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Working for regression, still some bugs for EP.

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Ricardo Andrade 2013-01-30 16:00:03 +00:00
parent 29eb61d65e
commit d8eb155622
2 changed files with 50 additions and 36 deletions
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55
GPy/models/sparse_GP.py
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@ -10,6 +10,7 @@ from GP import GP
from ..inference.EP import Full,DTC,FITC
from ..inference.likelihoods import likelihood,probit,poisson,gaussian
#Still TODO:
# make use of slices properly (kernel can now do this)
# enable heteroscedatic noise (kernel will need to compute psi2 as a (NxMxM) array)
@ -35,12 +36,6 @@ class sparse_GP(GP):
:type beta: float
:param normalize_(X|Y) : whether to normalize the data before computing (predictions will be in original scales)
:type normalize_(X|Y): bool
:parm likelihood: a GPy likelihood, defaults to gaussian
:param method_ep: sparse approximation used by Expectation Propagation algorithm, defaults to DTC
:type M: string (Full|DTC|FITC)
:param epsilon_ep: convergence criterion for the Expectation Propagation algorithm, defaults to 0.1
:param powerep: power-EP parameters [$\eta$,$\delta$], defaults to [1.,1.]
:type powerep: list
"""
def __init__(self,X,Y=None,kernel=None,X_uncertainty=None,beta=100.,Z=None,Zslices=None,M=10,normalize_X=False,normalize_Y=False,likelihood=None,method_ep='DTC',epsilon_ep=1e-3,power_ep=[1.,1.]):
@ -70,20 +65,21 @@ class sparse_GP(GP):
else:
self.method_ep = method_ep
#normalise X uncertainty also
if self.has_uncertain_inputs:
self.X_uncertainty /= np.square(self._Xstd)
def _set_params(self, p):
self.Z = p[:self.M*self.Q].reshape(self.M, self.Q)
if not self.EP:
self.beta = p[self.M*self.Q]
#self.beta = np.repeat(p[self.M*self.Q],self.N)[:,None]
self.kern._set_params(p[self.Z.size + 1:])
self.beta2 = self.beta**2
else:
self.kern._set_params(p[self.Z.size:])
if self.Y is None:
self.Y = np.ones([self.N,1])
self._compute_kernel_matrices()
self._computations() #NOTE At this point computations of dL are not needed
self._computations()
def _get_params(self):
if not self.EP:
@ -97,19 +93,22 @@ class sparse_GP(GP):
else:
return sum([['iip_%i_%i'%(i,j) for i in range(self.Z.shape[0])] for j in range(self.Z.shape[1])],[]) + self.kern._get_param_names_transformed()
def _compute_kernel_matrices(self):
# kernel computations, using BGPLVM notation
#TODO: slices for psi statistics (easy enough)
self.Kmm = self.kern.K(self.Z)
if self.has_uncertain_inputs:
if not self.EP:
self.psi0 = self.kern.psi0(self.Z,self.X, self.X_uncertainty)#.sum()
self.psi0 = self.kern.psi0(self.Z,self.X, self.X_uncertainty)#.sum() NOTE psi0 is now a vector
self.psi1 = self.kern.psi1(self.Z,self.X, self.X_uncertainty).T
self.psi2 = self.kern.psi2(self.Z,self.X, self.X_uncertainty)#FIXME add beta vector
self.psi2 = self.kern.psi2(self.Z,self.X, self.X_uncertainty)
#self.psi2_beta_scaled = ?
else:
raise NotImplementedError, "uncertain_inputs not yet supported for EP"
else:
self.psi0 = self.kern.Kdiag(self.X,slices=self.Xslices)#.sum() FIXME
self.psi0 = self.kern.Kdiag(self.X,slices=self.Xslices)#.sum()
self.psi1 = self.kern.K(self.Z,self.X)
self.psi2 = np.dot(self.psi1,self.psi1.T)
self.psi2_beta_scaled = np.dot(self.psi1,self.beta*self.psi1.T)
@ -124,22 +123,29 @@ class sparse_GP(GP):
self.B = np.eye(self.M) + self.A
self.Bi, self.LB, self.LBi, self.B_logdet = pdinv(self.B)
self.LLambdai = np.dot(self.LBi, self.Lmi)
self.trace_K = self.psi0.sum() - np.trace(self.A)
self.LBL_inv = mdot(self.Lmi.T, self.Bi, self.Lmi)
self.C = mdot(self.LLambdai, self.psi1V)
self.G = mdot(self.LBL_inv, self.psi1VVpsi1, self.LBL_inv.T)
self.trace_K_beta_scaled = (self.psi0*self.beta).sum() - np.trace(self.A)
if not self.EP:
self.trace_K = self.psi0.sum() - np.trace(self.A)/self.beta
# Compute dL_dpsi
self.dL_dpsi0 = - 0.5 * self.D * self.beta.flatten() * np.ones(self.N)
self.dL_dpsi1 = mdot(self.LLambdai.T,self.C,self.V.T)
#self.dL_dpsi2 = - 0.5 * self.beta * (self.D*(self.LBL_inv - self.Kmmi) + self.G)
self.dL_dpsi2 = - 0.5 * (self.D*(self.LBL_inv - self.Kmmi) + self.G)
if not self.EP:
self.dL_dpsi0 = - 0.5 * self.D * self.beta * np.ones(self.N)
if self.has_uncertain_inputs:
self.dL_dpsi2 = - 0.5 * self.beta * (self.D*(self.LBL_inv - self.Kmmi) + self.G)
else:
self.dL_dpsi2_ = - 0.5 * (self.D*(self.LBL_inv - self.Kmmi) + self.G)
else:
self.dL_dpsi0 = - 0.5 * self.D * self.beta.flatten()
if not self.has_uncertain_inputs:
self.dL_dpsi2_ = - 0.5 * (self.D*(self.LBL_inv - self.Kmmi) + self.G)
# Compute dL_dKmm
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.*mdot(self.LBL_inv, self.psi2_beta_scaled, 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.psi2_beta_scaled) - np.dot(self.LBL_inv, self.psi1VVpsi1), self.Kmmi) + 0.5*self.G # dE
def approximate_likelihood(self):
@ -164,7 +170,7 @@ class sparse_GP(GP):
else:
A = -0.5*self.D*(self.N*np.log(2.*np.pi) - np.sum(np.log(self.beta)))
D = -0.5*self.trbetaYYT
B = -0.5*self.D*self.trace_K
B = -0.5*self.D*self.trace_K_beta_scaled
C = -0.5*self.D * self.B_logdet
E = +0.5*np.sum(self.psi1VVpsi1 * self.LBL_inv)
return A+B+C+D+E
@ -194,7 +200,7 @@ class sparse_GP(GP):
dL_dtheta += self.kern.dpsi2_dtheta(self.dL_dpsi2,self.Z,self.X, self.X_uncertainty) # for multiple_beta, dL_dpsi2 will be a different shape
else:
#re-cast computations in psi2 back to psi1:
dL_dpsi1 = self.dL_dpsi1 + 2.*np.dot(self.dL_dpsi2,self.psi1)
dL_dpsi1 = self.dL_dpsi1 + 2.*np.dot(self.dL_dpsi2_,self.beta.T*self.psi1) #dL_dpsi1 = self.dL_dpsi1 + 2.*np.dot(self.dL_dpsi2,self.psi1)
dL_dtheta += self.kern.dK_dtheta(dL_dpsi1,self.Z,self.X)
dL_dtheta += self.kern.dKdiag_dtheta(self.dL_dpsi0, self.X)
@ -210,7 +216,7 @@ class sparse_GP(GP):
dL_dZ += self.kern.dpsi2_dZ(self.dL_dpsi2,self.Z,self.X, self.X_uncertainty)
else:
#re-cast computations in psi2 back to psi1:
dL_dpsi1 = self.dL_dpsi1 + 2.*np.dot(self.dL_dpsi2,self.psi1)
dL_dpsi1 = self.dL_dpsi1 + 2.*np.dot(self.dL_dpsi2_,self.beta.T*self.psi1)#dL_dpsi1 = self.dL_dpsi1 + 2.*np.dot(self.dL_dpsi2,self.psi1)
dL_dZ += self.kern.dK_dX(dL_dpsi1,self.Z,self.X)
return dL_dZ
@ -229,16 +235,14 @@ class sparse_GP(GP):
Kxx = self.kern.K(Xnew)
var = Kxx - mdot(Kx.T, (self.Kmmi - self.LBL_inv), Kx)
if not self.EP:
var += np.eye(Xnew.shape[0])/self.beta # TODO: This beta doesn't belong here in the EP case.
var += np.eye(Xnew.shape[0])/self.beta
else:
raise NotImplementedError, "full_cov = True not implemented for EP"
#var = np.diag(var)[:,None]
#phi = self.likelihood.predictive_mean(mu,var)
else:
Kxx = self.kern.Kdiag(Xnew)
var = Kxx - np.sum(Kx*np.dot(self.Kmmi - self.LBL_inv, Kx),0)
if not self.EP:
var += 1./self.beta # TODO: This beta doesn't belong here in the EP case.
var += 1./self.beta
else:
phi = self.likelihood.predictive_mean(mu,var)
return mu,var,phi
@ -247,7 +251,6 @@ class sparse_GP(GP):
"""
Plot the fitted model: just call the GP_regression plot function and then add inducing inputs
"""
#GP_regression.plot(self,*args,**kwargs)
GP.plot(self,*args,**kwargs)
if self.Q==1:
pb.plot(self.Z,self.Z*0+pb.ylim()[0],'k|',mew=1.5,markersize=12)