dd_delta_aic.m

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function e = dd_delta_aic(w,x)
%DD_DELTA_AIC compute the Akaike Information Criterion for MoG
%
% e = dd_delta_aic(w,x)
%
% Compute the (difference in) Akaike Information Criterion of a
% trained model w on data x. In this version we compute:
%
%     e = -2 LL + 2 #param
%
% where LL is the loglikelihood on the set x, and *not* the deviance
% between two models. In order to make it true AIC, you have to
% subtract the LL for the saturated model.
%
% also see dd_error, dd_roc, dd_auc

% Copyright: D. Tax, R.P.W. Duin, [e-mail]
% Faculty of Applied Physics, Delft University of Technology
% P.O. Box 5046, 2600 GA Delft, The Netherlands


[W,labl,map,d] = mapping(w);
if ~is_occ(w)
  error('DD_AIC: this AIC is only defined for one-class classifiers');
end

p = w*x; p = +p(:,1);

switch map
  case 'gauss_dd'
    nrparam = d + d*(d+1)/2;  %mean and cov.matrix
    
  case 'mog_dd'
    c = size(W.m,1);
    [n,d] = size(x);
    covtype = ndims(W.c);
    if ((covtype==2)&(size(W.c,2)==1)), covtype = 1; end

    % the number of parameters
    % for all covariance versions, the priors and the means are the same:
    nrparam = c + c*d;
    switch covtype
      case 1
        nrparam = nrparam + c;
      case 2
        nrparam = nrparam + c*d;
      case 3
        nrparam = nrparam + c*d*(d+1)/2;
      otherwise
        error('Type of covariance matrix not recognized')
    end
  otherwise
    error('AIC cannot be computed for this mapping!');
end

% For the loglikelihood:
e = -2*sum(log(p)) + 2*nrparam;
%strangely this one does not seem to work!:
%e = -2*sum(log(sum(p,2))) + 2*nrparam/n;

return