Mathematical Perspectives on Neural Networks

By Paul Smolensky; Michael C. Mozer et al. | Go to book overview

17 Hidden Markov Models and Some Connections with Artificial Neural Nets

Arthur Nádas and Robert L. Mercer

IBM T.J. Watson Research Center


1. INTRODUCTION

One of the motivating forces behind the mathematical development of hidden Markov models1 has been the need of statisticians, engineers, and computer scientists for time-series models that are at the same time sufficiently simple for practical computation and sufficiently complex to allow effective modeling of highly nonstationary processes. The list of such processes includes sampled versions of continuous processes, such as the speech signal, the various signals arising in image processing, signals associated with handwriting, and the like. The list also includes inherently discrete processes, such as those arising in the textual (as opposed to acoustic) study of language, statistical language translation, and coding. Another force behind this development was the emergence of the finite-state machine as a basic tool of computer science.

The seminal work in the mathematical development of HMMs is that of Baum ( 1972) and his collaborators ( Baum & Egon 1967, Baum & Petrie 1966, Baum, Petries, Soules, & Weiss 1970, Baum & Sell 1968, Ferguson, ed. 1980). The algorithmic aspect of this work was paralleled, extended, and applied to the problems of coding, large vocabulary natural language continuous speech recognition, probabilistic parsing, and statistical language translation by Bahl and Jelinek ( 1975); Bahl, Cocke, Jelinek, and Raviv ( 1974); Bahl, Jelinek, and Mercer ( 1983); Bakis ( 1976); Brown et al. ( 1990); and Jelinek ( 1969, 1975, 1976, 1985). For an early independent use of HMMs in speech recognition see

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1
HMMs are also called 'Markov source models' in communications engineering and information theory. The name 'probabilistic functions of Markov chains' is also in use.

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