## Forward Equations for the Segment HMM

### February 21, 2009

This is a derivation of the forward equations for the Segment HMM to follow on from my last post. Again I should say that this mostly based on Kevin Murphy’s Segment HMM tutorial which you should probably be reading instead of these posts.

## Segment HMMs

### February 21, 2009

I’ve been finding out about segment HMMs. They’re a generalisation of explicit state duration HMMs and a specific case of the hierarchical HMM. I’ll describe them a bit in this post, and then describe the forward algorithm in the next post. Both posts will be culled mostly from Kevin Murphy’s Segment HMM tutorial. All of the errors in this post will be mine, as I’m trying to interpret Kevin’s stuff without using the Dynamic Bayesian Networks, which I’m starting to think is a horrible mistake on my part.

Instead of this post you should probably read a tech report from Cambridge called The Theory of Segmental Hidden Markov Models, which is from the early 90s, and also stuff about hierarchical HMMs, which I think generalise segment HMMs, starting with The Hierarchical Hidden Markov Model: Analysis and Applications by Fine, Singer and Tishby in 1998 and maybe Kevin’s 2001 NIPS paper Linear Time Inference in Hierarchical HMMs.