Short Notes on HMM (Hidden Markov Model)

1. Regarding calibration

Numerical optimization is computatinoal intensive and prone to local max, but it is able to estimate any general model specification. On the other hand, EM algorithms such as Baum-Welch are more reliable in seeking global max, but they are only capable of backing out the parameters of models with distributions that are fully described by moments (Gaussian, Poisson, ...)

2. Problem with HMM, and extensions

As Soltan discusses in his paper, ordinary HMM is by definition prone to instability due to the exponentiated matrix structure. The instability dominates in the long run, meaning that state occupancy duration estimation of ordinary HMM is usually unreliable. There are two ways to go: 1) HSMM (a.k.a. explicit duration HMM, inhomogeneous HMM, etc.), or 2) Treat duration as an extra degree of state space (see Soltan).

References:

http://www.reza-soltan.com/papers/3.pdf

http://sist.sysu.edu.cn/~syu/HSMM_bibliography.htm