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A rate-distortion framework for MCMC algorithms: geometry and factorization of multivariate Markov chains
- Publication Year :
- 2024
-
Abstract
- We introduce a framework rooted in a rate distortion problem for Markov chains, and show how a suite of commonly used Markov Chain Monte Carlo (MCMC) algorithms are specific instances within it, where the target stationary distribution is controlled by the distortion function. Our approach offers a unified variational view on the optimality of algorithms such as Metropolis-Hastings, Glauber dynamics, the swapping algorithm and Feynman-Kac path models. Along the way, we analyze factorizability and geometry of multivariate Markov chains. Specifically, we demonstrate that induced chains on factors of a product space can be regarded as information projections with respect to a particular divergence. This perspective yields Han--Shearer type inequalities for Markov chains as well as applications in the context of large deviations and mixing time comparison.<br />Comment: 63 pages, 6 figures
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2404.12589
- Document Type :
- Working Paper