A Geometric Reduction Approach for Identity Testing of Reversible Markov Chains

Geoffrey Wolfer; Shun Watanabe

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arXiv · 2302.08059

A Geometric Reduction Approach for Identity Testing of Reversible Markov Chains

Geoffrey Wolfer·Shun Watanabe

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Abstract

We consider the problem of testing the identity of a reversible Markov chain against a reference from a single trajectory of observations. Employing the recently introduced notion of a lumping-congruent Markov embedding, we show that, at least in a mildly restricted setting, testing identity to a reversible chain reduces to testing to a symmetric chain over a larger state space and recover state-of-the-art sample complexity for the problem.

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Geoffrey Wolfer, Shun Watanabe. 2023-02-16. A Geometric Reduction Approach for Identity Testing of Reversible Markov Chains. https://arxiv.org/abs/2302.08059

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