# ITE / code / H_I_D / base_estimators / DMMDonline_estimation.m

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 function [D] = DMMDonline_estimation(X,Y,co) %Estimates divergence (D) of X and Y (X(:,t), Y(:,t) is the t^th sample) using the MMD (maximum mean discrepancy) method, online. The number of samples in X [=size(X,2)] and Y [=size(Y,2)] must be equal. Cost parameters are provided in the cost object co. % %We make use of the naming convention 'D_estimation', to ease embedding new divergence estimation methods. % %REFERENCE: % Arthur Gretton, Karsten M. Borgwardt, Malte J. Rasch, Bernhard Schölkopf and Alexander Smola. A Kernel Two-Sample Test. Journal of Machine Learning Research 13 (2012) 723-773. See Lemma 14. % %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 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 . %co.mult:OK. %verification: [dX,num_of_samplesX] = size(X); [dY,num_of_samplesY] = size(Y); %size(X) must be equal to size(Y): if num_of_samplesX~=num_of_samplesY disp('Warning: there must be equal number of samples in X and Y. Minimum of the sample numbers has been taken.'); end if dX~=dY disp('Error: the dimension of X and Y must be equal.'); end num_of_samples = min(num_of_samplesX,num_of_samplesY); %Number of samples must be even: if ~all_even(num_of_samples) disp('Warning: the number of samples must be even, the last sample is discarded.'); num_of_samples = num_of_samples - 1; end %initialization: odd_indices = [1:2:num_of_samples]; even_indices = [2:2:num_of_samples]; %Xi,Xj,Yi,Yj: Xi = X(:,odd_indices); Xj = X(:,even_indices); Yi = Y(:,odd_indices); Yj = Y(:,even_indices); D = (K(Xi,Xj,co) + K(Yi,Yj,co) - K(Xi,Yj,co) - K(Xj,Yi,co)) / (num_of_samples/2); %----------------------------- function [s] = K(U,V,co) %Computes \sum_i kernel(U(:,i),V(:,i)), RBF (Gaussian) kernel is used with std=co.sigma s = sum( exp(-sum((U-V).^2,1)/(2*co.sigma^2)) ); 
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