diff --git a/GPy/core/model.py b/GPy/core/model.py index cc8ae2c4..0804f277 100644 --- a/GPy/core/model.py +++ b/GPy/core/model.py @@ -467,3 +467,5 @@ class model(parameterised): if ll_change < epsilon: stop = True iteration += 1 + if stop: + print "%s iterations." %iteration diff --git a/GPy/models/__init__.py b/GPy/models/__init__.py index 22aa803c..f442dc67 100644 --- a/GPy/models/__init__.py +++ b/GPy/models/__init__.py @@ -11,3 +11,4 @@ from warped_GP import warpedGP from sparse_GPLVM import sparse_GPLVM from uncollapsed_sparse_GP import uncollapsed_sparse_GP from Bayesian_GPLVM import Bayesian_GPLVM +from generalized_FITC import generalized_FITC diff --git a/GPy/models/generalized_FITC.py b/GPy/models/generalized_FITC.py new file mode 100644 index 00000000..505f442a --- /dev/null +++ b/GPy/models/generalized_FITC.py @@ -0,0 +1,207 @@ +# Copyright (c) 2012, GPy authors (see AUTHORS.txt). +# Licensed under the BSD 3-clause license (see LICENSE.txt) + +import numpy as np +import pylab as pb +from ..util.linalg import mdot, jitchol, chol_inv, pdinv, trace_dot +from ..util.plot import gpplot +from .. import kern +from scipy import stats, linalg +from sparse_GP import sparse_GP + +class generalized_FITC(sparse_GP): + """ + Naish-Guzman, A. and Holden, S. (2008) implemantation of EP with FITC. + + :param X: inputs + :type X: np.ndarray (N x Q) + :param likelihood: a likelihood instance, containing the observed data + :type likelihood: GPy.likelihood.(Gaussian | EP) + :param kernel : the kernel/covariance function. See link kernels + :type kernel: a GPy kernel + :param X_uncertainty: The uncertainty in the measurements of X (Gaussian variance) + :type X_uncertainty: np.ndarray (N x Q) | None + :param Z: inducing inputs (optional, see note) + :type Z: np.ndarray (M x Q) | None + :param Zslices: slices for the inducing inputs (see slicing TODO: link) + :param M : Number of inducing points (optional, default 10. Ignored if Z is not None) + :type M: int + :param normalize_(X|Y) : whether to normalize the data before computing (predictions will be in original scales) + :type normalize_(X|Y): bool + """ + + def __init__(self, X, likelihood, kernel, Z, X_uncertainty=None, Xslices=None,Zslices=None, normalize_X=False): + + self.Z = Z + self.M = self.Z.shape[0] + self._precision = likelihood.precision + + sparse_GP.__init__(self, X, likelihood, kernel=kernel, Z=self.Z, X_uncertainty=None, Xslices=None,Zslices=None, normalize_X=False) + + def _set_params(self, p): + self.Z = p[:self.M*self.Q].reshape(self.M, self.Q) + self.kern._set_params(p[self.Z.size:self.Z.size+self.kern.Nparam]) + self.likelihood._set_params(p[self.Z.size+self.kern.Nparam:]) + self._compute_kernel_matrices() + self._computations() + self._FITC_computations() + + def update_likelihood_approximation(self): + """ + Approximates a non-gaussian likelihood using Expectation Propagation + + For a Gaussian (or direct: TODO) likelihood, no iteration is required: + this function does nothing + """ + if self.has_uncertain_inputs: + raise NotImplementedError, "FITC approximation not implemented for uncertain inputs" + else: + self.likelihood.fit_FITC(self.Kmm,self.psi1,self.psi0) + self._precision = self.likelihood.precision # Save the true precision + self.likelihood.precision = self._precision/(1. + self._precision*self.Diag0[:,None]) # Add the diagonal element of the FITC approximation + self._set_params(self._get_params()) # update the GP + + def _FITC_computations(self): + """ + FITC approximation doesn't have the correction term in the log-likelihood bound, + but adds a diagonal term to the covariance matrix: diag(Knn - Qnn). + This function: + - computes the FITC diagonal term + - removes the extra terms computed in the sparse_GP approximation + - computes the likelihood gradients wrt the true precision. + """ + #NOTE the true precison is now '_precison' not 'precision' + if self.likelihood.is_heteroscedastic: + + # Compute generalized FITC's diagonal term of the covariance + self.Qnn = mdot(self.psi1.T,self.Kmmi,self.psi1) + self.Diag0 = self.psi0 - np.diag(self.Qnn) + self.Diag = self.Diag0/(1.+ self.Diag0 * self._precision.flatten()) + + self.P = (self.Diag / self.Diag0)[:,None] * self.psi1.T + self.RPT0 = np.dot(self.Lmi,self.psi1) + self.L = np.linalg.cholesky(np.eye(self.M) + np.dot(self.RPT0,(1./self.Diag0 - self.Diag/(self.Diag0**2))[:,None]*self.RPT0.T)) + self.R,info = linalg.flapack.dtrtrs(self.L,self.Lmi,lower=1) + self.RPT = np.dot(self.R,self.P.T) + self.Sigma = np.diag(self.Diag) + np.dot(self.RPT.T,self.RPT) + self.w = self.Diag * self.likelihood.v_tilde + self.gamma = np.dot(self.R.T, np.dot(self.RPT,self.likelihood.v_tilde)) + self.mu = self.w + np.dot(self.P,self.gamma) + + # Remove extra term from dL_dpsi1 + self.dL_dpsi1 += -mdot(self.Kmmi,self.psi1*self.likelihood.precision.flatten().reshape(1,self.N)) #dB + else: + raise NotImplementedError, "homoscedastic fitc not implemented" + # Remove extra term from dL_dpsi1 + #self.dL_dpsi1 += -mdot(self.Kmmi,self.psi1*self.likelihood.precision) #dB + + sf = self.scale_factor + sf2 = sf**2 + + # Remove extra term from dL_dKmm + self.dL_dKmm += 0.5 * self.D * mdot(self.Lmi.T, self.A, self.Lmi)*sf2 # dB + self.dL_dpsi0 = None + + #the partial derivative vector for the likelihood + if self.likelihood.Nparams == 0: + self.partial_for_likelihood = None + elif self.likelihood.is_heteroscedastic: + raise NotImplementedError, "heteroscedastic derivates not implemented" + else: + raise NotImplementedError, "homoscedastic derivatives not implemented" + #likelihood is not heterscedatic + #self.partial_for_likelihood = - 0.5 * self.N*self.D*self.likelihood.precision + 0.5 * np.sum(np.square(self.likelihood.Y))*self.likelihood.precision**2 + #self.partial_for_likelihood += 0.5 * self.D * trace_dot(self.Bi,self.A)*self.likelihood.precision + #self.partial_for_likelihood += self.likelihood.precision*(0.5*trace_dot(self.psi2_beta_scaled,self.E*sf2) - np.trace(self.Cpsi1VVpsi1)) + #TODO partial derivative vector for the likelihood not implemented + + def dL_dtheta(self): + """ + Compute and return the derivative of the log marginal likelihood wrt the parameters of the kernel + """ + dL_dtheta = self.kern.dK_dtheta(self.dL_dKmm,self.Z) + if self.has_uncertain_inputs: + raise NotImplementedError, "heteroscedatic derivates not implemented" + else: + #NOTE in sparse_GP this would include the gradient wrt psi0 + dL_dtheta += self.kern.dK_dtheta(self.dL_dpsi1,self.Z,self.X) + return dL_dtheta + + + def log_likelihood(self): + """ Compute the (lower bound on the) log marginal likelihood """ + sf2 = self.scale_factor**2 + if self.likelihood.is_heteroscedastic: + 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) + else: + A = -0.5*self.N*self.D*(np.log(2.*np.pi) + np.log(self.likelihood._variance)) -0.5*self.likelihood.precision*self.likelihood.trYYT + C = -0.5*self.D * (self.B_logdet + self.M*np.log(sf2)) + D = 0.5*np.trace(self.Cpsi1VVpsi1) + return A+C+D + + def _raw_predict(self, Xnew, slices, full_cov=False): + if self.likelihood.is_heteroscedastic: + """ + Make a prediction for the generalized FITC model + + Arguments + --------- + X : Input prediction data - Nx1 numpy array (floats) + """ + # q(u|f) = N(u| R0i*mu_u*f, R0i*C*R0i.T) + + # Ci = I + (RPT0)Di(RPT0).T + # C = I - [RPT0] * (D+[RPT0].T*[RPT0])^-1*[RPT0].T + # = I - [RPT0] * (D + self.Qnn)^-1 * [RPT0].T + # = I - [RPT0] * (U*U.T)^-1 * [RPT0].T + # = I - V.T * V + U = np.linalg.cholesky(np.diag(self.Diag0) + self.Qnn) + V,info = linalg.flapack.dtrtrs(U,self.RPT0.T,lower=1) + C = np.eye(self.M) - np.dot(V.T,V) + mu_u = np.dot(C,self.RPT0)*(1./self.Diag0[None,:]) + #self.C = C + #self.RPT0 = np.dot(self.R0,self.Knm.T) P0.T + #self.mu_u = mu_u + #self.U = U + # q(u|y) = N(u| R0i*mu_H,R0i*Sigma_H*R0i.T) + mu_H = np.dot(mu_u,self.mu) + self.mu_H = mu_H + Sigma_H = C + np.dot(mu_u,np.dot(self.Sigma,mu_u.T)) + # q(f_star|y) = N(f_star|mu_star,sigma2_star) + Kx = self.kern.K(self.Z, Xnew) + KR0T = np.dot(Kx.T,self.Lmi.T) + mu_star = np.dot(KR0T,mu_H) + if full_cov: + Kxx = self.kern.K(Xnew) + var = Kxx + np.dot(KR0T,np.dot(Sigma_H - np.eye(self.M),KR0T.T)) + else: + Kxx = self.kern.Kdiag(Xnew) + Kxx_ = self.kern.K(Xnew) + var_ = Kxx_ + np.dot(KR0T,np.dot(Sigma_H - np.eye(self.M),KR0T.T)) + var = (Kxx + np.sum(KR0T.T*np.dot(Sigma_H - np.eye(self.M),KR0T.T),0))[:,None] + return mu_star[:,None],var + """ + Kx = self.kern.K(self.Z, Xnew) + mu = mdot(Kx.T, self.C/self.scale_factor, self.psi1V) + if full_cov: + Kxx = self.kern.K(Xnew) + var = Kxx - mdot(Kx.T, (self.Kmmi - self.C/self.scale_factor**2), Kx) #NOTE this won't work for plotting + else: + Kxx = self.kern.Kdiag(Xnew) + var = Kxx - np.sum(Kx*np.dot(self.Kmmi - self.C/self.scale_factor**2, Kx),0) + a = kjk + return mu,var[:,None] + """ + else: + raise NotImplementedError, "homoscedastic fitc not implemented" + """ + Kx = self.kern.K(self.Z, Xnew) + mu = mdot(Kx.T, self.C/self.scale_factor, self.psi1V) + if full_cov: + Kxx = self.kern.K(Xnew) + var = Kxx - mdot(Kx.T, (self.Kmmi - self.C/self.scale_factor**2), Kx) #NOTE this won't work for plotting + else: + Kxx = self.kern.Kdiag(Xnew) + var = Kxx - np.sum(Kx*np.dot(self.Kmmi - self.C/self.scale_factor**2, Kx),0) + return mu,var[:,None] + """