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85 lines
3.4 KiB
Matlab
85 lines
3.4 KiB
Matlab
function pcbc_prob_1gaussian_prior()
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%Test encoding and decoding of simple, monomodal, gaussian probability distributions when network weights are modified so as to include a prior
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inputs=[-180:5:180];
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centres=[-180:10:180];
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priorMean=0;
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priorStd=60;
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priorDist=code(priorMean,inputs,priorStd);
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%define weights, to produce a 1d basis function network, where nodes have gaussian RFs. Strength of RFs is modulated by prior distribution.
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W=[];
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for c=centres
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W=[W;code(c,inputs,10,0,1).*priorDist];
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end
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[n,m]=size(W);
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%define test cases
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stdx=20;
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X=zeros(m,3);
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X(:,1)=code(93,inputs,20,0,0,stdx)';
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X(:,2)=code(93,inputs,30,0,0,stdx)';
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X(:,3)=code(-30,inputs,20,0,0,stdx)';
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X(:,4)=code(-30,inputs,40,0,0,stdx)';
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for k=1:size(X,2)
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x=X(:,k);
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[y,e,r]=dim_activation(W,x);
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figure(k),clf
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plot_result1(x,r,y,inputs,centres);
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plot(x'.*priorDist,'LineWidth',3); %plot true posterior
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print(gcf, '-dpdf', ['probability_1gaussian_prior',int2str(k),'.pdf']);
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end
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%test performance over many trials
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trials=1e5
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compare_means=zeros(trials,3);
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compare_vars=zeros(trials,3);
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for k=1:trials
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likelihoodMean=180*rand-90;
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likelihoodStd=15+30*rand;
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x=code(likelihoodMean,inputs,likelihoodStd,1,0,stdx)'; %noisy PPC
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[y,e,r]=dim_activation(W,x);
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[posteriortrueMean,posteriortrueVar]=stats_gaussian_combination([likelihoodMean,priorMean],[likelihoodStd.^2,priorStd.^2]);
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[likelihoodmuact,likelihoodvaract]=decode(x',inputs);
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[posteriormuact, posteriorvaract]=stats_gaussian_combination([likelihoodmuact,priorMean],[likelihoodvaract,priorStd.^2]);
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[posteriormuest,posteriorvarest]=decode(r',inputs);
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compare_means(k,:)=[posteriortrueMean,posteriormuact,posteriormuest];
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compare_vars(k,:)=[posteriortrueVar,posteriorvaract,posteriorvarest];
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end
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toplot=1:100;
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figure(size(X,2)+1),clf
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plot(compare_means(toplot,2),compare_means(toplot,3),'o','MarkerFaceColor','b','MarkerSize',6);
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hold on
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plot([-100,100],[-100,100],'k--','LineWidth',2)
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set(gca,'YTick',[-90:90:90],'XTick',[-90:90:90],'FontSize',15)
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axis('equal','tight')
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xlabel('Optimal Estimate of Mean ');
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ylabel('Network Estimate of Mean ')
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set(gcf,'PaperSize',[10 8],'PaperPosition',[0 0.25 10 7.5],'PaperOrientation','Portrait');
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print(gcf, '-dpdf', ['probability_1gaussian_prior_mean_accuracy.pdf']);
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figure(size(X,2)+2),clf
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plot(compare_vars(toplot,2),compare_vars(toplot,3),'o','MarkerFaceColor','b','MarkerSize',6);
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hold on
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plot([100,1500],[100,1500],'k--','LineWidth',2)
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set(gca,'YTick',[400:400:1200],'YTickLabel',' ','XTick',[400:400:1200],'FontSize',15)
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text([100,100,100]-10,[400:400:1200],int2str([400:400:1200]'),'Rotation',90,'VerticalAlignment','bottom','HorizontalAlignment','center','FontSize',15)
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axis('equal','tight')
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xlabel({'Optimal Estimate of \sigma^2 ';' '});
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ylabel({'Network Estimate of \sigma^2 ';' '});
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set(gcf,'PaperSize',[10 8],'PaperPosition',[0 0.25 10 7.5],'PaperOrientation','Portrait');
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print(gcf, '-dpdf', ['probability_1gaussian_prior_var_accuracy.pdf']);
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error=abs(compare_means(:,2)-compare_means(:,3));
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disp('Comparing Means (difference between network and optimal estimate)')
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disp([' Max=',num2str(max(error)),' Median=',num2str(median(error)),' Mean=',num2str(mean(error))]);
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error=100.*abs(compare_vars(:,2)-compare_vars(:,3))./compare_vars(:,2);
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disp('Comparing Variances (% difference between network and optimal estimate)')
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disp([' Max=',num2str(max(error)),' Median=',num2str(median(error)),' Mean=',num2str(mean(error))]);
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