From eee4b9c45fa77a38e53a7e692af956e8ff69c78c Mon Sep 17 00:00:00 2001 From: James Hensman Date: Fri, 3 May 2013 17:06:26 +0100 Subject: [PATCH] various stability working on sparse GP (with MZ) --- GPy/models/sparse_GP.py | 52 ++++++++++++++++++++--------------------- 1 file changed, 26 insertions(+), 26 deletions(-) diff --git a/GPy/models/sparse_GP.py b/GPy/models/sparse_GP.py index 5db3340a..f04c9bd5 100644 --- a/GPy/models/sparse_GP.py +++ b/GPy/models/sparse_GP.py @@ -76,12 +76,12 @@ class sparse_GP(GP): #invert Kmm self.Kmmi, self.Lm, self.Lmi, self.Kmm_logdet = pdinv(self.Kmm) - #The rather complex computations of psi2_beta_scaled and self.A + #The rather complex computations of self.A if self.likelihood.is_heteroscedastic: assert self.likelihood.D == 1 #TODO: what if the likelihood is heterscedatic and there are multiple independent outputs? if self.has_uncertain_inputs: - self.psi2_beta_scaled = (self.psi2*(self.likelihood.precision.flatten().reshape(self.N,1,1)/sf2)).sum(0) - evals, evecs = linalg.eigh(self.psi2_beta_scaled) + psi2_beta_scaled = (self.psi2*(self.likelihood.precision.flatten().reshape(self.N,1,1)/sf2)).sum(0) + evals, evecs = linalg.eigh(psi2_beta_scaled) clipped_evals = np.clip(evals,0.,1e6) # TODO: make clipping configurable if not np.allclose(evals, clipped_evals): print "Warning: clipping posterior eigenvalues" @@ -90,23 +90,23 @@ class sparse_GP(GP): self.A = tdot(tmp) else: tmp = self.psi1*(np.sqrt(self.likelihood.precision.flatten().reshape(1,self.N))/sf) - self.psi2_beta_scaled = tdot(tmp) + #self.psi2_beta_scaled = tdot(tmp) tmp, _ = linalg.lapack.flapack.dtrtrs(self.Lm,np.asfortranarray(tmp),lower=1) self.A = tdot(tmp) else: if self.has_uncertain_inputs: - self.psi2_beta_scaled = (self.psi2*(self.likelihood.precision/sf2)).sum(0) - evals, evecs = linalg.eigh(self.psi2_beta_scaled) + psi2_beta_scaled = (self.psi2*(self.likelihood.precision/sf2)).sum(0) + evals, evecs = linalg.eigh(psi2_beta_scaled) clipped_evals = np.clip(evals,0.,1e6) # TODO: make clipping configurable if not np.allclose(evals, clipped_evals): print "Warning: clipping posterior eigenvalues" tmp = evecs*np.sqrt(clipped_evals) - self.psi2_beta_scaled = tdot(tmp) + #self.psi2_beta_scaled = tdot(tmp) tmp, _ = linalg.lapack.flapack.dtrtrs(self.Lm,np.asfortranarray(tmp),lower=1) self.A = tdot(tmp) else: tmp = self.psi1*(np.sqrt(self.likelihood.precision)/sf) - self.psi2_beta_scaled = tdot(tmp) + #self.psi2_beta_scaled = tdot(tmp) tmp, _ = linalg.lapack.flapack.dtrtrs(self.Lm,np.asfortranarray(tmp),lower=1) self.A = tdot(tmp) @@ -121,16 +121,16 @@ class sparse_GP(GP): #back substutue C into psi1V tmp,info1 = linalg.lapack.flapack.dtrtrs(self.Lm,np.asfortranarray(self.psi1V),lower=1,trans=0) + self._LBi_Lmi_psi1V,_ = linalg.lapack.flapack.dtrtrs(self.LB,np.asfortranarray(tmp),lower=1,trans=0) self._P = tdot(tmp) tmp,info2 = linalg.lapack.flapack.dpotrs(self.LB,tmp,lower=1) self.Cpsi1V,info3 = linalg.lapack.flapack.dtrtrs(self.Lm,tmp,lower=1,trans=1) #self.Cpsi1V = np.dot(self.C,self.psi1V) - self.Cpsi1VVpsi1 = np.dot(self.Cpsi1V,self.psi1V.T) #TODO: this dot can be eliminated - self.E = tdot(self.Cpsi1V/sf) + # Compute dL_dpsi # FIXME: this is untested for the heterscedastic + uncertin inputs case self.dL_dpsi0 = - 0.5 * self.D * (self.likelihood.precision * np.ones([self.N,1])).flatten() self.dL_dpsi1 = np.dot(self.Cpsi1V,self.V.T) @@ -159,14 +159,12 @@ class sparse_GP(GP): # Compute dL_dKmm - #self.dL_dKmm = -0.5 * self.D * mdot(self.Lmi.T, self.A, self.Lmi)*sf2 # dB - #self.dL_dKmm += -0.5 * self.D * (- self.C/sf2 - 2.*mdot(self.C, self.psi2_beta_scaled, self.Kmmi) + self.Kmmi) # dC - #self.dL_dKmm += np.dot(np.dot(self.E*sf2, self.psi2_beta_scaled) - self.Cpsi1VVpsi1, self.Kmmi) + 0.5*self.E # dD - tmp = linalg.lapack.flapack.dtrtrs(self.Lm,np.asfortranarray(self.B),lower=1,trans=1)[0] - self.dL_dKmm = -0.5*self.D*sf2*linalg.lapack.flapack.dtrtrs(self.Lm,np.asfortranarray(tmp.T),lower=1,trans=1)[0] - tmp = np.dot(self.D*self.C + self.E*sf2,self.psi2_beta_scaled) - self.Cpsi1VVpsi1 - tmp = linalg.lapack.flapack.dpotrs(self.Lm,np.asfortranarray(tmp.T),lower=1)[0].T - self.dL_dKmm += 0.5*(self.D*self.C/sf2 + self.E) +tmp # d(C+D) + tmp = tdot(self._LBi_Lmi_psi1V) + self.DBi_plus_BiPBi = backsub_both_sides(self.LB, self.D*np.eye(self.M) + tmp) + tmp = -0.5*self.DBi_plus_BiPBi/sf2 + tmp += -0.5*self.B*sf2*self.D + tmp += self.D*np.eye(self.M) + self.dL_dKmm = backsub_both_sides(self.Lm,tmp) #the partial derivative vector for the likelihood if self.likelihood.Nparams ==0: @@ -182,8 +180,9 @@ class sparse_GP(GP): #likelihood is not heterscedatic self.partial_for_likelihood = - 0.5 * self.N*self.D*self.likelihood.precision + 0.5 * self.likelihood.trYYT*self.likelihood.precision**2 self.partial_for_likelihood += 0.5 * self.D * (self.psi0.sum()*self.likelihood.precision**2 - np.trace(self.A)*self.likelihood.precision*sf2) - self.partial_for_likelihood += 0.5 * self.D * 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)) + #self.partial_for_likelihood += 0.5 * self.D * 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.sum(np.square(self._LBi_Lmi_psi1V))) + self.partial_for_likelihood += self.likelihood.precision*(0.5*trace_dot(self.A,self.DBi_plus_BiPBi) - np.sum(np.square(self._LBi_Lmi_psi1V))) @@ -197,7 +196,7 @@ class sparse_GP(GP): A = -0.5*self.N*self.D*(np.log(2.*np.pi) + np.log(self.likelihood._variance)) -0.5*self.likelihood.precision*self.likelihood.trYYT B = -0.5*self.D*(np.sum(self.likelihood.precision*self.psi0) - np.trace(self.A)*sf2) C = -0.5*self.D * (self.B_logdet + self.M*np.log(sf2)) - D = 0.5*np.trace(self.Cpsi1VVpsi1) + D = 0.5*np.sum(np.square(self._LBi_Lmi_psi1V)) return A+B+C+D def _set_params(self, p): @@ -207,11 +206,12 @@ class sparse_GP(GP): self._compute_kernel_matrices() #if self.auto_scale_factor: # self.scale_factor = np.sqrt(self.psi2.sum(0).mean()*self.likelihood.precision) - if self.auto_scale_factor: - if self.likelihood.is_heteroscedastic: - self.scale_factor = max(100,np.sqrt(self.psi2_beta_scaled.sum(0).mean())) - else: - self.scale_factor = np.sqrt(self.psi2.sum(0).mean()*self.likelihood.precision) + #if self.auto_scale_factor: + #if self.likelihood.is_heteroscedastic: + #self.scale_factor = max(100,np.sqrt(self.psi2_beta_scaled.sum(0).mean())) + #else: + #self.scale_factor = np.sqrt(self.psi2.sum(0).mean()*self.likelihood.precision) + self.scale_factor = 1. self._computations() def _get_params(self):