Newsgroups: comp.speech
Path: pavo.csi.cam.ac.uk!pipex!uunet!seas.gwu.edu!marshall
From: marshall@seas.gwu.edu (Christopher Marshall)
Subject: HMM with null transitions
Message-ID: <1992Oct5.192354.9578@seas.gwu.edu>
Originator: marshall@seas.gwu.edu
Sender: news@seas.gwu.edu
Organization: George Washington University
Date: Mon, 5 Oct 1992 19:23:54 GMT
Lines: 33

Hi everyone!  Great newsgroup!

I have been waiting for just such a newsgroup.  I am just starting
my master's thesis in speech recognition and I have been studying
hidden markov models.  I understand most of the technical issues
of HMMs except how to implement null transitions.

I am working with HMMs in which a symbol is output when the model
changes state, as opposed to HMMs where symbols are output when
the model occupies a state.  For transition based HMMs, it is sometimes
useful to consider transitions which do not cause a symbol to be
output.  These are called null transitions.

I have been looking through papers and books on HMMs and can not
find any good discussion on how to incorporate null transitions
into the solution of the evaluation, decoding, and learning 
problems.

I am trying to figure out how to solve the evaluation problem
for an HMM with null transitions.

Specifically:

Let Y1..YT be a random variables representing an output sequence of length
T.

For a given HMM, evaluate P(Y1..YT = y1..yT).

I am dying to understand how this works. Please help!

Chris Marshall
marshall@seas.gwu.edu

