Bayesian classification of Hidden Markov Models

We develop a recursive maximum a posteriori classification algorithm for discrete valued stochastic processes modelled by Hidden Markov Models. The classification algorithm solves recursively the following problem: given a collection of HMM's (P-theta,Q(theta)), theta epsilon theta, and a sequence of observations y1,...,yt from a stochastic process {Y-t}(infinity)(t=1), find the HMM that has maximum posterior probability of producing yl,...,yt. This algorithm is a modification (for discrete valued stochastic processes) of the Lainiotis partition algorithm [1,2]. We prove that, subject to ergodicity and positivity assumptions on {Yt}(infinity)(t=1), our algorithm will converge to the ''right'' (in the cross entropy sense) HMM as t --> infinity, for almost all sequences y(1), y(2),.... Finally, we give an example of the application of our algorithm to the classification of speech signals.