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Recursive Estimation of High-Order Markov Chains: Approximation by Finite Mixtures
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SYSNO ASEP 0444151 Document Type V - Research Report R&D Document Type The record was not marked in the RIV Title Recursive Estimation of High-Order Markov Chains: Approximation by Finite Mixtures Author(s) Kárný, Miroslav (UTIA-B) RID, ORCID Number of authors 1 Issue data ÚTIA AV ČR, v.v.i, 2015 Series Research Report Series number 2350 Number of pages 28 s. Publication form Print - P Language eng - English Country CZ - Czech Republic 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 Annotation A high-order Markov chain is a universal model of stochastic relations between discrete-valued variables. The exact estimation of its transition probabilities suers from the curse of dimensionality. It requires an excessive amount of informative observations as well as an extreme memory for storing the corresponding su cient 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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