ITE / code / H_I_D / base_estimators / IHoeffding_estimation.m

function [I] = IHoeffding_estimation(Y,ds,co)
%Estimates mutual information (I) using the multivariate version of Hoeffding's Phi. 
%   Y: Y(:,t) is the t^th sample.
%  ds: subspace dimensions.
%  co: initialized mutual information estimator object.
%   Sandra Gaiser, Martin Ruppert, Friedrich Schmid. A multivariate version of Hoeffding's Phi-Square. Journal of Multivariate Analysis. 101 (2010) 2571-2586.
%Copyright (C) 2012 Zoltan Szabo ("", "szzoli (at) cs (dot) elte (dot) hu")
%This file is part of the ITE (Information Theoretical Estimators) Matlab/Octave toolbox.
%ITE is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by
%the Free Software Foundation, either version 3 of the License, or (at your option) any later version.
%This software is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of
%MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License for more details.
%You should have received a copy of the GNU General Public License along with ITE. If not, see <>.

if one_dimensional_problem(ds)
    [d,num_of_samples] = size(Y);
    U = copula_transformation(Y);

        term1 = Hoeffding_term1(U);
        if co.small_sample_adjustment
            term2 = -2 * sum(prod(1-U.^2-(1-U)/num_of_samples,1)) / (num_of_samples * 2^d);
            term2 = -2 * sum(prod(1-U.^2,1)) / (num_of_samples * 2^d);
        if co.small_sample_adjustment
            term3 = ( (num_of_samples-1) * (2*num_of_samples-1) / (3*2*num_of_samples^2) )^d;
            term3 = 1/3^d;
        I = term1 + term2 + term3;        
    if co.mult%multiplicative constant, if needed
        if co.small_sample_adjustment
            t1 = sum((1 - [1:num_of_samples-1]/num_of_samples).^d .* (2*[1:num_of_samples-1]-1)) / num_of_samples^2;
            t2 = -2 * sum( ( (num_of_samples * (num_of_samples-1) - [1:num_of_samples] .* ([1:num_of_samples]-1)) / (2*num_of_samples^2) ).^d ) / num_of_samples;
            t3 = term3;
            inv_hd = t1 + t2 + t3;%1/h(d,n)
            inv_hd = 2/((d+1)*(d+2)) - factorial(d)/(2^d*prod([0:d]+1/2)) + 1/3^d;%1/h(d)
        I = I / inv_hd;
	I = sqrt(abs(I));
    disp('Error: the subspaces must be one-dimensional for this estimator.');
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