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Log-Likelihood derivatives
We have to minimize  w.r.t.  and .

Therefore, let us calculate its derivatives w.r.t. the hyperparameters :

we get :   
where  = expectation calculated with  X samples
which are images following the probability law :  .
We must also calculate two types of expectations :
   a priori law :  to take into account the constraints
  a posteriori law   w.r.t. the data

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André Jalobeanu - 24 Aug 1998