Exponential Bounds for Convergence of Entropy Rate Approximations in Hidden Markov Models Satisfying a Path-Mergeability Condition

Nicholas F. Travers

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arXiv · 1211.6181

Exponential Bounds for Convergence of Entropy Rate Approximations in Hidden Markov Models Satisfying a Path-Mergeability Condition

Nicholas F. Travers

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Abstract

A hidden Markov model (HMM) is said to have path-mergeable states if for any two states i,j there exists 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 topolgies and easily testable.

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BibTeX RIS

Nicholas F. Travers. 2012-11-27. Exponential Bounds for Convergence of Entropy Rate Approximations in Hidden Markov Models Satisfying a Path-Mergeability Condition. https://arxiv.org/abs/1211.6181

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