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changes to the uncollapsed GP

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This commit is contained in:
James Hensman 2013-02-19 17:36:51 +00:00
parent 70e2076cd4
commit 735a340315
1 changed files with 21 additions and 21 deletions
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42
GPy/models/uncollapsed_sparse_GP.py
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@ -27,10 +27,10 @@ class uncollapsed_sparse_GP(sparse_GP):
""" """
def __init__(self, X, likelihood, kernel, Z, q_u=None, **kwargs): def __init__(self, X, likelihood, kernel, Z, q_u=None, **kwargs):
self.D = Y.shape[1] self.M = Z.shape[0]
self.M = kwargs['Z'].shape[0]
if q_u is None: if q_u is None:
q_u = np.hstack((np.random.randn(self.M*self.D),-0.5*np.eye(self.M).flatten())) q_u = np.hstack((np.random.randn(self.M*likelihood.D),-0.5*np.eye(self.M).flatten()))
self.likelihood = likelihood
self.set_vb_param(q_u) self.set_vb_param(q_u)
sparse_GP.__init__(self, X, likelihood, kernel, Z, **kwargs) sparse_GP.__init__(self, X, likelihood, kernel, Z, **kwargs)
@ -62,21 +62,21 @@ class uncollapsed_sparse_GP(sparse_GP):
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])
# Compute dL_dpsi # Compute dL_dpsi
self.dL_dpsi0 = - 0.5 * self.D * self.beta * np.ones(self.N) self.dL_dpsi0 = - 0.5 * self.likelihood.D * self.beta * np.ones(self.N)
self.dL_dpsi1 = np.dot(self.VmT,self.Kmmi).T # This is the correct term for E I think... self.dL_dpsi1 = np.dot(self.VmT,self.Kmmi).T # This is the correct term for E I think...
self.dL_dpsi2 = 0.5 * self.beta * self.D * (self.Kmmi - mdot(self.Kmmi,self.q_u_expectation[1],self.Kmmi)) self.dL_dpsi2 = 0.5 * self.beta * self.likelihood.D * (self.Kmmi - mdot(self.Kmmi,self.q_u_expectation[1],self.Kmmi))
# Compute dL_dKmm # Compute dL_dKmm
tmp = self.beta*mdot(self.psi2,self.Kmmi,self.q_u_expectation[1]) -np.dot(self.q_u_expectation[0],self.psi1V.T) tmp = self.beta*mdot(self.psi2,self.Kmmi,self.q_u_expectation[1]) -np.dot(self.q_u_expectation[0],self.psi1V.T)
tmp += tmp.T tmp += tmp.T
tmp += self.D*(-self.beta*self.psi2 - self.Kmm + self.q_u_expectation[1]) tmp += self.likelihood.D*(-self.beta*self.psi2 - self.Kmm + self.q_u_expectation[1])
self.dL_dKmm = 0.5*mdot(self.Kmmi,tmp,self.Kmmi) self.dL_dKmm = 0.5*mdot(self.Kmmi,tmp,self.Kmmi)
#Compute the gradient of the log likelihood wrt noise variance #Compute the gradient of the log likelihood wrt noise variance
#TODO: suport heteroscedatic noise #TODO: suport heteroscedatic noise
dbeta = 0.5 * self.N*self.D/self.beta dbeta = 0.5 * self.N*self.likelihood.D/self.beta
dbeta += - 0.5 * self.D * self.trace_K dbeta += - 0.5 * self.likelihood.D * self.trace_K
dbeta += - 0.5 * self.D * np.sum(self.q_u_expectation[1]*mdot(self.Kmmi,self.psi2,self.Kmmi)) dbeta += - 0.5 * self.likelihood.D * np.sum(self.q_u_expectation[1]*mdot(self.Kmmi,self.psi2,self.Kmmi))
dbeta += - 0.5 * self.trYYT dbeta += - 0.5 * self.trYYT
dbeta += np.sum(np.dot(self.Y.T,self.projected_mean)) dbeta += np.sum(np.dot(self.Y.T,self.projected_mean))
self.partial_for_likelihood = -dbeta*self.likelihood.precision**2 self.partial_for_likelihood = -dbeta*self.likelihood.precision**2
@ -85,9 +85,9 @@ class uncollapsed_sparse_GP(sparse_GP):
""" """
Compute the (lower bound on the) log marginal likelihood Compute the (lower bound on the) log marginal likelihood
""" """
A = -0.5*self.N*self.D*(np.log(2.*np.pi) - np.log(self.beta)) A = -0.5*self.N*self.likelihood.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.likelihood.D*self.trace_K
C = -0.5*self.D *(self.Kmm_logdet-self.q_u_logdet + np.sum(self.Lambda * self.q_u_expectation[1]) - self.M) C = -0.5*self.likelihood.D *(self.Kmm_logdet-self.q_u_logdet + np.sum(self.Lambda * self.q_u_expectation[1]) - self.M)
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
@ -100,21 +100,21 @@ class uncollapsed_sparse_GP(sparse_GP):
tmp = self.Kmmi- mdot(self.Kmmi,self.q_u_cov,self.Kmmi) tmp = self.Kmmi- mdot(self.Kmmi,self.q_u_cov,self.Kmmi)
if full_cov: if full_cov:
Kxx = self.kern.K(Xnew) Kxx = self.kern.K(Xnew)
var = Kxx - mdot(Kx,tmp,Kx.T) + np.eye(Xnew.shape[0])/self.beta var = Kxx - mdot(Kx,tmp,Kx.T)
else: else:
Kxx = self.kern.Kdiag(Xnew) Kxx = self.kern.Kdiag(Xnew)
var = Kxx - np.sum(Kx*np.dot(Kx,tmp),1) + 1./self.beta var = (Kxx - np.sum(Kx*np.dot(Kx,tmp),1))[:,None]
return mu,var return mu,var
def set_vb_param(self,vb_param): def set_vb_param(self,vb_param):
"""set the distribution q(u) from the canonical parameters""" """set the distribution q(u) from the canonical parameters"""
self.q_u_prec = -2.*vb_param[self.M*self.D:].reshape(self.M,self.M) self.q_u_prec = -2.*vb_param[-self.M**2:].reshape(self.M, self.M)
self.q_u_cov, q_u_Li, q_u_L, tmp = pdinv(self.q_u_prec) self.q_u_cov, q_u_Li, q_u_L, tmp = pdinv(self.q_u_prec)
self.q_u_logdet = -tmp self.q_u_logdet = -tmp
self.q_u_mean = np.dot(self.q_u_cov,vb_param[:self.M*self.D].reshape(self.M,self.D)) self.q_u_mean = np.dot(self.q_u_cov,vb_param[:self.M*self.likelihood.D].reshape(self.M,self.likelihood.D))
self.q_u_expectation = (self.q_u_mean, np.dot(self.q_u_mean,self.q_u_mean.T)+self.q_u_cov) self.q_u_expectation = (self.q_u_mean, np.dot(self.q_u_mean,self.q_u_mean.T)+self.q_u_cov*self.likelihood.D)
self.q_u_canonical = (np.dot(self.q_u_prec, self.q_u_mean),-0.5*self.q_u_prec) self.q_u_canonical = (np.dot(self.q_u_prec, self.q_u_mean),-0.5*self.q_u_prec)
#TODO: computations now? #TODO: computations now?
@ -133,8 +133,8 @@ class uncollapsed_sparse_GP(sparse_GP):
Note that the natural gradient in either is given by the gradient in the other (See Hensman et al 2012 Fast Variational inference in the conjugate exponential Family) Note that the natural gradient in either is given by the gradient in the other (See Hensman et al 2012 Fast Variational inference in the conjugate exponential Family)
""" """
dL_dmmT_S = -0.5*self.Lambda-self.q_u_canonical[1] dL_dmmT_S = -0.5*self.Lambda-self.q_u_canonical[1]
#dL_dm = np.dot(self.Kmmi,self.psi1V) - np.dot(self.Lambda,self.q_u_mean) dL_dm = np.dot(self.Kmmi,self.psi1V) - np.dot(self.Lambda,self.q_u_mean)
dL_dm = np.dot(self.Kmmi,self.psi1V) - self.q_u_canonical[0] #dL_dm = np.dot(self.Kmmi,self.psi1V) - self.q_u_canonical[0]
#dL_dSim = #dL_dSim =
#dL_dmhSi = #dL_dmhSi =
@ -144,9 +144,9 @@ class uncollapsed_sparse_GP(sparse_GP):
def plot(self, *args, **kwargs): def plot(self, *args, **kwargs):
""" """
add the distribution q(u) to the plot from sparse_GP_regression add the distribution q(u) to the plot from sparse_GP
""" """
sparse_GP_regression.plot(self,*args,**kwargs) sparse_GP.plot(self,*args,**kwargs)
if self.Q==1: if self.Q==1:
pb.errorbar(self.Z[:,0],self.q_u_expectation[0][:,0],yerr=2.*np.sqrt(np.diag(self.q_u_cov)),fmt=None,ecolor='b') pb.errorbar(self.Z[:,0],self.q_u_expectation[0][:,0],yerr=2.*np.sqrt(np.diag(self.q_u_cov)),fmt=None,ecolor='b')