2026/05/12 by Buu Phan, Gergely Flamich, Ashish Khisti +1 · 1 voice
Computer Science · Mathematics · #Bottleneck #Convergence (economics) #Gaussian Processes and Bayesian Inference #Generative Adversarial Networks and Image Synthesis #Hybrid Monte Carlo #Importance sampling #Markov Chains and Monte Carlo Methods #Markov chain #Markov chain Monte Carlo #Markov process #Monte Carlo method #Variable-order Markov model #cs.IT #stat.CO
paper · pdf · doi:10.48550/arxiv.2605.12807
openalex publication_date 2026/05/12 · arxiv published 2026/05/12 · arxiv updated 2026/05/12 · openalex created_date 2026/05/15 · openalex updated_date 2026/07/28
Convergence diagnosis for Markov chain Monte Carlo is a matter of fundamental importance in computational statistics: it determines the resources allocated to a particular sampling problem and influences the practitioner's view of the quality of estimates obtained from a Markov chain. Motivated by this, we contribute to the emerging class of coupling-based convergence diagnostic algorithms. Concretely, we study coupling multiple Metropolis-Hastings chains using multi-marginal coupling. We introduce a natural objective for this setting and establish lower and upper bounds by drawing connections to list-level distribution coupling and distributed pairwise-matching problems. This analysis ultimately leads to a shared-randomness Poisson Monte Carlo construction for coupling multiple Markov chains. In this process, we avoid a key dimension-dependent bottleneck in the runtime complexity of classical Poisson Monte Carlo by developing an adaptive rule for updating the point process, yielding significant gains in high-dimensional settings. Experiments on grand couplings of Markov chains show that our methods improve coalescence rates across dimensions, reducing meeting times by up to 50% compared with existing baselines.