Computing X_i in the foward-backward function

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What steps will reproduce the problem?
Looking at the code, I think there is a problem with one of the equations.


What is the expected output? What do you see instead?

As per Equation 37 in Rabiner's paper*, I think the Xi_t denominator/numerator  
should be calculated with the (t)'th element from the alpha table, whereas in 
the code, the (t+1)'th element from the alpha table is used.

In other words, I believe this is what the code should look like:

 Xi_t_denominator = self.__log_add(Xi_t_denominator, self.alpha_table[t][st_from] + self.trans_matrix[st_from][st_to] + self.emit_matrix[st_to][ot_next] + self.beta_table[t + 1][st_to])

* A Tutorial on Hidden Markov Models and Selected Applications in Speech 
Recognition, Rabiner, L.R., IEEE, 1989

What version of the product are you using? On what operating system?

Windows 7, Jan 1 2013 version of the hmm_faster.py

Original issue reported on code.google.com by [email protected] on 9 Oct 2013 at 8:46