Script to understand calculation of log probability of the Dirichlet in high dimensions.

DebugHighDimDirichletLogProb

% Script to understand calculation of log probability of the Dirichlet
%   in high dimensions.
% Requires: Minka's fastfit toolbox
%    http://research.microsoft.com/en-us/um/people/minka/software/fastfit/
% For complete problem description, check out
% http://stats.stackexchange.com/questions/36111/calculating-log-prob-of-dirichlet-distribution-in-high-dimensions

concParam = 0.01;
EPS = 1e-15;

fprintf( '        [1 0...0]  [unif 0..0] [ unif ]\n');
for K= [4 10 50 100 500 1000];    
    lambda = concParam*ones( 1, K );
    
    % ------------------------------------------ Create 3 possible outcomes
    X = zeros(3, K);
    % First, consider a very sharply peaked distribution
    %   only the first dimension has significant mass
    X(1,:) = [1 eps+zeros(1,K-1)];
    
    % Next, consider a "halfway" uniform distribution,
    %   half the K dims have significant mass, others negligible
    X(2,1:K/2) = [ones(1,K/2)];
    X(2,:) = ( X(2,:)+EPS )./sum( X(2,:) );
    
    % Last, consider a fully uniform distribution
    X(3,:) = ones(1,K)/K;
    
    % ------------------------------------------ Calc log prob of each one
    logPr = zeros( 1, 3);
    for aa = 1:3
        logPr(aa) = dirichlet_logProb( lambda, X(aa,:) );
    end
    fprintf( 'K=%4d  % .2e  % .2e  % .2e\n', K, logPr);
    
end