Geometry and Duality of Alternating Markov Chains

Deven Mithal; Lorenzo Orecchia

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arXiv · 2410.12721

Geometry and Duality of Alternating Markov Chains

Deven Mithal·Lorenzo Orecchia

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Abstract

In this note, we realize the half-steps of a general class of Markov chains as alternating projections with respect to the reverse Kullback-Leibler divergence between convex sets of joint probability distributions. Using this characterization, we provide a geometric proof of an information-theoretic duality between the Markov chains defined by the even and odd half-steps of the alternating projection scheme.

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Deven Mithal, Lorenzo Orecchia. 2024-10-16. Geometry and Duality of Alternating Markov Chains. https://arxiv.org/abs/2410.12721

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