%
% Problem EPage 392
% 
% Examples 9.7
% 
% Written by:
% -- 
% John L. Weatherwax                2008-02-20
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----

%
% use hold-one-out cross validation to estimate the probability of error 
% 1) using a parametric approach (multi-dimensional Gaussian)
% 

%forge=forge(:,1); genuine=genuine(:,1); 
%forge=forge(:,2); genuine=genuine(:,2); 
%forge=forge(:,3); genuine=genuine(:,3); 
%forge=forge(:,4); genuine=genuine(:,4);

ncc = 0; 
[nc_f,d] = size(forge);
[nc_g,d] = size(genuine); 
n = nc_f + nc_g; 

% freeze the estimate of the FORGED data: 
%
mu_f = mean(forge); 
cv_f = cov(forge); 
for i=1:nc_g,         % create a classifier WITHOUT the genuine point "i":
  genuine_train = genuine; 
  x = genuine(i,:);
  genuine_train(i,:)=[];
  mu_g = mean(genuine_train); 
  cv_g = cov(genuine_train); 
  p_g = mvnpdf( x, mu_g, cv_g );
  p_f = mvnpdf( x, mu_f, cv_f ); 
  if( p_g > p_f )    % <- genuine WINS
    ncc=ncc+1; 
  else               % <- genuine LOOSES ... do nothing 
    %
  end
end
% freeze the estimate of the GENUINE data: 
%
mu_g = mean(genuine); 
cv_g = cov(genuine); 
for i=1:nc_f,         % create a classifier WITHOUT the forge point "i":
  forge_train = forge; 
  x = forge(i,:);
  forge_train(i,:)=[];
  mu_f = mean(forge_train); 
  cv_f = cov(forge_train); 
  p_g = mvnpdf( x, mu_g, cv_g );
  p_f = mvnpdf( x, mu_f, cv_f ); 
  if( p_g < p_f )    % <- forge WINS
    ncc=ncc+1; 
  else               % <- forge LOOSES ... do nothing 
    %
  end
end

pcc = ncc/n; 
fprintf('using a multidimensional Gaussian we estimate pcc=%10.5f\n',pcc);