I want to implement the T=Log( f ( x | client) ) - Log( f ( x | impostor) ) for decision boundary. My features for training and testing are 20*12. I have applied the voicebox matlab tool box. I write the following MATLAB code :
if max(lp_client)- max(lp_impostor) >0.35
disp('accept');
else
disp('reject');
end
Should I used mean of Log probability or max of Log probability ?
You should use sum of lp_client because of the probability nature of the estimate. If you have a sequence of independent events (feature independence is often assumed in this model), it's probability is a product of probabilies of the each event:
P (Seq | X ) = P(feat1 | x) * P(feat2 | X) ...
Or in log domain
logP (Seq | X) = logP (feat1 | x) + logP(feat2 | X)
So actually
logP ( x | client) = sum (lp_client)
and
logP(x | impostor) = sum (lp_impostor)