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

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  • Travers, Nicholas F.

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.

Suggested Citation

  • Travers, Nicholas F., 2014. "Exponential bounds for convergence of entropy rate approximations in hidden Markov models satisfying a path-mergeability condition," Stochastic Processes and their Applications, Elsevier, vol. 124(12), pages 4149-4170.
    • Handle: RePEc:eee:spapps:v:124:y:2014:i:12:p:4149-4170
    DOI: 10.1016/j.spa.2014.07.011
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    References listed on IDEAS

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    1. Douc, R. & Fort, G. & Moulines, E. & Priouret, P., 2009. "Forgetting the initial distribution for Hidden Markov Models," Stochastic Processes and their Applications, Elsevier, vol. 119(4), pages 1235-1256, April.
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