Identity Testing of Reversible Markov Chains

Sela Fried, Geoffrey Wolfer

Research output: Contribution to journalConference articlepeer-review

5 Scopus citations


We consider the problem of identity testing of Markov chain transition matrices based on a single trajectory of observations under the distance notion introduced by Daskalakis et al. (2018a) and further analyzed by Cherapanamjeri and Bartlett (2019). Both works made the restrictive assumption that the Markov chains under consideration are symmetric. In this work we relax the symmetry assumption and show that it is possible to perform identity testing under the much weaker assumption of reversibility, provided that the stationary distributions of the reference and of the unknown Markov chains are close under a distance notion related to the separation distance. Additionally, we provide intuition on the distance notion of Daskalakis et al. (2018a) by showing how it behaves under several natural operations. In particular, we address some of their open questions.

Original languageEnglish
Pages (from-to)798-817
Number of pages20
JournalProceedings of Machine Learning Research
StatePublished - 1 Jan 2022
Event25th International Conference on Artificial Intelligence and Statistics, AISTATS 2022 - Virtual, Online, Spain
Duration: 28 Mar 202230 Mar 2022

ASJC Scopus subject areas

  • Artificial Intelligence
  • Software
  • Control and Systems Engineering
  • Statistics and Probability


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