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some changes
This commit is contained in:
Ricardo
parent
00230d7b02
commit
8ab4c65227
2 changed files with 65 additions and 61 deletions
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@ -21,6 +21,15 @@ class FITC(sparse_GP):
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self.Z = Z
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self.M = self.Z.shape[0]
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self.true_precision = likelihood.precision
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#ERASEME
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#N = likelihood.Y.size
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#self.beta_star = np.random.rand(N,1)
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#self.Kmm_ = kernel.K(self.Z).copy()
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#self.Kmmi_,a,b,c = pdinv(self.Kmm_)
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#self.psi1_ = kernel.K(self.Z,X).copy()
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sparse_GP.__init__(self, X, likelihood, kernel=kernel, Z=self.Z, X_variance=None, normalize_X=False)
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def _set_params(self, p):
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@ -48,6 +57,7 @@ class FITC(sparse_GP):
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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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@ -56,7 +66,24 @@ class FITC(sparse_GP):
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self.Qnn = np.dot(Lmipsi1.T,Lmipsi1)
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self.Diag0 = self.psi0 - np.diag(self.Qnn)
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#TODO eraseme
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"""
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self.psi1 = self.psi1_
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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.M),lower=1)
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Lmipsi1 = np.dot(self.Lmi,self.psi1)
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#self.true_psi1 = self.kern.K(self.Z,self.X)
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#self.Qnn = mdot(self.true_psi1.T,self.Lmi.T,self.Lmi,self.true_psi1)
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self.Kmmi, a,b,c = pdinv(self.Kmm)
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self.Qnn = mdot(self.psi1.T,self.Kmmi,self.psi1)
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#self.Diag0 = self.psi0 #- np.diag(self.Qnn)
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self.Diag0 = - np.diag(self.Qnn)
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#Kmmi,Lm,Lmi,logdetK = pdinv(self.Kmm)
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#self.Lambda = self.Kmmi_ + mdot(self.Kmmi_,self.psi1_,self.beta_star*self.psi1_.T,self.Kmmi_) + np.eye(self.M)*100
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#self.Lambdai, LLm, LLmi, self.logdetLambda = pdinv(self.Lambda)
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"""
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#TODO uncomment
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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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@ -70,19 +97,16 @@ class FITC(sparse_GP):
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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.M) + self.A
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self.LB = jitchol(self.B)
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self.LBi,info = linalg.lapack.flapack.dtrtrs(self.LB,np.eye(self.M),lower=1)
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self.psi1V = np.dot(self.psi1, self.V_star)
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# back substutue C into psi1V
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tmp, info1 = 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(tmp), lower=1, trans=0)
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# dlogbeta_dtheta
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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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@ -90,7 +114,7 @@ class FITC(sparse_GP):
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dlogB_dpsi0 = -.5*self.kern.dKdiag_dtheta(self.beta_star,X=self.X)
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dlogB_dpsi1 = self.kern.dK_dtheta(b_psi1_Ki,self.X,self.Z)
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dlogB_dKmm = -.5*self.kern.dK_dtheta(Ki_pbp_Ki,X=self.Z)
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self.dlogB_dtheta = dlogB_dpsi0 + dlogB_dpsi1 + dlogB_dKmm
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self.dlogbeta_dtheta = dlogB_dpsi0 + dlogB_dpsi1 + dlogB_dKmm
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# dyby_dtheta
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Kmmi = np.dot(self.Lmi.T,self.Lmi)
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@ -113,20 +137,44 @@ class FITC(sparse_GP):
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dyby_dtheta += self.kern.dK_dtheta(dyby_dKmm,self.Z)
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self.dyby_dtheta = dyby_dtheta
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# dlogB_dtheta
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# dlogB_dtheta : C
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#C_B
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dlogKi_dKmm = -.5 * Kmmi
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dlogB_dtheta = self.kern.dK_dtheta(dlogKi_dKmm,self.Z)
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dC_B = -.5*Kmmi
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C_B = self.kern.dK_dtheta(dC_B,self.Z) #check
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#C_A
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#C_AA
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LBiLmi = np.dot(self.LBi,self.Lmi)
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partial = .5*np.dot(LBiLmi.T,LBiLmi)
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dlogB_dtheta += self.kern.dK_dtheta(partial,self.Z)
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LBL_inv = np.dot(LBiLmi.T,LBiLmi)
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dC_AA = .5*LBL_inv
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C_AA = self.kern.dK_dtheta(dC_AA,self.Z) #check
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#C_AB
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psi1beta = self.psi1*self.beta_star.T
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dC_ABA = mdot(LBL_inv,psi1beta,Kmmipsi1.T)
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C_ABA = self.kern.dK_dtheta(dC_ABA,self.Z)
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dC_ABB = -np.dot(psi1beta.T,LBL_inv) #check
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C_ABB = self.kern.dK_dtheta(dC_ABB,self.X,self.Z) #check
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# C_ABC
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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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dC_ABCA = .5 *alpha
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C_ABCA = self.kern.dKdiag_dtheta(dC_ABCA,self.X) #check
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C_ABCB = 0
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for psi1_n,alpha_n,X_n in zip(self.psi1.T,alpha,self.X):
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dC_ABCB_n = - alpha_n * np.dot(psi1_n[None,:],Kmmi)
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C_ABCB += self.kern.dK_dtheta(dC_ABCB_n,X_n[:,None],self.Z) #check
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C_ABCC = 0
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for psi1_n,alpha_n,X_n in zip(self.psi1.T,alpha,self.X):
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psin_K = np.dot(psi1_n[None,:],Kmmi)
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tmp = np.dot(psin_K.T,psin_K)
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dC_ABCC = .5 * alpha_n * tmp
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C_ABCC += self.kern.dK_dtheta(dC_ABCC,self.Z) #check
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self.dlogB_dtheta = C_B + C_AA + C_ABA + C_ABB + C_ABCA + C_ABCB + C_ABCC
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# the partial derivative vector for the likelihood
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@ -144,55 +192,9 @@ class FITC(sparse_GP):
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"""
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tmp, info2 = linalg.lapack.flapack.dpotrs(self.LB, tmp, lower=1)
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self.Cpsi1V, info3 = linalg.lapack.flapack.dtrtrs(self.Lm, tmp, lower=1, trans=1)
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# Compute dL_dKmm
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tmp = tdot(self._LBi_Lmi_psi1V)
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self.DBi_plus_BiPBi = backsub_both_sides(self.LB, self.D * np.eye(self.M) + tmp)
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tmp = -0.5 * self.DBi_plus_BiPBi
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tmp += -0.5 * self.B * self.D
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tmp += self.D * np.eye(self.M)
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self.dL_dKmm = backsub_both_sides(self.Lm, tmp)
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# Compute dL_dpsi # FIXME: this is untested for the heterscedastic + uncertain inputs case
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self.dL_dpsi0 = -0.5 * self.D * (self.likelihood.precision * np.ones([self.N, 1])).flatten()
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self.dL_dpsi1 = np.dot(self.Cpsi1V, self.likelihood.V.T)
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dL_dpsi2_beta = 0.5 * backsub_both_sides(self.Lm, self.D * np.eye(self.M) - self.DBi_plus_BiPBi)
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if self.likelihood.is_heteroscedastic:
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if self.has_uncertain_inputs:
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self.dL_dpsi2 = self.likelihood.precision[:, None, None] * dL_dpsi2_beta[None, :, :]
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else:
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self.dL_dpsi1 += 2.*np.dot(dL_dpsi2_beta, self.psi1 * self.likelihood.precision.reshape(1, self.N))
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self.dL_dpsi2 = None
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else:
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dL_dpsi2 = self.likelihood.precision * dL_dpsi2_beta
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if self.has_uncertain_inputs:
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# repeat for each of the N psi_2 matrices
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self.dL_dpsi2 = np.repeat(dL_dpsi2[None, :, :], self.N, axis=0)
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else:
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# subsume back into psi1 (==Kmn)
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self.dL_dpsi1 += 2.*np.dot(dL_dpsi2, self.psi1)
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self.dL_dpsi2 = None
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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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self.partial_for_likelihood = -0.5 * self.N * self.D * self.likelihood.precision + 0.5 * self.likelihood.trYYT * self.likelihood.precision ** 2
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self.partial_for_likelihood += 0.5 * self.D * (self.psi0.sum() * self.likelihood.precision ** 2 - np.trace(self.A) * self.likelihood.precision)
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self.partial_for_likelihood += self.likelihood.precision * (0.5 * np.sum(self.A * self.DBi_plus_BiPBi) - np.sum(np.square(self._LBi_Lmi_psi1V)))
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"""
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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.N * self.D * 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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A = -0.5 * self.N * self.D * 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.D * (np.sum(np.log(np.diag(self.LB))))
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"""
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A = -0.5 * self.N * self.D * 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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@ -201,7 +203,7 @@ class FITC(sparse_GP):
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D = 0.5 * np.sum(np.square(self._LBi_Lmi_psi1V))
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return A + C + D # +B
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"""
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return C
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return A+C
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def _log_likelihood_gradients(self):
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@ -209,9 +211,11 @@ class FITC(sparse_GP):
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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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dL_dtheta = self.dlogB_dtheta
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#dL_dtheta = self.dlogB_dtheta
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#dL_dtheta = self.dyby_dtheta
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dL_dtheta = self.dlogB_dtheta + self.dyby_dtheta
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#dL_dtheta = self.dlogbeta_dtheta + self.dyby_dtheta
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dL_dtheta = self.dlogB_dtheta
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dL_dtheta = self.dlogbeta_dtheta + self.dyby_dtheta + self.dlogB_dtheta
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"""
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dL_dtheta = self.kern.dK_dtheta(self.dL_dKmm, self.Z)
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if self.has_uncertain_inputs:
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@ -12,4 +12,4 @@ from sparse_GPLVM import sparse_GPLVM
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from Bayesian_GPLVM import Bayesian_GPLVM
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from mrd import MRD
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from generalized_FITC import generalized_FITC
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from FITC import FITC
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#from FITC import FITC
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