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Classification Among Hidden Markov Models

Authors S. Akshay, Hugo Bazille, Eric Fabre, Blaise Genest



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Author Details

S. Akshay
  • IIT Bombay, India
Hugo Bazille
  • Univ Rennes, Inria, IRISA, France
Eric Fabre
  • Univ Rennes, Inria, IRISA, France
Blaise Genest
  • Univ Rennes, CNRS, IRISA, France

Acknowledgements

We would like to thank Stefan Kiefer for his expert opinion, as well as anonymous reviewers for their constructive comments.

Cite AsGet BibTex

S. Akshay, Hugo Bazille, Eric Fabre, and Blaise Genest. Classification Among Hidden Markov Models. In 39th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 150, pp. 29:1-29:14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2019)
https://doi.org/10.4230/LIPIcs.FSTTCS.2019.29

Abstract

An important task in AI is one of classifying an observation as belonging to one class among several (e.g. image classification). We revisit this problem in a verification context: given k partially observable systems modeled as Hidden Markov Models (also called labeled Markov chains), and an execution of one of them, can we eventually classify which system performed this execution, just by looking at its observations? Interestingly, this problem generalizes several problems in verification and control, such as fault diagnosis and opacity. Also, classification has strong connections with different notions of distances between stochastic models. In this paper, we study a general and practical notion of classifiers, namely limit-sure classifiers, which allow misclassification, i.e. errors in classification, as long as the probability of misclassification tends to 0 as the length of the observation grows. To study the complexity of several notions of classification, we develop techniques based on a simple but powerful notion of stationary distributions for HMMs. We prove that one cannot classify among HMMs iff there is a finite separating word from their stationary distributions. This provides a direct proof that classifiability can be checked in PTIME, as an alternative to existing proofs using separating events (i.e. sets of infinite separating words) for the total variation distance. Our approach also allows us to introduce and tackle new notions of classifiability which are applicable in a security context.

Subject Classification

ACM Subject Classification
  • Theory of computation
Keywords
  • verification: probabilistic systems
  • partially observable systems

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References

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