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Recursive estimation of high-order Markov chains: Approximation by finite mixtures
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SYSNO ASEP 0447119 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Recursive estimation of high-order Markov chains: Approximation by finite mixtures Author(s) Kárný, Miroslav (UTIA-B) RID, ORCID Number of authors 1 Source Title Information Sciences. - : Elsevier - ISSN 0020-0255
Roč. 326, č. 1 (2016), s. 188-201Number of pages 14 s. Publication form Print - P Language eng - English Country US - United States Keywords Markov chain ; Approximate parameter estimation ; Bayesian recursive estimation ; Adaptive systems ; Kullback–Leibler divergence ; Forgetting Subject RIV BC - Control Systems Theory R&D Projects GA13-13502S GA ČR - Czech Science Foundation (CSF) Institutional support UTIA-B - RVO:67985556 UT WOS 000363348400013 EID SCOPUS 84943770986 DOI 10.1016/j.ins.2015.07.038 Annotation A high-order Markov chain is a universal model of stochastic relations between discrete-valued variables. The exact estimation of its transition probabilities suffers from the curse of dimensionality. It requires an excessive amount of informative observations as well as an extreme memory for storing the corresponding sufficient statistic. The paper bypasses this problem by considering a rich subset of Markov-chain models, namely, mixtures of low dimensional Markov chains, possibly with external variables. It uses Bayesian approximate estimation suitable for a subsequent decision making under uncertainty. The proposed recursive (sequential, one-pass) estimator updates a product of Dirichlet probability densities (pds) used as an approximate posterior pd, projects the result back to this class of pds and applies an improved data-dependent stabilised forgetting, which counteracts the dangerous accumulation of approximation errors. Workplace Institute of Information Theory and Automation Contact Markéta Votavová, votavova@utia.cas.cz, Tel.: 266 052 201. Year of Publishing 2016
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