Hidden Markov Chains, the Forward-Backward Algorithm, and Initial Statistics

Abstract

The objects listed in the title have proven to be useful and practical modeling tools in continuous speech recognition work and elsewhere. Nevertheless, there are natural and simple situations in which the forward-backward algorithm will be inadequate for its intended purpose of finding useful maximum likelihood estimates of the parameters of the distribution of a probabilistic function of a Markov chain (a “hidden Markov model” or “Markov source model”). We observe some difficulties that arise in the case of common (e.g., Gaussian) families of conditional distributions for the observables. These diffitions of Markov chains,” Ann. Math. Statist., vol. 41, pp. 164171,1970. Copyright © 1983 by The Institute of Electrical and Electronics Engineers, Inc.