91 lines
1.8 KiB
Matlab
91 lines
1.8 KiB
Matlab
%% load data:
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x = load('../data/decisions.mat');
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presented = x.presented;
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reported = x.reported;
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%% plot data:
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figure()
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plot(presented, 'ob', 'markersize', 10, 'markerfacecolor', 'b');
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hold on;
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plot(reported, 'or', 'markersize', 5, 'markerfacecolor', 'r');
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hold off
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ylim([0.5, 2.5])
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p1 = sum(presented == 1);
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p2 = sum(presented == 2);
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r1 = sum(reported == 1);
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r2 = sum(reported == 2);
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figure()
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bar([p1, p2, r1, r2]);
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set(gca, 'XTickLabel', {'p1', 'p2', 'r1', 'r2'});
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%% histogram:
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nxy = zeros(2, 2);
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for x = [1, 2]
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for y = [1, 2]
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nxy(x, y) = sum((presented == x) & (reported == y));
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end
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end
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figure()
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bar3(nxy)
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set(gca, 'XTickLabel', {'p1', 'p2'});
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set(gca, 'YTickLabel', {'r1', 'r2'});
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%% normalized histogram:
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pxy = nxy / sum(nxy(:));
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figure()
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imagesc(pxy)
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px = sum(nxy, 2) / sum(nxy(:));
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py = sum(nxy, 1) / sum(nxy(:));
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%% mutual information:
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miv = mi(nxy);
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%% permutation:
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np = 10000;
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mis = zeros(np, 1);
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for k = 1:np
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ppre = presented(randperm(length(presented)));
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prep = reported(randperm(length(reported)));
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pnxy = zeros(2, 2);
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for x = [1, 2]
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for y = [1, 2]
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pnxy(x, y) = sum((ppre == x) & (prep == y));
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end
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end
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mis(k) = mi(pnxy);
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end
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alpha = sum(mis>miv)/length(mis);
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fprintf('signifikance: %g\n', alpha);
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bins = [0.0:0.025:0.4];
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hist(mis, bins)
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hold on;
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plot([miv, miv], [0, np/10], '-r')
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hold off;
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xlabel('MI')
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ylabel('Count')
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%% maximum MI:
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n = 100000;
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pxs = [0:0.01:1.0];
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mis = zeros(length(pxs), 1);
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for k = 1:length(pxs)
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p = rand(n, 1);
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nxy = zeros(2, 2);
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nxy(1, 1) = sum(p<pxs(k));
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nxy(2, 2) = length(p) - nxy(1, 1);
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mis(k) = mi(nxy);
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%nxy(1, 2) = 0;
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%nxy(2, 1) = 0;
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%mi(nxy)
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end
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figure();
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plot(pxs, mis);
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hold on;
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plot([px(1), px(1)], [0, 1], '-r')
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hold off;
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xlabel('p(x=1)')
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ylabel('Max MI=Entropy')
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