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chenged a little of the notation in the sparse GP

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This should allow easier implementation of het. noise
This commit is contained in:
James Hensman 2012-12-08 15:15:31 -08:00
parent ab56f3f9b7
commit 5f2c2a04f8
2 changed files with 12 additions and 13 deletions
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15
GPy/models/sparse_GP_regression.py
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@ -87,11 +87,11 @@ class sparse_GP_regression(GP_regression):
self.psi1V = np.dot(self.psi1, self.V) self.psi1V = np.dot(self.psi1, self.V)
self.psi1VVpsi1 = np.dot(self.psi1V, self.psi1V.T) self.psi1VVpsi1 = np.dot(self.psi1V, self.psi1V.T)
self.Kmmi, self.Lm, self.Lmi, self.Kmm_logdet = pdinv(self.Kmm) self.Kmmi, self.Lm, self.Lmi, self.Kmm_logdet = pdinv(self.Kmm)
self.A = mdot(self.Lmi, self.psi2, self.Lmi.T) self.A = mdot(self.Lmi, self.beta*self.psi2, self.Lmi.T)
self.B = np.eye(self.M) + self.beta * self.A self.B = np.eye(self.M) + 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.LLambdai = np.dot(self.LBi, self.Lmi) self.LLambdai = np.dot(self.LBi, self.Lmi)
self.trace_K = self.psi0 - np.trace(self.A) self.trace_K = self.psi0 - np.trace(self.A)/self.beta
self.LBL_inv = mdot(self.Lmi.T, self.Bi, self.Lmi) self.LBL_inv = mdot(self.Lmi.T, self.Bi, self.Lmi)
self.C = mdot(self.LLambdai, self.psi1V) self.C = mdot(self.LLambdai, self.psi1V)
self.G = mdot(self.LBL_inv, self.psi1VVpsi1, self.LBL_inv.T) self.G = mdot(self.LBL_inv, self.psi1VVpsi1, self.LBL_inv.T)
@ -102,7 +102,7 @@ class sparse_GP_regression(GP_regression):
self.dL_dpsi2 = - 0.5 * self.beta * (self.D*(self.LBL_inv - self.Kmmi) + self.G) self.dL_dpsi2 = - 0.5 * self.beta * (self.D*(self.LBL_inv - self.Kmmi) + self.G)
# Compute dL_dKmm # Compute dL_dKmm
self.dL_dKmm = -0.5 * self.beta * self.D * mdot(self.Lmi.T, self.A, self.Lmi) # dB self.dL_dKmm = -0.5 * self.D * mdot(self.Lmi.T, self.A, self.Lmi) # dB
self.dL_dKmm += -0.5 * self.D * (- self.LBL_inv - 2.*self.beta*mdot(self.LBL_inv, self.psi2, self.Kmmi) + self.Kmmi) # dC self.dL_dKmm += -0.5 * self.D * (- self.LBL_inv - 2.*self.beta*mdot(self.LBL_inv, self.psi2, self.Kmmi) + self.Kmmi) # dC
self.dL_dKmm += np.dot(np.dot(self.G,self.beta*self.psi2) - np.dot(self.LBL_inv, self.psi1VVpsi1), self.Kmmi) + 0.5*self.G # dE self.dL_dKmm += np.dot(np.dot(self.G,self.beta*self.psi2) - np.dot(self.LBL_inv, self.psi1VVpsi1), self.Kmmi) + 0.5*self.G # dE
@ -126,15 +126,14 @@ class sparse_GP_regression(GP_regression):
def dL_dbeta(self): def dL_dbeta(self):
""" """
Compute the gradient of the log likelihood wrt beta. Compute the gradient of the log likelihood wrt beta.
TODO: suport heteroscedatic noise
""" """
#TODO: suport heteroscedatic noise
dA_dbeta = 0.5 * self.N*self.D/self.beta dA_dbeta = 0.5 * self.N*self.D/self.beta
dB_dbeta = - 0.5 * self.D * self.trace_K dB_dbeta = - 0.5 * self.D * self.trace_K
dC_dbeta = - 0.5 * self.D * np.sum(self.Bi*self.A) dC_dbeta = - 0.5 * self.D * np.sum(self.Bi*self.A)/self.beta
dD_dbeta = - 0.5 * self.trYYT dD_dbeta = - 0.5 * self.trYYT
tmp = mdot(self.LBi.T, self.LLambdai, self.psi1V) tmp = mdot(self.LBi.T, self.LLambdai, self.psi1V)
dE_dbeta = np.sum(np.square(self.C))/self.beta - 0.5 * np.sum(self.A * np.dot(tmp, tmp.T)) dE_dbeta = (np.sum(np.square(self.C)) - 0.5 * np.sum(self.A * np.dot(tmp, tmp.T)))/self.beta
return np.squeeze(dA_dbeta + dB_dbeta + dC_dbeta + dD_dbeta + dE_dbeta) return np.squeeze(dA_dbeta + dB_dbeta + dC_dbeta + dD_dbeta + dE_dbeta)

10
GPy/models/uncollapsed_sparse_GP.py
View file

@ -39,7 +39,7 @@ class uncollapsed_sparse_GP(sparse_GP_regression):
self.M = Z.shape[0] self.M = Z.shape[0]
else: else:
self.M = M self.M = M
q_u = np.hstack((np.ones(self.M*self.D),-0.5*np.eye(self.M).flatten())) q_u = np.hstack((np.zeros(self.M*self.D),-0.5*np.eye(self.M).flatten()))
self.set_vb_param(q_u) self.set_vb_param(q_u)
sparse_GP_regression.__init__(self, X, Y, M=M,*args, **kwargs) sparse_GP_regression.__init__(self, X, Y, M=M,*args, **kwargs)
@ -49,8 +49,8 @@ class uncollapsed_sparse_GP(sparse_GP_regression):
self.psi1V = np.dot(self.psi1, self.V) self.psi1V = np.dot(self.psi1, self.V)
self.psi1VVpsi1 = np.dot(self.psi1V, self.psi1V.T) self.psi1VVpsi1 = np.dot(self.psi1V, self.psi1V.T)
self.Kmmi, self.Lm, self.Lmi, self.Kmm_logdet = pdinv(self.Kmm) self.Kmmi, self.Lm, self.Lmi, self.Kmm_logdet = pdinv(self.Kmm)
self.A = self.beta * mdot(self.Lmi, self.psi2, self.Lmi.T) self.A = mdot(self.Lmi, self.beta*self.psi2, self.Lmi.T)
self.B = np.eye(self.M) * self.A self.B = np.eye(self.M) + self.A
self.Lambda = mdot(self.Lmi.T,self.B,self.Lmi) self.Lambda = mdot(self.Lmi.T,self.B,self.Lmi)
self.trace_K = self.psi0 - np.trace(self.A)/self.beta self.trace_K = self.psi0 - np.trace(self.A)/self.beta
self.projected_mean = mdot(self.psi1.T,self.Kmmi,self.q_u_expectation[0]) self.projected_mean = mdot(self.psi1.T,self.Kmmi,self.q_u_expectation[0])
@ -70,10 +70,10 @@ class uncollapsed_sparse_GP(sparse_GP_regression):
""" """
A = -0.5*self.N*self.D*(np.log(2.*np.pi) - np.log(self.beta)) A = -0.5*self.N*self.D*(np.log(2.*np.pi) - np.log(self.beta))
B = -0.5*self.beta*self.D*self.trace_K B = -0.5*self.beta*self.D*self.trace_K
C = -0.5*self.D *(self.Kmm_logdet + np.sum(self.Lambda * self.q_u_expectation[1]) + self.M/2.) C = -0.5*self.D *(self.Kmm_logdet + np.sum(self.Lambda * self.q_u_expectation[1]) - self.M*self.D)
D = -0.5*self.beta*self.trYYT D = -0.5*self.beta*self.trYYT
E = np.sum(np.dot(self.V.T,self.projected_mean)) E = np.sum(np.dot(self.V.T,self.projected_mean))
return A+B+C+D+E return A+B#+C+D+E
def dL_dbeta(self): def dL_dbeta(self):
""" """