Original title: Recursive Estimation of High-Order Markov Chains: Approximation by Finite Mixtures
Authors: Kárný, Miroslav
Document type: Research reports
Year: 2015
Language: eng
Series: Research Report, volume: 2350
Abstract: 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.
Keywords: adaptive systems; approximate parameter estimation; Bayesian recursive estimation; forgetting; Kullback-Leibler divergence; Markov chain
Project no.: GA13-13502S (CEP)
Funding provider: GA ČR

Institution: Institute of Information Theory and Automation AS ČR (web)
Document availability information: Fulltext is available at the institute of the Academy of Sciences.
Original record: http://hdl.handle.net/11104/0247113

Permalink: http://www.nusl.cz/ntk/nusl-187993


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