some small changes.

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 BGPLVM import Bayesian_GPLVM
+from generalized_FITC import generalized_FITC

GPy/models/generalized_FITC.py

@@ -0,0 +1,162 @@
+# 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
+from ..util.plot import gpplot
+from scipy import linalg
+from .. import kern
+from sparse_GP import sparse_GP
+
+"""
+import numpy as np
+import pylab as pb
+from scipy import stats, linalg
+from .. import kern
+from ..core import model
+from ..util.linalg import pdinv,mdot
+from ..util.plot import gpplot
+#from ..inference.Expectation_Propagation import FITC
+from ..likelihoods.EP import FITC
+from ..likelihoods import likelihood,probit
+"""
+
+class generalized_FITC(sparse_GP):
+    def __init__(self, X, likelihood, kernel, Z, X_uncertainty=None, Xslices=None,Zslices=None, normalize_X=False):
+    #def __init__(self, X, likelihood, kernel=None, inducing=10, epsilon_ep=1e-3, powerep=[1.,1.]):
+        """
+        Naish-Guzman, A. and Holden, S. (2008) implemantation of EP with FITC.
+
+        :param X: input observations
+        :param likelihood: Output's likelihood (likelihood class)
+        :param kernel: a GPy kernel
+        :param Z:  Either an array specifying the inducing points location or a scalar defining their number.
+        """
+
+        if type(Z) == int:
+            self.M = Z
+            self.Z = (np.random.random_sample(self.D*self.M)*(self.X.max()-self.X.min())+self.X.min()).reshape(self.M,-1)
+        elif type(Z) == np.ndarray:
+            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)
+        self.scale_factor = 100.
+
+    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.likelihood.precision/(1. + self.likelihood.precision*self.Diag0[:,None]) # Add the diagonal element of the FITC approximation
+            self._set_params(self._get_params()) # update the GP
+
+    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 _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.
+        This function:
+            - computes the diagonal term
+            - eliminates the extra terms computed in the sparse_GP approximation
+            - computes the likelihood gradients wrt the true precision.
+        """
+        # Compute FITC's diagonal term of the covariance
+        sf = self.scale_factor
+        sf2 = sf**2
+        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)
+        self.mu_tilde = (self.likelihood.v_tilde/self.likelihood.tau_tilde)[:,None]
+
+        # Remove extra term from dL_dpsi
+        self.dL_dpsi0 = np.zeros(self.N)
+        # Remove extra term from dL_dKmm
+        self.dL_dKmm = +0.5 * self.D * mdot(self.Lmi.T, self.A, self.Lmi)*sf2 # dB
+        #the partial derivative vector for the likelihood with the true precision
+        if self.likelihood.Nparams ==0:
+            #save computation here
+            self.partial_for_likelihood = None
+        elif self.likelihood.is_heteroscedastic:
+            raise NotImplementedError, "heteroscedatic derivates not implemented"
+        else:
+            beta = self.likelihood._precision # NOTE the true precison is now '_precison' not 'precision'
+            dbeta =   0.5 * self.N*self.D/beta - 0.5 * np.sum(np.square(self.likelihood.Y))
+            #dbeta += - 0.5 * self.D * (self.psi0.sum() - np.trace(self.A)/beta*sf2)
+            dbeta += - 0.5 * self.D * np.sum(self.Bi*self.A)/beta
+            dbeta += np.sum((self.C - 0.5 * mdot(self.C,self.psi2_beta_scaled,self.C) ) * self.psi1VVpsi1 )/beta
+            self.partial_for_likelihood = -dbeta*self.likelihood.precision**2
+
+
+
+
+    def _raw_predict(self, Xnew, slices, full_cov=True):
+        """
+        Make a prediction for the vsGP model
+
+        Arguments
+        ---------
+        X : Input prediction data - Nx1 numpy array (floats)
+        """
+        Kx = self.kern.K(self.Z, Xnew)
+        #K_x = self.kernel.K(self.Z,X)
+        if full_cov:
+            Kxx = self.kern.K(Xnew)
+        else:
+            Kxx = self.kern.K(Xnew)#FIXME
+            #raise NotImplementedError
+            #Kxx = self.kern.Kdiag(Xnew)
+
+        # 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)
+        KR0T = np.dot(Kx.T,self.Lmi.T)
+        mu_star = np.dot(KR0T,mu_H)
+        sigma2_star = Kxx + np.dot(KR0T,np.dot(Sigma_H - np.eye(self.M),KR0T.T))
+        vdiag = np.diag(sigma2_star)
+        return mu_star[:,None],vdiag[:,None]

GPy/models/sparse_GP.py

@@ -72,7 +72,7 @@ class sparse_GP(GP):
             self.psi2 = None
 
     def _computations(self):
-        # TODO find routine to multiply triangular matrices
+        #TODO: find routine to multiply triangular matrices
         #TODO: slices for psi statistics (easy enough)
 
         sf = self.scale_factor
@@ -106,7 +106,7 @@ class sparse_GP(GP):
         self.C = mdot(self.Lmi.T, self.Bi, self.Lmi)
         self.E = mdot(self.C, self.psi1VVpsi1/sf2, self.C.T)
 
-        # Compute dL_dpsi # FIXME: this is untested for the het. case
+        # Compute dL_dpsi # FIXME: this is untested for the heterscedastic + uncertin inputs case
         self.dL_dpsi0 = - 0.5 * self.D * (self.likelihood.precision * np.ones([self.N,1])).flatten()
         self.dL_dpsi1 = mdot(self.V, self.psi1V.T,self.C).T
         if self.likelihood.is_heteroscedastic:
@@ -180,7 +180,8 @@ class sparse_GP(GP):
         if self.has_uncertain_inputs:
             raise NotImplementedError, "EP approximation not implemented for uncertain inputs"
         else:
-            self.likelihood.fit_DTC(self.Kmm,self.psi1)
+            #self.likelihood.fit_DTC(self.Kmm,self.psi1)
+            self.likelihood.fit_FITC(self.Kmm,self.psi1,self.psi0)
             self._set_params(self._get_params()) # update the GP
 
     def log_likelihood(self):