Equivalence of Hidden Markov Models with Continuous Observations

Authors Oscar Darwin , Stefan Kiefer



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Author Details

Oscar Darwin
  • Department of Computer Science, Oxford University, UK
Stefan Kiefer
  • Department of Computer Science, Oxford University, UK

Acknowledgements

he authors would like to thank anonymous reviewers for their helpful comments and Nikhil Balaji for useful discussions on polynomial identity testing.

Cite AsGet BibTex

Oscar Darwin and Stefan Kiefer. Equivalence of Hidden Markov Models with Continuous Observations. In 40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 182, pp. 43:1-43:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)
https://doi.org/10.4230/LIPIcs.FSTTCS.2020.43

Abstract

We consider Hidden Markov Models that emit sequences of observations that are drawn from continuous distributions. For example, such a model may emit a sequence of numbers, each of which is drawn from a uniform distribution, but the support of the uniform distribution depends on the state of the Hidden Markov Model. Such models generalise the more common version where each observation is drawn from a finite alphabet. We prove that one can determine in polynomial time whether two Hidden Markov Models with continuous observations are equivalent.

Subject Classification

ACM Subject Classification
  • Theory of computation → Random walks and Markov chains
  • Mathematics of computing → Stochastic processes
  • Theory of computation → Logic and verification
Keywords
  • Markov chains
  • equivalence
  • probabilistic systems
  • verification

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