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improved stability of sparse GP for certain-input case

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James Hensman 2013-05-01 11:10:46 +01:00
parent 83510e7515
commit 94b199e3c7
1 changed files with 21 additions and 22 deletions
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43
GPy/models/sparse_GP.py
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@ -68,47 +68,49 @@ class sparse_GP(GP):
sf = self.scale_factor sf = self.scale_factor
sf2 = sf**2 sf2 = sf**2
#The rather complex computations of psi2_beta_scaled #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
if self.likelihood.is_heteroscedastic: if self.likelihood.is_heteroscedastic:
assert self.likelihood.D == 1 #TODO: what if the likelihood is heterscedatic and there are multiple independent outputs? assert self.likelihood.D == 1 #TODO: what if the likelihood is heterscedatic and there are multiple independent outputs?
if self.has_uncertain_inputs: if self.has_uncertain_inputs:
self.psi2_beta_scaled = (self.psi2*(self.likelihood.precision.flatten().reshape(self.N,1,1)/sf2)).sum(0) self.psi2_beta_scaled = (self.psi2*(self.likelihood.precision.flatten().reshape(self.N,1,1)/sf2)).sum(0)
tmp, _ = linalg.lapack.flapack.dtrtrs(self.Lm,self.psi2_beta_scaled.T,lower=1)
self.A, _ = linalg.lapack.flapack.dtrtrs(self.Lm,np.asfortranarray(tmp.T),lower=1)
else: else:
tmp = self.psi1*(np.sqrt(self.likelihood.precision.flatten().reshape(1,self.N))/sf) tmp = self.psi1*(np.sqrt(self.likelihood.precision.flatten().reshape(1,self.N))/sf)
#self.psi2_beta_scaled = np.dot(tmp,tmp.T)
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: else:
if self.has_uncertain_inputs: if self.has_uncertain_inputs:
self.psi2_beta_scaled = (self.psi2*(self.likelihood.precision/sf2)).sum(0) self.psi2_beta_scaled = (self.psi2*(self.likelihood.precision/sf2)).sum(0)
tmp, _ = linalg.lapack.flapack.dtrtrs(self.Lm,self.psi2_beta_scaled.T,lower=1)
self.A, _ = linalg.lapack.flapack.dtrtrs(self.Lm,np.asfortranarray(tmp.T),lower=1)
else: else:
tmp = self.psi1*(np.sqrt(self.likelihood.precision)/sf) tmp = self.psi1*(np.sqrt(self.likelihood.precision)/sf)
#self.psi2_beta_scaled = np.dot(tmp,tmp.T)
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)
self.Kmmi, self.Lm, self.Lmi, self.Kmm_logdet = pdinv(self.Kmm) #invert B and compute C. C is the posterior covariance of u
self.V = (self.likelihood.precision/self.scale_factor)*self.likelihood.Y
#Compute A = L^-1 psi2 beta L^-T
#self. A = mdot(self.Lmi,self.psi2_beta_scaled,self.Lmi.T)
tmp = linalg.lapack.flapack.dtrtrs(self.Lm,self.psi2_beta_scaled.T,lower=1)[0]
self.A = linalg.lapack.flapack.dtrtrs(self.Lm,np.asfortranarray(tmp.T),lower=1)[0]
self.B = np.eye(self.M)/sf2 + self.A self.B = np.eye(self.M)/sf2 + self.A
self.Bi, self.LB, self.LBi, self.B_logdet = pdinv(self.B) self.Bi, self.LB, self.LBi, self.B_logdet = pdinv(self.B)
self.psi1V = np.dot(self.psi1, self.V)
tmp = linalg.lapack.flapack.dtrtrs(self.Lm,np.asfortranarray(self.Bi),lower=1,trans=1)[0] tmp = linalg.lapack.flapack.dtrtrs(self.Lm,np.asfortranarray(self.Bi),lower=1,trans=1)[0]
self.C = linalg.lapack.flapack.dtrtrs(self.Lm,np.asfortranarray(tmp.T),lower=1,trans=1)[0] self.C = linalg.lapack.flapack.dtrtrs(self.Lm,np.asfortranarray(tmp.T),lower=1,trans=1)[0]
self.V = (self.likelihood.precision/self.scale_factor)*self.likelihood.Y
self.psi1V = np.dot(self.psi1, self.V)
#back substutue C into psi1V #back substutue C into psi1V
tmp,info1 = linalg.lapack.flapack.dtrtrs(self.Lm,np.asfortranarray(self.psi1V),lower=1,trans=0) tmp,info1 = linalg.lapack.flapack.dtrtrs(self.Lm,np.asfortranarray(self.psi1V),lower=1,trans=0)
self._P = tdot(tmp)
tmp,info2 = linalg.lapack.flapack.dpotrs(self.LB,tmp,lower=1) 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,info3 = linalg.lapack.flapack.dtrtrs(self.Lm,tmp,lower=1,trans=1)
#self.Cpsi1V = np.dot(self.C,self.psi1V) #self.Cpsi1V = np.dot(self.C,self.psi1V)
self.Cpsi1VVpsi1 = np.dot(self.Cpsi1V,self.psi1V.T) self.Cpsi1VVpsi1 = np.dot(self.Cpsi1V,self.psi1V.T) #TODO: this dot can be eliminated
self.E = tdot(self.Cpsi1V/sf) self.E = tdot(self.Cpsi1V/sf)
@ -130,24 +132,22 @@ class sparse_GP(GP):
self.dL_dpsi2 = None self.dL_dpsi2 = None
else: else:
#self.dL_dpsi2 = 0.5 * self.likelihood.precision * self.D * self.Kmmi # dB
#self.dL_dpsi2 += - 0.5 * self.likelihood.precision/sf2 * self.D * self.C # dC
#self.dL_dpsi2 += - 0.5 * self.likelihood.precision * self.E # dD
self.dL_dpsi2 = 0.5*self.likelihood.precision*(self.D*(self.Kmmi - self.C/sf2) -self.E) self.dL_dpsi2 = 0.5*self.likelihood.precision*(self.D*(self.Kmmi - self.C/sf2) -self.E)
if self.has_uncertain_inputs: if self.has_uncertain_inputs:
#repeat for each of the N psi_2 matrices #repeat for each of the N psi_2 matrices
self.dL_dpsi2 = np.repeat(self.dL_dpsi2[None,:,:],self.N,axis=0) self.dL_dpsi2 = np.repeat(self.dL_dpsi2[None,:,:],self.N,axis=0)
else: else:
#subsume back into psi1 (==Kmn)
self.dL_dpsi1 += 2.*np.dot(self.dL_dpsi2,self.psi1) self.dL_dpsi1 += 2.*np.dot(self.dL_dpsi2,self.psi1)
self.dL_dpsi2 = None self.dL_dpsi2 = None
# Compute dL_dKmm # Compute dL_dKmm
#self.dL_dKmm_old = -0.5 * self.D * mdot(self.Lmi.T, self.A, self.Lmi)*sf2 # dB #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 += -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 #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] 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] #dA 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 = 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 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) self.dL_dKmm += 0.5*(self.D*self.C/sf2 + self.E) +tmp # d(C+D)
@ -196,7 +196,6 @@ class sparse_GP(GP):
# self.scale_factor = max(1,np.sqrt(self.psi2_beta_scaled.sum(0).mean())) # self.scale_factor = max(1,np.sqrt(self.psi2_beta_scaled.sum(0).mean()))
# else: # else:
# self.scale_factor = np.sqrt(self.psi2.sum(0).mean()*self.likelihood.precision) # self.scale_factor = np.sqrt(self.psi2.sum(0).mean()*self.likelihood.precision)
#self.scale_factor = 1.
self._computations() self._computations()
def _get_params(self): def _get_params(self):