CHAPTER 6 - Hidden Markov Models

Abstract

This chapter elaborates on the Hidden Markov Models (HMM). In general, a HMM is a type of stochastic modeling appropriate for nonstationary stochastic sequences whose statistical properties undergo distinct random transitions among a set of, say, k different stationary processes. HMMs are used to model piecewise stationary processes. A stationary process is one whose statistical properties do not change with time. It is assumed that a set of observations (feature vectors), x1, x2, . , xN Є Rl are given. Each observation is allowed to be generated (emitted) by a different source. Each source is described by different statistical properties. Assuming two sources (stationary processes), k = 2, one may generate data points sequentially, according to either a Gaussian or a Chi-square distribution. Each observation may have been emitted by either of the two sources, but one does not have access to that information. A hidden Markov model is a way to model such a nonstationary process. During recognition, it is assumed that one has more than one HMM, each one described by a different set of parameters. Each HMM models a different piecewise stationary process. Given an observation sequence and a number, M, of HMMs (each one modeling a different process), the goal of the recognition phase is to decide which one of the HMMs is more likely to have emitted the received sequence.