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 HMMʹs (Pθ, Qθ), θ ∈ ⊖, and a sequence of observations y1, …, yt from a stochastic process {Yt}t=1∞, find the HMM that has maximum posterior probability of producing y1,…, 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}t= 1∞, our algorithm will converge to the “right” (in the cross entropy sense) HMM as t → ∞, for almost all sequences y1, y2,…. Finally, we give an example of the application of our algorithm to the classification of speech signals.