New arXiv paper factorizes multivariate Markov chains to speed up MCMC mixing
michaelchchoi · x · 2026-10-01
Michael C.H. Choi, Youjia Wang and Geoffrey Wolfer released an arXiv paper on the geometry and factorization of multivariate Markov chain transition matrices.
- Shows induced chains on factors of a product space are information projections under KL divergence
- Yields Han-Shearer type inequalities and submodularity of Markov chain entropy rate, with applications to large deviations and mixing time comparison
- Algorithmically, projection samplers based on lifted MCMC, a swapping algorithm, and factored filtering provably mix faster than the originals
- The swapping-based projection sampler resamples the highest-temperature coordinate each step, with mixing-time speedups proportional to temperature count and state-space dimension; bimodal numerical experiments confirm effectiveness
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