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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):
self.D = Y.shape[1]
self.M = kwargs['Z'].shape[0]
self.M = Z.shape[0]
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)
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])
# 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_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
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 += 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)
#Compute the gradient of the log likelihood wrt noise variance
#TODO: suport heteroscedatic noise
dbeta = 0.5 * self.N*self.D/self.beta
dbeta += - 0.5 * self.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.N*self.likelihood.D/self.beta
dbeta += - 0.5 * self.likelihood.D * self.trace_K
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 += np.sum(np.dot(self.Y.T,self.projected_mean))
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
"""
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
C = -0.5*self.D *(self.Kmm_logdet-self.q_u_logdet + np.sum(self.Lambda * self.q_u_expectation[1]) - self.M)
A = -0.5*self.N*self.likelihood.D*(np.log(2.*np.pi) - np.log(self.beta))
B = -0.5*self.beta*self.likelihood.D*self.trace_K
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
E = np.sum(np.dot(self.V.T,self.projected_mean))
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)
if full_cov:
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:
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
def set_vb_param(self,vb_param):
"""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_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)
#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)
"""
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) - self.q_u_canonical[0]
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_dSim =
#dL_dmhSi =
@ -144,9 +144,9 @@ class uncollapsed_sparse_GP(sparse_GP):
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:
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')