% Demonstrate different shrinkage priors for spm_mlm_bayes

clear all
close all

N=100;
d=10;
p=5;


x=randn(N,p);
W=randn(p,d);
W(4:5,:)=0;
e=2*randn(N,d);

y=x*W+e;
verbose=1;

% Global shrinkage 
mlm_global = spm_mlm_bayes (y,x,'global',verbose);

% Input-specific shrinkage 
mlm_in = spm_mlm_bayes (y,x,'input',verbose);

% Output-specific shrinkage
mlm_out = spm_mlm_bayes (y,x,'output',verbose);

disp('Comparison of shrinkage priors');
disp(sprintf('Log evidence for IS versus global = %1.2f',mlm_in.fm-mlm_global.fm));
disp(sprintf('Log evidence for OS versus global = %1.2f',mlm_out.fm-mlm_global.fm));
disp(sprintf('Log evidence for IS versus OS = %1.2f',mlm_in.fm-mlm_out.fm));

mlm=mlm_in;

figure
imagesc(mlm.wmean);
colormap gray
colorbar
ylabel('Inputs');
xlabel('Outputs');
title('Bayes Regression Coefficients');

figure
imagesc(mlm.wml);
colormap gray
colorbar
ylabel('Inputs');
xlabel('Outputs');
title('ML Regression Coefficients');