1. Zoltán Szabó
  2. ITE


ITE / code / H_I_D_A_C / meta_estimators / DJensenRenyi_HRenyi_estimation.m

function [D_JR] = DJensenRenyi_HRenyi_estimation(Y1,Y2,co)
%Estimates the Jensen-Renyi divergence of Y1 and Y2 using the relation: 
%D_JR(f_1,f_2) = H_{R,alpha}(w1*y^1+w2*y^2) - [w1*H_{R,alpha}(y^1) + w2*H_{R,alpha}(y^2)], where y^i has density f_i (i=1,2), w1*y^1+w2*y^2 is the mixture distribution of y^1 and y^2 with w1,w2 positive weights, and H_{R,alpha} denotes the Renyi entropy.
%   1)We use the naming convention 'D<name>_estimation' to ease embedding new divergence estimation methods.
%   2)This is a meta method: the Renyi entropy estimator can be arbitrary.
%  Y1: Y1(:,t) is the t^th sample from the first distribution.
%  Y2: Y2(:,t) is the t^th sample from the second distribution.
%  co: divergence estimator object.
%  A.B. Hamza and H. Krim. Jensen-Renyi divergence measure: theoretical and computational perspectives. In IEEE International Symposium on Information Theory (ISIT), page 257, 2003.
%Copyright (C) 2012 Zoltan Szabo ("http://nipg.inf.elte.hu/szzoli", "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 <http://www.gnu.org/licenses/>.


    if size(Y1,1)~=size(Y2,1)
        error('The dimension of the samples in Y1 and Y2 must be equal.');

w = co.w;
mixtureY = mixture_distribution(Y1,Y2,w);
D_JR =  H_estimation(mixtureY,co.member_co) - (w(1)*H_estimation(Y1,co.member_co) + w(2)*H_estimation(Y2,co.member_co));