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Assorted work on combining the EP and sparse methods
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James Hensman
parent
64280d7eb6
commit
5447d6fbfc
7 changed files with 95 additions and 44 deletions
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@ -6,7 +6,6 @@ import pylab as pb
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from ..util.linalg import mdot, jitchol, chol_inv, pdinv
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from ..util.plot import gpplot
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from .. import kern
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from ..inference.likelihoods import likelihood
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from GP import GP
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#Still TODO:
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@ -34,16 +33,15 @@ class sparse_GP(GP):
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:type normalize_(X|Y): bool
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"""
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def __init__(self,X,likelihood,kernel, X_uncertainty=None, Z=None,Zslices=None,M=10,normalize_X=False):
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self.scale_factor = 1000.0# a scaling factor to help keep the algorithm stable
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def __init__(self, X, likelihood, kernel, Z, X_uncertainty=None, Xslices=None,Zslices=None, normalize_X=False):
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self.scale_factor = 1.0# a scaling factor to help keep the algorithm stable
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self.Z = Z
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self.Zslices = Zslices
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self.Xslices = Xslices
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self.M = Z.shape[0]
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self.likelihood = likelihood
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if Z is None:
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self.Z = np.random.permutation(X.copy())[:M]
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self.M = M
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else:
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assert Z.shape[1]==X.shape[1]
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self.Z = Z
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self.M = Z.shape[0]
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if X_uncertainty is None:
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self.has_uncertain_inputs=False
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else:
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@ -51,7 +49,7 @@ class sparse_GP(GP):
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self.has_uncertain_inputs=True
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self.X_uncertainty = X_uncertainty
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GP.__init__(self, X, Y, kernel=kernel, normalize_X=normalize_X, Xslices=Xslices)
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GP.__init__(self, X, likelihood, kernel=kernel, normalize_X=normalize_X, Xslices=Xslices)
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#normalise X uncertainty also
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if self.has_uncertain_inputs:
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@ -67,7 +65,7 @@ class sparse_GP(GP):
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# kernel computations, using BGPLVM notation
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self.Kmm = self.kern.K(self.Z)
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if self.has_uncertain_inputs:
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self.psi0 = self.kern.psi0(self.Z,self.X, self.X_uncertainty).sum()
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self.psi0 = self.kern.psi0(self.Z,self.X, self.X_uncerTainty)
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self.psi1 = self.kern.psi1(self.Z,self.X, self.X_uncertainty).T
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self.psi2 = self.kern.psi2(self.Z,self.X, self.X_uncertainty)
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if self.likelihood.is_heteroscedastic:
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@ -76,17 +74,18 @@ class sparse_GP(GP):
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else:
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self.psi2_beta_scaled = (self.psi2*(self.likelihood.precision/sf2)).sum(0)
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else:
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self.psi0 = self.kern.Kdiag(self.X,slices=self.Xslices).sum()
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self.psi0 = self.kern.Kdiag(self.X,slices=self.Xslices)
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self.psi1 = self.kern.K(self.Z,self.X)
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if self.likelihood.is_heteroscedastic:
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tmp = self.psi1*(np.sqrt(self.likelihood.precision.reshape(self.N,1))/sf)
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else:
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tmp = self.psi1*(np.sqrt(self.likelihood.precision)/sf)
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self.psi2_beta_scaled = np.dot(tmp,tmp.T)
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self.psi2 = self.psi1.T[:,:,None]*self.psi1.T[:,None,:] # TODO: remove me for efficiency and stability
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self.Kmmi, self.Lm, self.Lmi, self.Kmm_logdet = pdinv(self.Kmm)
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self.V = (self.likelihood.precision/self.scale_factor)*self.Y
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self.V = (self.likelihood.precision/self.scale_factor)*self.likelihood.Y
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self.A = mdot(self.Lmi, self.psi2_beta_scaled, self.Lmi.T)
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self.B = np.eye(self.M)/sf2 + self.A
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@ -97,27 +96,38 @@ class sparse_GP(GP):
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self.C = mdot(self.Lmi.T, self.Bi, self.Lmi)
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self.E = mdot(self.C, self.psi1VVpsi1/sf2, self.C.T)
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# Compute dL_dpsi # FIXME
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self.dL_dpsi0 = - 0.5 * self.D * self.beta * np.ones(self.N)
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# Compute dL_dpsi # FIXME: this is untested for the het. case
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self.dL_dpsi0 = - 0.5 * self.D * self.likelihood.precision * np.ones(self.N)
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self.dL_dpsi1 = mdot(self.V, self.psi1V.T,self.C).T
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self.dL_dpsi2 = 0.5 * self.beta * self.D * self.Kmmi[None,:,:] # dB
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self.dL_dpsi2 += - 0.5 * self.beta/sf2 * self.D * self.C[None,:,:] # dC
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self.dL_dpsi2 += - 0.5 * self.beta * self.E[None,:,:] # dD
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if self.likelihood.is_heteroscedastic:
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self.dL_dpsi2 = 0.5 * self.likelihood.precision[:,None,None] * self.D * self.Kmmi[None,:,:] # dB
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self.dL_dpsi2 += - 0.5 * self.likelihood.precision[:,None,None]/sf2 * self.D * self.C[None,:,:] # dC
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self.dL_dpsi2 += - 0.5 * self.likelihood.precision[:,None,None]* self.E[None,:,:] # dD
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else:
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self.dL_dpsi2 = 0.5 * self.likelihood.precision * self.D * self.Kmmi[None,:,:] # dB
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self.dL_dpsi2 += - 0.5 * self.likelihood.precision/sf2 * self.D * self.C[None,:,:] # dC
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self.dL_dpsi2 += - 0.5 * self.likelihood.precision * self.E[None,:,:] # dD
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# Compute dL_dKmm
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self.dL_dKmm = -0.5 * self.D * mdot(self.Lmi.T, self.A, self.Lmi)*sf2 # dB
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self.dL_dKmm += -0.5 * self.D * (- self.C/sf2 - 2.*mdot(self.C, self.psi2_beta_scaled, self.Kmmi) + self.Kmmi) # dC
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self.dL_dKmm += np.dot(np.dot(self.E*sf2, self.psi2_beta_scaled) - np.dot(self.C, self.psi1VVpsi1), self.Kmmi) + 0.5*self.E # dD
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#the partial derivative vector for the likelihood
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self.partial_for_likelihood = - 0.5 * self.D*self.likelihood.precision + 0.5 * (self.likelihood.Y**2).sum(1)*self.likelihood.precision**2 #dA
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self.partial_for_likelihood += 0.5 * self.D * (self.psi0*self.likelihood.precision**2 - (self.psi2*self.Kmmi[None,:,:]*self.likelihood.precision[:,None,None]**2).sum(1).sum(1)/sf2) #dB
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#self.partial_for_likelihood += 0.5 * self.D * np.sum(self.Bi*self.A)*self.likelihood.precision #dC
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#self.partial_for_likelihood += -np.diag(np.dot((self.C - 0.5 * mdot(self.C,self.psi2_beta_scaled,self.C) ) , self.psi1VVpsi1 ))*self.likelihood.precision #dD
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def _set_params(self, p):
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self.Z = p[:self.M*self.Q].reshape(self.M, self.Q)
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self.beta = p[self.M*self.Q] # FIXME
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self.kern._set_params(p[self.Z.size + 1:])
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self.kern._set_params(p[self.Z.size:self.Z.size+self.kern.Nparam])
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self.likelihood._set_params(p[self.Z.size+self.kern.Nparam:])
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self._computations()
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def _get_params(self):
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return np.hstack([self.Z.flatten(),GP._get_params(self))
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return np.hstack([self.Z.flatten(),GP._get_params(self)])
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def _get_param_names(self):
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return sum([['iip_%i_%i'%(i,j) for i in range(self.Z.shape[0])] for j in range(self.Z.shape[1])],[]) + GP._get_param_names(self)
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@ -125,24 +135,17 @@ class sparse_GP(GP):
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def log_likelihood(self):
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""" Compute the (lower bound on the) log marginal likelihood """
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sf2 = self.scale_factor**2
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A = -0.5*self.N*self.D*(np.log(2.*np.pi) - np.log(self.beta)) -0.5*self.beta*self.trYYT # FIXME
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B = -0.5*self.D*(self.beta*self.psi0-np.trace(self.A)*sf2)# FIXME
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if self.likelihood.is_heteroscedastic:
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A = -0.5*self.N*self.D*np.log(2.*np.pi) +0.5*np.sum(np.log(self.likelihood.precision)) -0.5*np.sum(self.V*self.likelihood.Y)
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else:
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A = -0.5*self.N*self.D*(np.log(2.*np.pi) - np.log(self.likelihood.precision)) -0.5*self.likelihood.precision*self.likelihood.trYYT
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B = -0.5*self.D*(np.sum(self.likelihood.precision*self.psi0) - np.trace(self.A)*sf2)
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C = -0.5*self.D * (self.B_logdet + self.M*np.log(sf2))
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D = +0.5*np.sum(self.psi1VVpsi1 * self.C)
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return A+B+C+D
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def _log_likelihood_gradients(self):
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return np.hstack([self.dL_dZ().flatten(), GP._log_likelihood_gradients(self)])
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# FIXME: move this into the lieklihood class
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def dL_dbeta(self):
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sf2 = self.scale_factor**2
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dA_dbeta = 0.5 * self.N*self.D/self.beta - 0.5 * self.trYYT
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dB_dbeta = - 0.5 * self.D * (self.psi0 - np.trace(self.A)/self.beta*sf2)
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dC_dbeta = - 0.5 * self.D * np.sum(self.Bi*self.A)/self.beta
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dD_dbeta = np.sum((self.C - 0.5 * mdot(self.C,self.psi2_beta_scaled,self.C) ) * self.psi1VVpsi1 )/self.beta
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return np.squeeze(dA_dbeta + dB_dbeta + dC_dbeta + dD_dbeta)
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return np.hstack((self.dL_dZ().flatten(), self.dL_dtheta(), self.likelihood._gradients(partial=self.partial_for_likelihood)))
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def dL_dtheta(self):
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"""
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