Analyticity of Entropy Rates of Continuous-State Hidden Markov Models

Vladislav Z. B. Tadić, Arnaud Doucet

Research output: Contribution to journalArticle (Academic Journal)peer-review

1 Citation (Scopus)

Abstract

The analyticity of the entropy and relative entropy rates of continuous-state hidden Markov models is studied here. Using the analytic continuation principle and the stability properties of the optimal filter, the analyticity of these rates is shown for analytically parameterized models. The obtained results hold under relatively mild conditions and cover several classes of hidden Markov models met in practice. These results are relevant for several (theoretically and practically) important problems arising in statistical inference, system identification and information theory.
Original languageEnglish
Article number8804216
Pages (from-to)7950-7975
Number of pages26
JournalIEEE Transactions on Information Theory
Volume65
Issue number12
Early online date16 Aug 2019
DOIs
Publication statusPublished - 20 Nov 2019

Keywords

  • Hidden Markov models
  • entropy rate
  • relative entropy rate
  • log-likelihood
  • optimal filter
  • analytical continuation

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