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Gradients are working now
This commit is contained in:
Ricardo
parent
3cc9547cab
commit
cb4c363c11
1 changed files with 100 additions and 163 deletions
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@ -16,18 +16,6 @@ def backsub_both_sides(L,X):
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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(sparse_GP):
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def __init__(self, X, likelihood, kernel, Z, X_variance=None, normalize_X=False):
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#self.fixed_beta_star = np.random.rand(X.shape[0],1) #TODO erase
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sparse_GP.__init__(self, X, likelihood, kernel=kernel, Z=Z, X_variance=None, normalize_X=False)
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def _set_params(self, p):
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self.Z = p[:self.M*self.Q].reshape(self.M, self.Q)
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self.kern._set_params(p[self.Z.size:self.Z.size+self.kern.Nparam])
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self.likelihood._set_params(p[self.Z.size+self.kern.Nparam:])
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self._compute_kernel_matrices()
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self.scale_factor = 1.
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self._computations()
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def update_likelihood_approximation(self):
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"""
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@ -45,6 +33,7 @@ class FITC(sparse_GP):
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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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@profile
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def _computations(self):
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#factor Kmm
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@ -53,24 +42,16 @@ class FITC(sparse_GP):
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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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#self.true_V_star = self.V_star.copy() #TODO eraseme
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#self.true_beta_star = self.beta_star.copy() #TODO eraseme
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#self.beta_star = self.fixed_beta_star.copy() #TODO eraseme
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#self.V_star = self.beta_star * self.likelihood.Y #TODO eraseme
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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.D == 1 # TODO: what if the likelihood is heterscedatic and there are multiple independent outputs?
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assert self.likelihood.D == 1
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tmp = self.psi1 * (np.sqrt(self.beta_star.flatten().reshape(1, self.N)))
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#tmp = self.psi1 * (np.sqrt(self.true_beta_star.flatten().reshape(1, self.N))) #TODO eraseme
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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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@ -79,49 +60,110 @@ class FITC(sparse_GP):
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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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#self.psi1V = np.dot(self.psi1, self.true_V_star) # TODO eraseme
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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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# A:
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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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Ki_pbp_Ki = np.dot(Kmmipsi1,b_psi1_Ki)
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dA_dpsi0 = -0.5 * self.beta_star
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dA_dpsi1 = b_psi1_Ki
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dA_dKmm = -0.5 * np.dot(Kmmipsi1,b_psi1_Ki)
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dA_dtheta_1 = self.kern.dKdiag_dtheta(dA_dpsi0,X=self.X) + self.kern.dK_dtheta(dA_dpsi1,self.X,self.Z) + self.kern.dK_dtheta(dA_dKmm,X=self.Z)
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dA_dX_1 = self.kern.dK_dX(dA_dpsi1.T,self.Z,self.X) + 2. * self.kern.dK_dX(dA_dKmm,X=self.Z)
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# dyby_dtheta
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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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dyby_dpsi0 = .5 * self.kern.dKdiag_dtheta(self.V_star**2,self.X)
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psi1beta = self.psi1*self.beta_star.T
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H = self.Kmm + mdot(self.psi1,self.beta_star*self.psi1.T)
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Hi, LH, LHi, logdetH = pdinv(H)
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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 * mdot(self.V_star.T,pHip*self.beta_star).T
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dA_dpsi0_1 = -0.5 * self.beta_star
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dA_dpsi0 = .5 * self.V_star**2
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dC_dpsi0 = .5 *alpha
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dD_dpsi0 = 0.5*mdot(self.beta_star*pHip,self.V_star)**2
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dD_dpsi1 = gamma_1
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dD_dpsi1 += -mdot(psi1beta.T,Hi,self.psi1,gamma_1)
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dD_dpsi0 += -self.V_star * mdot(self.V_star.T,pHip*self.beta_star).T
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dA_dpsi1 = b_psi1_Ki
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dC_dpsi1 = -np.dot(psi1beta.T,LBL_inv)
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dA_dKmm = -0.5 * np.dot(Kmmipsi1,b_psi1_Ki)
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dC_dKmm = -.5*Kmmi
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dC_dKmm += .5*LBL_inv
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dC_dKmm += mdot(LBL_inv,psi1beta,Kmmipsi1.T)
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dD_dKmm = -.5 * mdot(Hi,self.psi1,gamma_1)
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dA_dpsi0_theta = self.kern.dKdiag_dtheta(dA_dpsi0,X=self.X)
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dA_dpsi1_theta = 0
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dA_dpsi1_X = 0
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for psi1_n,V_n,X_n in zip(self.psi1.T,self.V_star,self.X):
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dA_dpsi1 = -V_n**2 * np.dot(psi1_n[None,:],Kmmi)
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dA_dpsi1_theta += self.kern.dK_dtheta(dA_dpsi1,X_n[None,:],self.Z)
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dA_dpsi1_X += self.kern.dK_dX(dA_dpsi1.T,self.Z,X_n[None,:])
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dA_dKmm_theta = 0
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dA_dKmm_X = 0
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for psi1_n,V_n,X_n in zip(self.psi1.T,self.V_star,self.X):
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_dC_dpsi1_dtheta = 0
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_dC_dpsi1_dX = 0
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_dC_dKmm_dtheta = 0
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_dC_dKmm_dX = 0
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_dD_dpsi1_dtheta_1 = 0
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_dD_dpsi1_dX_1 = 0
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_dD_dKmm_dtheta_1 = 0
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_dD_dKmm_dX_1 = 0
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_dD_dpsi1_dtheta_2 = 0
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_dD_dpsi1_dX_2 = 0
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_dD_dKmm_dtheta_2 = 0
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_dD_dKmm_dX_2 = 0
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for psi1_n,V_n,X_n,alpha_n,gamma_n,gamma_k in zip(self.psi1.T,self.V_star,self.X,alpha,gamma_2,gamma_3):
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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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dA_dKmm = .5*V_n**2 * tmp
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dA_dKmm_theta += self.kern.dK_dtheta(dA_dKmm,self.Z)
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dA_dKmm_X += 2.*self.kern.dK_dX(dA_dKmm,self.Z)
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_dA_dpsi1 = -V_n**2 * np.dot(psi1_n[None,:],Kmmi)
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_dC_dpsi1 = - alpha_n * np.dot(psi1_n[None,:],Kmmi)
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_dD_dpsi1_1 = - gamma_n**2 * np.dot(psi1_n[None,:],Kmmi)
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_dD_dpsi1_2 = 2. * gamma_k * np.dot(psi1_n[None,:],Kmmi)
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_dA_dKmm = .5*V_n**2 * np.dot(psin_K.T,psin_K)
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_dC_dKmm = .5 * alpha_n * np.dot(psin_K.T,psin_K)
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_dD_dKmm_1 = .5*gamma_n**2 * np.dot(psin_K.T,psin_K)
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_dD_dKmm_2 = - gamma_n * np.dot(psin_K.T,psin_K)
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dA_dpsi1_theta += self.kern.dK_dtheta(_dA_dpsi1,X_n[None,:],self.Z)
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_dC_dpsi1_dtheta += self.kern.dK_dtheta(_dC_dpsi1,X_n[None,:],self.Z)
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_dD_dpsi1_dtheta_1 += self.kern.dK_dtheta(_dD_dpsi1_1,X_n[None,:],self.Z)
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_dD_dpsi1_dtheta_2 += self.kern.dK_dtheta(_dD_dpsi1_2,X_n[None,:],self.Z)
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dA_dKmm_theta += self.kern.dK_dtheta(_dA_dKmm,self.Z)
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_dC_dKmm_dtheta += self.kern.dK_dtheta(_dC_dKmm,self.Z)
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_dD_dKmm_dtheta_1 += self.kern.dK_dtheta(_dD_dKmm_1,self.Z)
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_dD_dKmm_dtheta_2 += self.kern.dK_dtheta(_dD_dKmm_2,self.Z)
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dA_dpsi1_X += self.kern.dK_dX(_dA_dpsi1.T,self.Z,X_n[None,:])
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_dC_dpsi1_dX += self.kern.dK_dX(_dC_dpsi1.T,self.Z,X_n[None,:])
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_dD_dpsi1_dX_1 += self.kern.dK_dX(_dD_dpsi1_1.T,self.Z,X_n[None,:])
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_dD_dpsi1_dX_2 += self.kern.dK_dX(_dD_dpsi1_2.T,self.Z,X_n[None,:])
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dA_dKmm_X += 2.*self.kern.dK_dX(_dA_dKmm,self.Z)
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_dC_dKmm_dX += 2.*self.kern.dK_dX(_dC_dKmm,self.Z)
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_dD_dKmm_dX_1 += 2.*self.kern.dK_dX(_dD_dKmm_1,self.Z)
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_dD_dKmm_dX_2 += 2.*self.kern.dK_dX(_dD_dKmm_2,self.Z)
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dA_dX_1 = self.kern.dK_dX(dA_dpsi1.T,self.Z,self.X) + 2. * self.kern.dK_dX(dA_dKmm,X=self.Z)
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dA_dtheta_1 = self.kern.dKdiag_dtheta(dA_dpsi0_1,X=self.X) + self.kern.dK_dtheta(dA_dpsi1,self.X,self.Z) + self.kern.dK_dtheta(dA_dKmm,X=self.Z)
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dA_dtheta_2 = dA_dpsi0_theta + dA_dpsi1_theta + dA_dKmm_theta
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dA_dX_2 = dA_dpsi1_X + dA_dKmm_X
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@ -129,117 +171,18 @@ class FITC(sparse_GP):
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self.dA_dtheta = dA_dtheta_1 + dA_dtheta_2
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self.dA_dX = dA_dX_1 + dA_dX_2
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# dlogB_dtheta : C
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#C_B
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dC_dKmm = -.5*Kmmi
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#C_A
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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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dC_dKmm += .5*LBL_inv
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#C_AB
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psi1beta = self.psi1*self.beta_star.T
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dC_dKmm += mdot(LBL_inv,psi1beta,Kmmipsi1.T)
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dC_dpsi1 = -np.dot(psi1beta.T,LBL_inv)
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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_dpsi0 = .5 *alpha
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_dC_dpsi1_dtheta = 0
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_dC_dpsi1_dX = 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_dpsi1 = - alpha_n * np.dot(psi1_n[None,:],Kmmi)
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_dC_dpsi1_dtheta += self.kern.dK_dtheta(_dC_dpsi1,X_n[None,:],self.Z) #check
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_dC_dpsi1_dX += self.kern.dK_dX(_dC_dpsi1.T,self.Z,X_n[None,:])
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_dC_dKmm_dtheta = 0
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_dC_dKmm_dX = 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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_dC_dKmm = .5 * alpha_n * np.dot(psin_K.T,psin_K)
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_dC_dKmm_dtheta += self.kern.dK_dtheta(_dC_dKmm,self.Z) #check
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_dC_dKmm_dX += 2.*self.kern.dK_dX(_dC_dKmm,self.Z)
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#self.dlogB_dtheta = dCB_dKmm_theta + dCAA_dKmm_theta + dCABA_dKmm_theta + dCABB_dpsi1_theta + dCABCA_dpsi0_theta + dCABCB_dpsi1_theta + dCABCC_dKmm_theta
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self.dlogB_dtheta = self.kern.dK_dtheta(dC_dKmm,self.Z) + self.kern.dK_dtheta(dC_dpsi1,self.X,self.Z) + self.kern.dKdiag_dtheta(dC_dpsi0,self.X) + _dC_dpsi1_dtheta + _dC_dKmm_dtheta
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self.dlogB_dX = 2.*self.kern.dK_dX(dC_dKmm,self.Z) + self.kern.dK_dX(dC_dpsi1.T,self.Z,self.X) + _dC_dpsi1_dX + _dC_dKmm_dX
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# dD_dtheta
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H = self.Kmm + mdot(self.psi1,self.beta_star*self.psi1.T)
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Hi, LH, LHi, logdetH = pdinv(H)
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# D_B
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gamma_1 = mdot(VVT,self.psi1.T,Hi)
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dD_B = gamma_1
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D_B = self.kern.dK_dtheta(dD_B,self.X,self.Z)
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self.dD_dtheta = self.kern.dKdiag_dtheta(dD_dpsi0,self.X) + self.kern.dK_dtheta(dD_dKmm,self.Z) + self.kern.dK_dtheta(dD_dpsi1,self.X,self.Z) + _dD_dpsi1_dtheta_2 + _dD_dKmm_dtheta_2 + _dD_dpsi1_dtheta_1 + _dD_dKmm_dtheta_1
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dD_dpsi1 = gamma_1
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# D_C
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dD_CA = -.5 * mdot(Hi,self.psi1,gamma_1)
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D_CA = self.kern.dK_dtheta(dD_CA,self.Z)
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dD_dKmm = -.5 * mdot(Hi,self.psi1,gamma_1)
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# D_CB
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dD_CBA = - mdot(psi1beta.T,Hi,self.psi1,gamma_1)
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D_CBA = self.kern.dK_dtheta(dD_CBA,self.X,self.Z)
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dD_dpsi1 += -mdot(psi1beta.T,Hi,self.psi1,gamma_1)
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# D_CBB
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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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D_CBBA = .5 * self.kern.dKdiag_dtheta(gamma_2**2,self.X)
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dD_dpsi0 = 0.5*mdot(self.beta_star*pHip,self.V_star)**2
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_dD_dpsi1_dtheta_1 = 0
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_dD_dpsi1_dX_1 = 0
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for psi1_n,gamma_n,X_n in zip(self.psi1.T,gamma_2,self.X):
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_dD_dpsi1 = - gamma_n**2 * np.dot(psi1_n[None,:],Kmmi)
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_dD_dpsi1_dtheta_1 += self.kern.dK_dtheta(_dD_dpsi1,X_n[None,:],self.Z)
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_dD_dpsi1_dX_1 += self.kern.dK_dX(_dD_dpsi1.T,self.Z,X_n[None,:])
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_dD_dKmm_dtheta_1 = 0
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_dD_dKmm_dX_1 = 0
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for psi1_n,gamma_n,X_n in zip(self.psi1.T,gamma_2,self.X):
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psin_K = np.dot(psi1_n[None,:],Kmmi)
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_dD_dKmm = .5*gamma_n**2 * np.dot(psin_K.T,psin_K)
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_dD_dKmm_dtheta_1 += self.kern.dK_dtheta(_dD_dKmm,self.Z)
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_dD_dKmm_dX_1 += 2.*self.kern.dK_dX(_dD_dKmm,self.Z)
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# D_A
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gamma_3 = self.V_star * mdot(self.V_star.T,pHip*self.beta_star).T
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dD_AA = - gamma_3
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D_AA = self.kern.dKdiag_dtheta(dD_AA,self.X)
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dD_dpsi0 += -self.V_star * mdot(self.V_star.T,pHip*self.beta_star).T
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_dD_dpsi1_dtheta_2 = 0
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_dD_dpsi1_dX_2 = 0
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for psi1_n,gamma_n,X_n in zip(self.psi1.T,gamma_3,self.X):
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_dD_dpsi = 2. * gamma_n * np.dot(psi1_n[None,:],Kmmi)
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_dD_dpsi1_dtheta_2 += self.kern.dK_dtheta(_dD_dpsi,X_n[None,:],self.Z)
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_dD_dpsi1_dX_2 += self.kern.dK_dX(_dD_dpsi.T,self.Z,X_n[None,:])
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_dD_dKmm_dtheta_2 = 0
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_dD_dKmm_dX_2 = 0
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for psi1_n,gamma_n,X_n in zip(self.psi1.T,gamma_3,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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dD_AC = - gamma_n * tmp
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_dD_dKmm_dtheta_2 += self.kern.dK_dtheta(dD_AC,self.Z)
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_dD_dKmm_dX_2 += 2.*self.kern.dK_dX(dD_AC,self.Z)
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self.dD_dtheta = D_AA + _dD_dpsi1_dtheta_2 + _dD_dKmm_dtheta_2 + D_B + D_CA + D_CBA + D_CBBA + _dD_dpsi1_dtheta_1 + _dD_dKmm_dtheta_1
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self.dD_dtheta = self.kern.dKdiag_dtheta(dD_dpsi0,self.X) + self.kern.dK_dtheta(dD_dKmm,self.Z) + self.kern.dK_dtheta(dD_dpsi1.T,self.Z,self.X) + _dD_dpsi1_dtheta_2 + _dD_dKmm_dtheta_2 + _dD_dpsi1_dtheta_1 + _dD_dKmm_dtheta_1
|
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self.dD_dX = 2.*self.kern.dK_dX(dD_dKmm,self.Z) + self.kern.dK_dX(dD_dpsi1.T,self.Z,self.X) + _dD_dpsi1_dX_2 + _dD_dKmm_dX_2 + _dD_dpsi1_dX_1 + _dD_dKmm_dX_1
|
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|
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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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|
@ -249,7 +192,6 @@ class FITC(sparse_GP):
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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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#dbstar_dnoise = self.likelihood.precision * (self.true_beta_star**2 * self.Diag0[:,None] - self.true_beta_star) #TODO erase
|
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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)
|
||||
|
|
@ -270,15 +212,13 @@ class FITC(sparse_GP):
|
|||
dD_dnoise = dD_dnoise_1 + dD_dnoise_2
|
||||
|
||||
self.partial_for_likelihood = dA_dnoise + dC_dnoise + dD_dnoise
|
||||
self.partial_for_likelihood = dD_dnoise
|
||||
|
||||
def log_likelihood(self):
|
||||
""" Compute the (lower bound on the) log marginal likelihood """
|
||||
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)
|
||||
C = -self.D * (np.sum(np.log(np.diag(self.LB))))
|
||||
D = 0.5 * np.sum(np.square(self._LBi_Lmi_psi1V))
|
||||
#return A + C + D
|
||||
return D
|
||||
return A + C + D
|
||||
|
||||
def _log_likelihood_gradients(self):
|
||||
pass
|
||||
|
|
@ -289,7 +229,6 @@ class FITC(sparse_GP):
|
|||
raise NotImplementedError, "FITC approximation not implemented for uncertain inputs"
|
||||
else:
|
||||
dL_dtheta = self.dA_dtheta + self.dlogB_dtheta + self.dD_dtheta
|
||||
dL_dtheta = self.dD_dtheta #TODO eraseme
|
||||
return dL_dtheta
|
||||
|
||||
def dL_dZ(self):
|
||||
|
|
@ -297,25 +236,23 @@ class FITC(sparse_GP):
|
|||
raise NotImplementedError, "FITC approximation not implemented for uncertain inputs"
|
||||
else:
|
||||
dL_dZ = self.dA_dX + self.dlogB_dX + self.dD_dX
|
||||
dL_dZ = self.dD_dX #TODO eraseme
|
||||
return dL_dZ
|
||||
|
||||
def _raw_predict(self, Xnew, which_parts, full_cov=False):
|
||||
|
||||
|
||||
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.M) + np.dot(self.RPT0,((1. - Iplus_Dprod_i)/self.Diag0)[:,None]*self.RPT0.T))
|
||||
self.R,info = linalg.flapack.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)
|
||||
|
||||
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.M) + np.dot(self.RPT0,((1. - Iplus_Dprod_i)/self.Diag0)[:,None]*self.RPT0.T))
|
||||
self.R,info = linalg.flapack.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
|
||||
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue