maxgauss.m

this is speech recognition file

function [u,v,p,r] = maxgauss(m,c,d)
%MAXGAUSS determine gaussian approximation to max of a gaussian vector [p,u,v,r]=(m,c,d)
%
% Inputs:
%       m(N,1) is the mean vector of length N
%       c(N,N) is Covariance matrix (or c(N,1) is vector of covariances)
%       d(N,K) is Covariance w.r.t some other variables
%
% Outputs:
%       u is mean(max(x)) where x is the random variable of length N
%       v is var(max(x))
%       p(N,1) is prob of each element being the max
%       r(1,K) is covariance between max(x) and the variables corresponding to the columns of d
%
% To find the min instead of max, just negate m and u.

% The algorithm combines the elements of m in pairs in sequence as suggested
% in [1]. Errors are introduced because max(x(i),x(j)) is wrongly assumed to be
% gaussian. To minimize the errors, we use a greedy algorithm (approximately as
% in [2]) in which the chosen pair has the greatest imbalance in selection probability.
%
%
% Refs: [1] C. E. Clark. The greatest of a finite set of random variables.
%           Operations Research, 9(2):145