Context Tree Estimation in Variable Length Hidden Markov Models

Details Context Tree Estimation in Variable Length Hidden Markov Models Context Tree Estimation in Variable Length Hidden Markov Models

2011-09-02

arxiv.org/abs/1109.0392v2

Computer Science

Information Theory

Scientific paper

We address the issue of context tree estimation in variable length hidden Markov models. We propose an estimator of the context tree of the hidden Markov process which needs no prior upper bound on the depth of the context tree. We prove that the estimator is strongly consistent. This uses information-theoretic mixture inequalities in the spirit of Finesso and Lorenzo(Consistent estimation of the order for Markov and hidden Markov chains(1990)) and E.Gassiat and S.Boucheron (Optimal error exponents in hidden Markov model order estimation(2003)). We propose an algorithm to efficiently compute the estimator and provide simulation studies to support our result.

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