
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# self.RPT0 = np.dot(self.R0,self.Knm.T) P0.T
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# self.mu_u = mu_u
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# self.U = U
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# q(u|y) = N(u| R0i*mu_H,R0i*Sigma_H*R0i.T)
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mu_H = np.dot(mu_u, self.mu)
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self.mu_H = mu_H
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Sigma_H = C + np.dot(mu_u, np.dot(self.Sigma, mu_u.T))
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# q(f_star|y) = N(f_star|mu_star,sigma2_star)
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Kx = self.kern.K(self.Z, Xnew, which_parts=which_parts)
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KR0T = np.dot(Kx.T, self.Lmi.T)
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mu_star = np.dot(KR0T, mu_H)
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if full_cov:
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Kxx = self.kern.K(Xnew, which_parts=which_parts)
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var = Kxx + np.dot(KR0T, np.dot(Sigma_H - np.eye(self.num_inducing), KR0T.T))
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else:
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Kxx = self.kern.Kdiag(Xnew, which_parts=which_parts)
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var = (Kxx + np.sum(KR0T.T * np.dot(Sigma_H - np.eye(self.num_inducing), KR0T.T), 0))[:, None]
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return mu_star[:, None], var
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else:
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raise NotImplementedError, "homoscedastic fitc not implemented"
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"""
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Kx = self.kern.K(self.Z, Xnew)
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mu = mdot(Kx.T, self.C/self.scale_factor, self.psi1V)
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if full_cov:
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Kxx = self.kern.K(Xnew)
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var = Kxx - mdot(Kx.T, (self.Kmmi - self.C/self.scale_factor**2), Kx) #NOTE this won't work for plotting
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else:
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Kxx = self.kern.Kdiag(Xnew)
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var = Kxx - np.sum(Kx*np.dot(self.Kmmi - self.C/self.scale_factor**2, Kx),0)
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return mu,var[:,None]
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"""
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@ -1,219 +0,0 @@
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# Copyright (c) 2012, GPy authors (see AUTHORS.txt).
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# Licensed under the BSD 3-clause license (see LICENSE.txt)
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import numpy as np
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from scipy import linalg
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from GPy.core.sparse_gp import SparseGP
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from GPy.util.linalg import mdot
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def backsub_both_sides(L, X):
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""" Return L^-T * X * L^-1, assumuing X is symmetrical and L is lower cholesky"""
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tmp, _ = linalg.lapack.flapack.dtrtrs(L, np.asfortranarray(X), lower=1, trans=1)
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return linalg.lapack.flapack.dtrtrs(L, np.asfortranarray(tmp.T), lower=1, trans=1)[0].T
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class GeneralizedFITC(SparseGP):
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"""
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Naish-Guzman, A. and Holden, S. (2008) implemantation of EP with FITC.
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:param X: inputs
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:type X: np.ndarray (N x input_dim)
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:param likelihood: a likelihood instance, containing the observed data
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:type likelihood: GPy.likelihood.(Gaussian | EP)
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:param kernel : the kernel/covariance function. See link kernels
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:type kernel: a GPy kernel
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:param X_variance: The variance in the measurements of X (Gaussian variance)
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:type X_variance: np.ndarray (N x input_dim) | None
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:param Z: inducing inputs (optional, see note)
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:type Z: np.ndarray (num_inducing x input_dim) | None
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:param num_inducing : Number of inducing points (optional, default 10. Ignored if Z is not None)
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:type num_inducing: int
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:param normalize_(X|Y) : whether to normalize the data before computing (predictions will be in original scales)
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:type normalize_(X|Y): bool
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"""
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def __init__(self, X, likelihood, kernel, Z, X_variance=None, normalize_X=False):
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self.Z = Z
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self.num_inducing = self.Z.shape[0]
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self.true_precision = likelihood.precision
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super(GeneralizedFITC, self).__init__(X, likelihood, kernel=kernel, Z=self.Z, X_variance=X_variance, normalize_X=normalize_X)
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self._set_params(self._get_params())
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def _set_params(self, p):
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self.Z = p[:self.num_inducing * self.input_dim].reshape(self.num_inducing, self.input_dim)
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self.kern._set_params(p[self.Z.size:self.Z.size + self.kern.num_params])
|
||||
self.likelihood._set_params(p[self.Z.size + self.kern.num_params:])
|
||||
self._compute_kernel_matrices()
|
||||
self._computations()
|
||||
self._FITC_computations()
|
||||
|
||||
def update_likelihood_approximation(self):
|
||||
"""
|
||||
Approximates a non-gaussian likelihood using Expectation Propagation
|
||||
|
||||
For a Gaussian (or direct: TODO) likelihood, no iteration is required:
|
||||
this function does nothing
|
||||
|
||||
Diag(Knn - Qnn) is added to the noise term to use the tools already implemented in SparseGP.
|
||||
The true precison is now 'true_precision' not 'precision'.
|
||||
"""
|
||||
if self.has_uncertain_inputs:
|
||||
raise NotImplementedError, "FITC approximation not implemented for uncertain inputs"
|
||||
else:
|
||||
self.likelihood.fit_FITC(self.Kmm, self.psi1, self.psi0)
|
||||
self.true_precision = self.likelihood.precision # Save the true precision
|
||||
self.likelihood.precision = self.true_precision / (1. + self.true_precision * self.Diag0[:, None]) # Add the diagonal element of the FITC approximation
|
||||
self._set_params(self._get_params()) # update the GP
|
||||
|
||||
def _FITC_computations(self):
|
||||
"""
|
||||
FITC approximation doesn't have the correction term in the log-likelihood bound,
|
||||
but adds a diagonal term to the covariance matrix: diag(Knn - Qnn).
|
||||
This function:
|
||||
- computes the FITC diagonal term
|
||||
- removes the extra terms computed in the SparseGP approximation
|
||||
- computes the likelihood gradients wrt the true precision.
|
||||
"""
|
||||
# NOTE the true precison is now 'true_precision' not 'precision'
|
||||
if self.likelihood.is_heteroscedastic:
|
||||
|
||||
# Compute generalized FITC's diagonal term of the covariance
|
||||
self.Lmi, info = linalg.lapack.flapack.dtrtrs(self.Lm, np.eye(self.num_inducing), lower=1)
|
||||
Lmipsi1 = np.dot(self.Lmi, self.psi1)
|
||||
self.Qnn = np.dot(Lmipsi1.T, Lmipsi1)
|
||||
# self.Kmmi, Lm, Lmi, Kmm_logdet = pdinv(self.Kmm)
|
||||
# self.Qnn = mdot(self.psi1.T,self.Kmmi,self.psi1)
|
||||
# a = kj
|
||||
self.Diag0 = self.psi0 - np.diag(self.Qnn)
|
||||
Iplus_Dprod_i = 1. / (1. + self.Diag0 * self.true_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 = linalg.lapack.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)
|
||||
|
||||
# Remove extra term from dL_dpsi1
|
||||
self.dL_dpsi1 -= mdot(self.Lmi.T,Lmipsi1 * self.likelihood.precision.flatten().reshape(1,self.num_data))
|
||||
#self.Kmmi, Lm, Lmi, Kmm_logdet = pdinv(self.Kmm)
|
||||
#self.dL_dpsi1 -= mdot(self.Kmmi,self.psi1*self.likelihood.precision.flatten().reshape(1,self.num_data)) #dB
|
||||
|
||||
#########333333
|
||||
# self.Bi, self.LB, self.LBi, self.B_logdet = pdinv(self.B)
|
||||
#########333333
|
||||
|
||||
|
||||
|
||||
else:
|
||||
raise NotImplementedError, "homoscedastic fitc not implemented"
|
||||
# Remove extra term from dL_dpsi1
|
||||
# self.dL_dpsi1 += -mdot(self.Kmmi,self.psi1*self.likelihood.precision) #dB
|
||||
|
||||
sf = self.scale_factor
|
||||
sf2 = sf ** 2
|
||||
|
||||
# Remove extra term from dL_dKmm
|
||||
self.dL_dKmm += 0.5 * self.input_dim * mdot(self.Lmi.T, self.A, self.Lmi) * sf2 # dB
|
||||
self.dL_dpsi0 = None
|
||||
|
||||
# the partial derivative vector for the likelihood
|
||||
if self.likelihood.Nparams == 0:
|
||||
self.partial_for_likelihood = None
|
||||
elif self.likelihood.is_heteroscedastic:
|
||||
raise NotImplementedError, "heteroscedastic derivates not implemented"
|
||||
else:
|
||||
raise NotImplementedError, "homoscedastic derivatives not implemented"
|
||||
#likelihood is not heterscedatic
|
||||
#self.partial_for_likelihood = - 0.5 * self.num_data*self.input_dim*self.likelihood.precision + 0.5 * np.sum(np.square(self.likelihood.Y))*self.likelihood.precision**2
|
||||
#self.partial_for_likelihood += 0.5 * self.input_dim * trace_dot(self.Bi,self.A)*self.likelihood.precision
|
||||
#self.partial_for_likelihood += self.likelihood.precision*(0.5*trace_dot(self.psi2_beta_scaled,self.E*sf2) - np.trace(self.Cpsi1VVpsi1))
|
||||
#TODO partial derivative vector for the likelihood not implemented
|
||||
|
||||
def dL_dtheta(self):
|
||||
"""
|
||||
Compute and return the derivative of the log marginal likelihood wrt the parameters of the kernel
|
||||
"""
|
||||
dL_dtheta = self.kern.dK_dtheta(self.dL_dKmm, self.Z)
|
||||
if self.has_uncertain_inputs:
|
||||
raise NotImplementedError, "heteroscedatic derivates not implemented"
|
||||
else:
|
||||
# NOTE in SparseGP this would include the gradient wrt psi0
|
||||
dL_dtheta += self.kern.dK_dtheta(self.dL_dpsi1, self.Z, self.X)
|
||||
return dL_dtheta
|
||||
|
||||
|
||||
def log_likelihood(self):
|
||||
""" Compute the (lower bound on the) log marginal likelihood """
|
||||
sf2 = self.scale_factor ** 2
|
||||
if self.likelihood.is_heteroscedastic:
|
||||
A = -0.5*self.num_data*self.input_dim*np.log(2.*np.pi) +0.5*np.sum(np.log(self.likelihood.precision)) -0.5*np.sum(self.V*self.likelihood.Y)
|
||||
else:
|
||||
A = -0.5*self.num_data*self.input_dim*(np.log(2.*np.pi) + np.log(self.likelihood._variance)) -0.5*self.likelihood.precision*self.likelihood.trYYT
|
||||
C = -self.input_dim * (np.sum(np.log(np.diag(self.LB))) + 0.5*self.num_inducing*np.log(sf2))
|
||||
#C = -0.5*self.input_dim * (self.B_logdet + self.num_inducing*np.log(sf2))
|
||||
D = 0.5*np.sum(np.square(self._LBi_Lmi_psi1V))
|
||||
#self.Cpsi1VVpsi1 = np.dot(self.Cpsi1V,self.psi1V.T)
|
||||
#D_ = 0.5*np.trace(self.Cpsi1VVpsi1)
|
||||
return A + C + D
|
||||
|
||||
def _raw_predict(self, Xnew, which_parts, full_cov=False):
|
||||
if self.likelihood.is_heteroscedastic:
|
||||
"""
|
||||
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 = linalg.flapack.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)
|
||||
Kxx_ = self.kern.K(Xnew, which_parts=which_parts) # TODO: RA, is this line needed?
|
||||
var_ = Kxx_ + np.dot(KR0T, np.dot(Sigma_H - np.eye(self.num_inducing), KR0T.T)) # TODO: RA, is this line needed?
|
||||
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, "homoscedastic fitc 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]
|
||||
"""
|
||||
Loading…
Add table
Add a link
Reference in a new issue