The realization problem for hidden Markov models
type: Item
instance of: scholarly article
title: The realization problem for hidden Markov models
zbMATH Open document ID: 0949.93015
DOI: 10.1007/PL00009846
author: Brian D. O. Anderson
published in: MCSS. Mathematics of Control, Signals, and Systems
publication date: 2000-12-11T00:00:00Z
review text: Let \(X\) be a discrete-time finite-state Markov process and let \(Y=h(X,Z)\), where \(Z\) is some i.i.d. sequence, and where the output \(Y\) can take a finite number of values. This paper considers the realization question: given the probabilities of all finite-length output strings, under what circumstances and how can one construct an \(X\) as above and a mapping \(h\) as above such that for some \(Z\) as above \(Y=h(X,Z)\) generates finite-length output strings with the given probabilities. The theory presented in this paper is an extension of recent theoretical developments in the positive realization problem of linear system theory. This paper is clearly written and ends with a section ``conclusion'' that stimulates further research in this area.
Mathematics Subject Classification ID: 93B15
Mathematics Subject Classification ID: 93E03
zbMATH DE Number: 1310094
zbMATH Keywords: hidden Markov models
zbMATH Keywords: discrete-time finite-state Markov process
zbMATH Keywords: positive realization problem
zbMATH Keywords: linear system theory
reviewed by: Johannes W. Nieuwenhuis
MaRDI profile type: Publication
full work available at URL: pl00009846
OpenAlex ID: W2086073068
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description: scientific article; zbMATH DE number 1310094