On the total variation distance of labelled Markov chains

Chen, Taolue and Kiefer, S. (2014) On the total variation distance of labelled Markov chains. In: UNSPECIFIED (ed.) CSL-LICS '14 Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS). New York, U.S.: ACM, 33:1-33:10. ISBN 9781450328869.

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Official URL: https://doi.org/10.1145/2603088.2603099

Abstract

Labelled Markov chains (LMCs) are widely used in probabilistic verification, speech recognition, computational biology, and many other fields. Checking two LMCs for equivalence is a classical problem subject to extensive studies, while the total variation distance provides a natural measure for the "inequivalence" of two LMCs: it is the maximum difference between probabilities that the LMCs assign to the same event. In this paper we develop a theory of the total variation distance between two LMCs, with emphasis on the algorithmic aspects: (1) we provide a polynomial-time algorithm for determining whether two LMCs have distance 1, i.e., whether they can almost always be distinguished; (2) we provide an algorithm for approximating the distance with arbitrary precision; and (3) we show that the threshold problem, i.e., whether the distance exceeds a given threshold, is NP-hard and hard for the square-root-sum problem. We also make a connection between the total variation distance and Bernoulli convolutions.

Metadata

Item Type:	Book Section
School:	Birkbeck Faculties and Schools > Faculty of Science > School of Computing and Mathematical Sciences
Depositing User:	Taolue Chen
Date Deposited:	27 Sep 2017 11:18
Last Modified:	09 Aug 2023 12:42
URI:	https://eprints.bbk.ac.uk/id/eprint/19660

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