Hidden Markov processes

• Published in: IEEE transactions on information theory Vol. 48; no. 6; pp. 1518 - 1569
• Main Authors: Ephraim, Y., Merhav, N.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.06.2002; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Asymptotic properties; Autoregressive processes; Channels; Decoding; Density; Discrete time systems; Encoding; Entropy; Ergodic processes; Estimating; Hidden Markov models; Information; Markov processes; Maximum likelihood estimation; Memoryless systems; Reviews; State estimation; Statistics; Theory
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2002.1003838

An overview of statistical and information-theoretic aspects of hidden Markov processes (HMPs) is presented. An HMP is a discrete-time finite-state homogeneous Markov chain observed through a discrete-time memoryless invariant channel. In recent years, the work of Baum and Petrie (1966) on finite-state finite-alphabet HMPs was expanded to HMPs with finite as well as continuous state spaces and a general alphabet. In particular, statistical properties and ergodic theorems for relative entropy densities of HMPs were developed. Consistency and asymptotic normality of the maximum-likelihood (ML) parameter estimator were proved under some mild conditions. Similar results were established for switching autoregressive processes. These processes generalize HMPs. New algorithms were developed for estimating the state, parameter, and order of an HMP, for universal coding and classification of HMPs, and for universal decoding of hidden Markov channels. These and other related topics are reviewed.