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generalized_FITC removed
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Ricardo Andrade
parent
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1 changed files with 0 additions and 162 deletions
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# Copyright (c) 2012, GPy authors (see AUTHORS.txt).
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# Licensed under the BSD 3-clause license (see LICENSE.txt)
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import numpy as np
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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 scipy import linalg
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from .. import kern
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from sparse_GP import sparse_GP
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"""
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import numpy as np
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import pylab as pb
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from scipy import stats, linalg
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from .. import kern
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from ..core import model
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from ..util.linalg import pdinv,mdot
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from ..util.plot import gpplot
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#from ..inference.Expectation_Propagation import FITC
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from ..likelihoods.EP import FITC
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from ..likelihoods import likelihood,probit
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"""
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class generalized_FITC(sparse_GP):
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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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#def __init__(self, X, likelihood, kernel=None, inducing=10, epsilon_ep=1e-3, powerep=[1.,1.]):
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"""
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Naish-Guzman, A. and Holden, S. (2008) implemantation of EP with FITC.
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:param X: input observations
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:param likelihood: Output's likelihood (likelihood class)
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:param kernel: a GPy kernel
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:param Z: Either an array specifying the inducing points location or a scalar defining their number.
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"""
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if type(Z) == int:
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self.M = Z
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self.Z = (np.random.random_sample(self.D*self.M)*(self.X.max()-self.X.min())+self.X.min()).reshape(self.M,-1)
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elif type(Z) == np.ndarray:
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self.Z = Z
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self.M = self.Z.shape[0]
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self._precision = likelihood.precision
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sparse_GP.__init__(self, X, likelihood, kernel=kernel, Z=self.Z, X_uncertainty=None, Xslices=None,Zslices=None, normalize_X=False)
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self.scale_factor = 100.
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def update_likelihood_approximation(self):
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"""
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Approximates a non-gaussian likelihood using Expectation Propagation
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For a Gaussian (or direct: TODO) likelihood, no iteration is required:
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this function does nothing
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"""
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if self.has_uncertain_inputs:
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raise NotImplementedError, "FITC approximation not implemented for uncertain inputs"
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else:
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self.likelihood.fit_FITC(self.Kmm,self.psi1,self.psi0)
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self._precision = self.likelihood.precision # Save the true precision
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self.likelihood.precision = self.likelihood.precision/(1. + self.likelihood.precision*self.Diag0[:,None]) # Add the diagonal element of the FITC approximation
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self._set_params(self._get_params()) # update the GP
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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.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._compute_kernel_matrices()
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self._computations()
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self._FITC_computations()
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def _FITC_computations(self):
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"""
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FITC approximation doesn't have the correction term in the log-likelihood bound,
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but adds a diagonal term to the covariance matrix.
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This function:
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- computes the diagonal term
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- eliminates the extra terms computed in the sparse_GP approximation
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- computes the likelihood gradients wrt the true precision.
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"""
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# Compute FITC's diagonal term of the covariance
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sf = self.scale_factor
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sf2 = sf**2
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self.Qnn = mdot(self.psi1.T,self.Kmmi,self.psi1)
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self.Diag0 = self.psi0 - np.diag(self.Qnn)
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self.Diag = self.Diag0/(1.+ self.Diag0 * self._precision.flatten())
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self.P = (self.Diag / self.Diag0)[:,None] * self.psi1.T
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self.RPT0 = np.dot(self.Lmi,self.psi1)
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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))
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self.R,info = linalg.flapack.dtrtrs(self.L,self.Lmi,lower=1)
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self.RPT = np.dot(self.R,self.P.T)
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self.Sigma = np.diag(self.Diag) + np.dot(self.RPT.T,self.RPT)
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self.w = self.Diag * self.likelihood.v_tilde
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self.gamma = np.dot(self.R.T, np.dot(self.RPT,self.likelihood.v_tilde))
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self.mu = self.w + np.dot(self.P,self.gamma)
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self.mu_tilde = (self.likelihood.v_tilde/self.likelihood.tau_tilde)[:,None]
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# Remove extra term from dL_dpsi
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self.dL_dpsi0 = np.zeros(self.N)
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# Remove extra term from 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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#the partial derivative vector for the likelihood with the true precision
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if self.likelihood.Nparams ==0:
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#save computation here
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self.partial_for_likelihood = None
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elif self.likelihood.is_heteroscedastic:
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raise NotImplementedError, "heteroscedatic derivates not implemented"
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else:
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beta = self.likelihood._precision # NOTE the true precison is now '_precison' not 'precision'
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dbeta = 0.5 * self.N*self.D/beta - 0.5 * np.sum(np.square(self.likelihood.Y))
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#dbeta += - 0.5 * self.D * (self.psi0.sum() - np.trace(self.A)/beta*sf2)
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dbeta += - 0.5 * self.D * np.sum(self.Bi*self.A)/beta
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dbeta += np.sum((self.C - 0.5 * mdot(self.C,self.psi2_beta_scaled,self.C) ) * self.psi1VVpsi1 )/beta
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self.partial_for_likelihood = -dbeta*self.likelihood.precision**2
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def _raw_predict(self, Xnew, slices, full_cov=True):
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"""
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Make a prediction for the vsGP model
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Arguments
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---------
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X : Input prediction data - Nx1 numpy array (floats)
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"""
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Kx = self.kern.K(self.Z, Xnew)
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#K_x = self.kernel.K(self.Z,X)
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if full_cov:
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Kxx = self.kern.K(Xnew)
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else:
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Kxx = self.kern.K(Xnew)#FIXME
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#raise NotImplementedError
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#Kxx = self.kern.Kdiag(Xnew)
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# q(u|f) = N(u| R0i*mu_u*f, R0i*C*R0i.T)
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# Ci = I + (RPT0)Di(RPT0).T
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# C = I - [RPT0] * (D+[RPT0].T*[RPT0])^-1*[RPT0].T
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# = I - [RPT0] * (D + self.Qnn)^-1 * [RPT0].T
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# = I - [RPT0] * (U*U.T)^-1 * [RPT0].T
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# = I - V.T * V
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U = np.linalg.cholesky(np.diag(self.Diag0) + self.Qnn)
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V,info = linalg.flapack.dtrtrs(U,self.RPT0.T,lower=1)
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C = np.eye(self.M) - np.dot(V.T,V)
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mu_u = np.dot(C,self.RPT0)*(1./self.Diag0[None,:])
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#self.C = C
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#self.RPT0 = np.dot(self.R0,self.Knm.T) P0.T
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#self.mu_u = mu_u
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#self.U = U
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# q(u|y) = N(u| R0i*mu_H,R0i*Sigma_H*R0i.T)
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mu_H = np.dot(mu_u,self.mu)
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self.mu_H = mu_H
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Sigma_H = C + np.dot(mu_u,np.dot(self.Sigma,mu_u.T))
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# q(f_star|y) = N(f_star|mu_star,sigma2_star)
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KR0T = np.dot(Kx.T,self.Lmi.T)
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mu_star = np.dot(KR0T,mu_H)
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sigma2_star = Kxx + np.dot(KR0T,np.dot(Sigma_H - np.eye(self.M),KR0T.T))
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vdiag = np.diag(sigma2_star)
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return mu_star[:,None],vdiag[:,None]
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