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Log-likelihood,predictions and plotting are working.
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Ricardo
parent
bb1e0021d7
commit
d1a0883c12
4 changed files with 64 additions and 56 deletions
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@ -7,7 +7,7 @@ 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 GP import GP
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from ..inference.EP import Full
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from ..inference.EP import Full,DTC,FITC
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from ..inference.likelihoods import likelihood,probit,poisson,gaussian
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#Still TODO:
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@ -36,6 +36,8 @@ class sparse_GP(GP):
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:param normalize_(X|Y) : whether to normalize the data before computing (predictions will be in original scales)
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:type normalize_(X|Y): bool
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:parm likelihood: a GPy likelihood, defaults to gaussian
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:param method_ep: sparse approximation used by Expectation Propagation algorithm, defaults to DTC
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:type M: string (Full|DTC|FITC)
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:param epsilon_ep: convergence criterion for the Expectation Propagation algorithm, defaults to 0.1
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:param powerep: power-EP parameters [$\eta$,$\delta$], defaults to [1.,1.]
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:type powerep: list
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@ -58,17 +60,22 @@ class sparse_GP(GP):
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self.X_uncertainty = X_uncertainty
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GP.__init__(self, X=X, Y=Y, kernel=kernel, normalize_X=normalize_X, normalize_Y=normalize_Y,likelihood=likelihood,epsilon_ep=epsilon_ep,power_ep=power_ep)
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self.trYYT = np.sum(np.square(self.Y)) if not self.EP else None
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#normalise X uncertainty also
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if self.has_uncertain_inputs:
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self.X_uncertainty /= np.square(self._Xstd)
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if not self.EP:
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self.trYYT = np.sum(np.square(self.Y))
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else:
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self.method_ep = method_ep
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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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if not self.EP:
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#self.beta = p[self.M*self.Q]
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self.beta = np.repeat(p[self.M*self.Q],self.N)[:,None]
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self.beta = p[self.M*self.Q]
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#self.beta = np.repeat(p[self.M*self.Q],self.N)[:,None]
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self.kern._set_params(p[self.Z.size + 1:])
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self.beta2 = self.beta**2
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else:
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@ -76,7 +83,7 @@ class sparse_GP(GP):
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if self.Y is None:
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self.Y = np.ones([self.N,1])
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self._compute_kernel_matrices()
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self._computations()
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self._computations() #NOTE At this point computations of dL are not needed
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def _get_params(self):
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if not self.EP:
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@ -123,24 +130,29 @@ class sparse_GP(GP):
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self.G = mdot(self.LBL_inv, self.psi1VVpsi1, self.LBL_inv.T)
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# Compute dL_dpsi
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self.dL_dpsi0 = - 0.5 * self.D * self.beta * np.ones([self.N,1])
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self.dL_dpsi0 = - 0.5 * self.D * self.beta.flatten() * np.ones(self.N)
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self.dL_dpsi1 = mdot(self.LLambdai.T,self.C,self.V.T)
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self.dL_dpsi2 = - 0.5 * self.beta * (self.D*(self.LBL_inv - self.Kmmi) + self.G)
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#self.dL_dpsi2 = - 0.5 * self.beta * (self.D*(self.LBL_inv - self.Kmmi) + self.G)
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self.dL_dpsi2 = - 0.5 * (self.D*(self.LBL_inv - self.Kmmi) + self.G)
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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) # dB
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self.dL_dKmm += -0.5 * self.D * (- self.LBL_inv - 2.*self.beta*mdot(self.LBL_inv, self.psi2, self.Kmmi) + self.Kmmi) # dC
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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
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#self.dL_dKmm += -0.5 * self.D * (- self.LBL_inv - 2.*self.beta*mdot(self.LBL_inv, self.psi2, self.Kmmi) + self.Kmmi) # dC
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self.dL_dKmm += -0.5 * self.D * (- self.LBL_inv - 2.*mdot(self.LBL_inv, self.psi2_beta_scaled, self.Kmmi) + self.Kmmi) # dC
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#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
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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
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def approximate_likelihood(self):
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assert not isinstance(self.likelihood, gaussian), "EP is only available for non-gaussian likelihoods"
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if self.ep_proxy == 'DTC':
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if self.method_ep == 'DTC':
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self.ep_approx = DTC(self.Kmm,self.likelihood,self.psi1,epsilon=self.epsilon_ep,power_ep=[self.eta,self.delta])
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elif self.ep_proxy == 'FITC':
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elif self.method_ep == 'FITC':
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self.ep_approx = FITC(self.Kmm,self.likelihood,self.psi1,self.psi0,epsilon=self.epsilon_ep,power_ep=[self.eta,self.delta])
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else:
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self.ep_approx = Full(self.X,self.likelihood,self.kernel,inducing=None,epsilon=self.epsilon_ep,power_ep=[self.eta,self.delta])
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self.beta, self.Y, self.Z_ep = self.ep_approx.fit_EP()
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print "Aqui toy"
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self.trbetaYYT = np.sum(np.square(self.Y)*self.beta)
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self._computations()
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def log_likelihood(self):
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@ -149,30 +161,11 @@ class sparse_GP(GP):
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"""
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if not self.EP:
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A = -0.5*self.N*self.D*(np.log(2.*np.pi) - np.log(self.beta))
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D = -0.5*self.beta*self.trYYT
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else:
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A = -0.5*self.D*(self.N*np.log(2.*np.pi) - np.sum(np.log(self.beta)))
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B = -0.5*self.D*self.trace_K
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C = -0.5*self.D * self.B_logdet
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D = -0.5*self.beta*self.trYYT
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E = +0.5*np.sum(self.psi1VVpsi1 * self.LBL_inv)
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return A+B+C+D+E
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def log_likelihood(self):
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"""
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Compute the (lower bound on the) log marginal likelihood
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"""
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beta_logdet = self.N*self.D*np.log(self.beta) if not self.EP else self.D*np.sum(np.log(self.beta))
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if self.hetero_noise:
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A = foo
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B = bar
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D = -0.5*self.trbetaYYT
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else:
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A = -0.5*self.N*self.D*(np.log(2.*np.pi)) - 0.5*beta_logdet
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B = -0.5*self.beta*self.D*self.trace_K if not self.EP else -0.5*self.D*self.trace_K
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D = -0.5*self.beta*self.trYYT
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B = -0.5*self.D*self.trace_K
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C = -0.5*self.D * self.B_logdet
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E = +0.5*np.sum(self.psi1VVpsi1 * self.LBL_inv)
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return A+B+C+D+E
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@ -223,21 +216,33 @@ class sparse_GP(GP):
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return dL_dZ
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def _log_likelihood_gradients(self):
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return np.hstack([self.dL_dZ().flatten(), self.dL_dbeta(), self.dL_dtheta()])
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if not self.EP:
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return np.hstack([self.dL_dZ().flatten(), self.dL_dbeta(), self.dL_dtheta()])
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else:
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return np.hstack([self.dL_dZ().flatten(), self.dL_dtheta()])
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def _raw_predict(self, Xnew, slices, full_cov=False):
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"""Internal helper function for making predictions, does not account for normalisation"""
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Kx = self.kern.K(self.Z, Xnew)
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mu = mdot(Kx.T, self.LBL_inv, self.psi1V)
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phi = None
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if full_cov:
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noise_term = np.eye(Xnew.shape[0])/self.beta if not self.EP else 0
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Kxx = self.kern.K(Xnew)
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var = Kxx - mdot(Kx.T, (self.Kmmi - self.LBL_inv), Kx) + noise_term
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var = Kxx - mdot(Kx.T, (self.Kmmi - self.LBL_inv), Kx)
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if not self.EP:
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var += np.eye(Xnew.shape[0])/self.beta # TODO: This beta doesn't belong here in the EP case.
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else:
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raise NotImplementedError, "full_cov = True not implemented for EP"
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#var = np.diag(var)[:,None]
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#phi = self.likelihood.predictive_mean(mu,var)
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else:
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noise_term = 1./self.beta if not self.EP else 0
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Kxx = self.kern.Kdiag(Xnew)
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var = Kxx - np.sum(Kx*np.dot(self.Kmmi - self.LBL_inv, Kx),0) + noise_term
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return mu,var,None#TODO add phi for EP
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var = Kxx - np.sum(Kx*np.dot(self.Kmmi - self.LBL_inv, Kx),0)
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if not self.EP:
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var += 1./self.beta # TODO: This beta doesn't belong here in the EP case.
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else:
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phi = self.likelihood.predictive_mean(mu,var)
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return mu,var,phi
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def plot(self, *args, **kwargs):
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"""
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