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Recursive Estimation of High-Order Markov Chains: Approximation by Finite Mixtures

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    SYSNO ASEP0444151
    Document TypeV - Research Report
    R&D Document TypeThe record was not marked in the RIV
    TitleRecursive Estimation of High-Order Markov Chains: Approximation by Finite Mixtures
    Author(s) Kárný, Miroslav (UTIA-B) RID, ORCID
    Number of authors1
    Issue dataÚTIA AV ČR, v.v.i, 2015
    SeriesResearch Report
    Series number2350
    Number of pages28 s.
    Publication formPrint - P
    Languageeng - English
    CountryCZ - Czech Republic
    KeywordsMarkov chain ; approximate parameter estimation ; Bayesian recursive estimation ; adaptive systems ; Kullback-Leibler divergence ; forgetting
    Subject RIVBC - Control Systems Theory
    R&D ProjectsGA13-13502S GA ČR - Czech Science Foundation (CSF)
    Institutional supportUTIA-B - RVO:67985556
    AnnotationA 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.
    WorkplaceInstitute of Information Theory and Automation
    ContactMarkéta Votavová, votavova@utia.cas.cz, Tel.: 266 052 201.
    Year of Publishing2016
Number of the records: 1  

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