www.pudn.com > gpml.rar > approximations.m, change:2007-06-27,size:1936b
% approximations: Exact inference for Gaussian process classification is % intractable, and approximations are necessary. Different approximation % techniques have been implemented, which all rely on a Gaussian approximation % to the non-Gaussian posterior: % % approxEP the Expectation Propagation (EP) algorithm % approxLA Laplace's method % % which are used by the Gaussian process classification funtion binaryGP.m. % The interface to the approximation methods is the following: % % function [alpha, sW, L, nlZ, dnlZ] = approx..(hyper, covfunc, lik, x, y) % % where: % % hyper is a column vector of hyperparameters % covfunc is the name of the covariance function (see covFunctions.m) % lik is the name of the likelihood function (see likelihoods.m) % x is a n by D matrix of training inputs % y is a (column) vector (of size n) of binary +1/-1 targets % nlZ is the returned value of the negative log marginal likelihood % dnlZ is a (column) vector of partial derivatives of the negative % log marginal likelihood wrt each hyperparameter % alpha is a (sparse or full column vector) containing inv(K)*m, where K % is the prior covariance matrix and m the approx posterior mean % sW is a (sparse or full column) vector containing diagonal of sqrt(W) % the approximate posterior covariance matrix is inv(inv(K)+W) % L is a (sparse or full) matrix, L = chol(sW*K*sW+eye(n)) % % Usually, the approximate posterior to be returned admits the form % N(m=K*alpha, V=inv(inv(K)+W)), where alpha is a vector and W is diagonal; % if not, then L contains instead -inv(K+inv(W)), and sW is unused. % % For more information on the individual approximation methods and their % implementations, see the separate approx??.m files. See also binaryGP.m % % Copyright (c) by Carl Edward Rasmussen and Hannes Nickisch, 2007-06-25.