Exponential bounds for convergence of entropy rate approximations in hidden Markov models satisfying a path-mergeability condition

Nicholas F. Travers

Stochastic Processes and their Applications, 2014, vol. 124, issue 12, 4149-4170

Abstract: A hidden Markov model (HMM) is said to have path-mergeable states if for any two states i,j there exist a word w and state k such that it is possible to transition from both i and j to k while emitting w. We show that for a finite HMM with path-mergeable states the block estimates of the entropy rate converge exponentially fast. We also show that the path-mergeability property is asymptotically typical in the space of HMM topologies and easily testable.

Keywords: Hidden Markov model; Entropy rate; Exponential convergence; Path-mergeable (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1016/j.spa.2014.07.011

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