I've implemented the classic HMM model from Rabiner's tutorial for gesture recognition and it has worked well. Now, I'm trying to implement the HMM Threshold Model which calls for an HMM with null transitions.

Null transitions do not provide any output symbols and the threshold model has 2 states which are connected to all the others through null transitions. How do I model this so that I can still use the Viterbi algorithm to evaluate the likelihood of an observed sequence?


In "Statistical methods for speech recognition", Jelinek gives a method of merging null transitions to create a new HMM that emits after every transition.

Alternatively, you might be able to run the Viterbi algorithm on a 3-dimensional lattice (rather than the standard (hidden states) X (emitted symbols) 2d lattice). The best example of this is probably for the Profile HMM ("Profile hidden Markov models." S.R. Eddy).

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