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

0444151 - ÚTIA 2016 CZ eng V - Výzkumná zpráva
Kárný, Miroslav
Recursive Estimation of High-Order Markov Chains: Approximation by Finite Mixtures.
ÚTIA AV ČR, v.v.i, 2015. 28 s. Research Report, 2350.
Grant CEP: GA ČR GA13-13502S
Institucionální podpora: RVO:67985556
Klíčová slova: Markov chain * approximate parameter estimation * Bayesian recursive estimation * adaptive systems * Kullback-Leibler divergence * forgetting
Kód oboru RIV: BC - Teorie a systémy řízení

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.
Trvalý link: http://hdl.handle.net/11104/0247113