binarylaplacegp.m

高斯过程在回归和分类问题中的应用

function varargout = binaryLaplaceGP(hyper, covfunc, lik, varargin)

% binaryLaplaceGP - Laplace's approximation for binary Gaussian process
% classification. Two modes are possible: training or testing: if no test
% cases are supplied, then the approximate negative log marginal likelihood
% and its partial derivatives wrt the hyperparameters is computed; this mode is
% used to fit the hyperparameters. If test cases are given, then the test set
% predictive probabilities are returned. The program is flexible in allowing
% several different likelihood functions and a multitude of covariance
% functions.
%
% usage: [nlZ, dnlZ     ] = binaryLaplaceGP(hyper, covfunc, lik, x, y);
%    or: [p, mu, s2, nlZ] = binaryLaplaceGP(hyper, covfunc, lik, x, y, xstar);
%
% where:
%
%   hyper    is a (column) vector of hyperparameters
%   covfunc  is the name of the covariance function (see below)
%   lik      is the name of the likelihood function (see below)
%   x        is a n by D matrix of training inputs
%   y        is a (column) vector (of size n) of binary +1/-1 targets 
%   xstar    is a nn by D matrix of test inputs
%   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 log hyperparameter
%   p        is a (column) vector (of length nn) of predictive probabilities
%   mu       is a (column) vector (of length nn) of predictive latent means
%   s2       is a (column) vector (of length nn) of predictive latent variances
%
% The length of the vector of log hyperparameters depends on the covariance
% function, as specified by the "covfunc" input to the function, specifying the
% name of a covariance function. A number of different covariance function are
% implemented, and it is not difficult to add new ones. See "help covFunctions"
% for the details.
%
% The shape of the likelihood function is given by the "lik" input to the
% function, specifying the name of the likelihood function. The two implemented
% likelihood functions are:
%   
%   logistic      the logistic function: 1/(1+exp(-x)) 
%   cumGauss      the cumulative Gaussian (error function)
%
% The function can conveniently be used with the "minimize" function to train
% a Gaussian process, eg:
%
% [hyper, fX, i] = minimize(hyper, 'binaryLaplaceGP', length, 'covSEiso',
%                                                             'logistic', x, y);
%
% Copyright (c) 2004, 2005, 2006, 2007 by Carl Edward Rasmussen, 2007-02-19.

if nargin<5 || nargin>6
  disp('Usage: [nlZ, dnlZ     ] = binaryLaplaceGP(hyper, covfunc, lik, x, y);')
  disp('   or: [p, mu, s2, nlZ] = binaryLaplaceGP(hyper, covfunc, lik, x, y, xstar);')
  return
end

% Note, this function is just a wrapper provided for backward compatibility,
% the functionality is now provided by the more general binaryGP function.

varargout = cell(nargout, 1);    % allocate the right number of output arguments
[varargout{:}] = binaryGP(hyper, 'approxLA', covfunc, lik, varargin{:});