# ITE / code / H_I_D_A_C / base_estimators / DMMD_online_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 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 function [D] = DMMD_online_estimation(Y1,Y2,co) %Estimates divergence (D) of Y1 and Y2 using the MMD (maximum mean discrepancy) method, online. % %We use the naming convention 'D_estimation' to ease embedding new divergence estimation methods. % %INPUT: % Y1: Y1(:,t) is the t^th sample from the first distribution. % Y2: Y2(:,t) is the t^th sample from the second distribution. Note: the number of samples in Y1 [=size(Y1,2)] and Y2 [=size(Y2,2)] must be equal; otherwise their minimum is taken. % co: divergence estimator object. % %REFERENCE: % Arthur Gretton, Karsten M. Borgwardt, Malte J. Rasch, Bernhard Scholkopf 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/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 . %co.mult:OK. %verification: [dY1,num_of_samplesY1] = size(Y1); [dY2,num_of_samplesY2] = size(Y2); %size(Y1) must be equal to size(Y2): if num_of_samplesY1~=num_of_samplesY2 warning('There must be equal number of samples in Y1 and Y2 for this estimator. Minimum of the sample numbers has been taken.'); end if dY1~=dY2 error('The dimension of the samples in Y1 and Y2 must be equal.'); end num_of_samples = min(num_of_samplesY1,num_of_samplesY2); %Number of samples must be even: if ~all_even(num_of_samples) 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]; %Y1i,Y1j,Y2i,Y2j: Y1i = Y1(:,odd_indices); Y1j = Y1(:,even_indices); Y2i = Y2(:,odd_indices); Y2j = Y2(:,even_indices); switch co.kernel case 'RBF' D = (K_RBF(Y1i,Y1j,co) + K_RBF(Y2i,Y2j,co) - K_RBF(Y1i,Y2j,co) - K_RBF(Y1j,Y2i,co)) / (num_of_samples/2); case 'linear' D = (K_linear(Y1i,Y1j) + K_linear(Y2i,Y2j) - K_linear(Y1i,Y2j) - K_linear(Y1j,Y2i)) / (num_of_samples/2); otherwise error('Kernel=?'); end %----------------------------- function [s] = K_RBF(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)) ); %-------- function [s] = K_linear(U,V) %Computes \sum_i kernel(U(:,i),V(:,i)) in case of a linear kernel s = sum(dot(U,V)); 
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