{"paper":{"title":"Multi-Marginal Couplings for Metropolis-Hastings","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"Multi-marginal couplings with adaptive Poisson Monte Carlo reduce meeting times for multiple Metropolis-Hastings chains by up to 50 percent.","cross_cats":["cs.IT","math.IT"],"primary_cat":"stat.CO","authors_text":"Ashish Khisti, Buu Phan, Gergely Flamich, Shahab Asoodeh","submitted_at":"2026-05-12T22:59:47Z","abstract_excerpt":"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"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"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.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The adaptive rule for updating the point process preserves the validity of the multi-marginal coupling while removing the dimension-dependent runtime bottleneck.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Multi-marginal couplings combined with an adaptive shared-randomness Poisson Monte Carlo method improve coalescence rates for multiple Metropolis-Hastings chains, cutting meeting times by up to 50%.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Multi-marginal couplings with adaptive Poisson Monte Carlo reduce meeting times for multiple Metropolis-Hastings chains by up to 50 percent.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"761a91710c71190b481c718f40b9413a03e1b2a68b26c3c18f43f60185324094"},"source":{"id":"2605.12807","kind":"arxiv","version":1},"verdict":{"id":"d49ce706-634f-41b9-8051-cc91f3a2477d","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T19:18:35.114651Z","strongest_claim":"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.","one_line_summary":"Multi-marginal couplings combined with an adaptive shared-randomness Poisson Monte Carlo method improve coalescence rates for multiple Metropolis-Hastings chains, cutting meeting times by up to 50%.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The adaptive rule for updating the point process preserves the validity of the multi-marginal coupling while removing the dimension-dependent runtime bottleneck.","pith_extraction_headline":"Multi-marginal couplings with adaptive Poisson Monte Carlo reduce meeting times for multiple Metropolis-Hastings chains by up to 50 percent."},"references":{"count":29,"sample":[{"doi":"","year":1903,"title":"Pairwise optimal coupling of multiple random variables.arXiv preprint arXiv:1903.00632, 2019","work_id":"8f80251f-30e1-429b-9f28-02dc1dec5c4c","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2019,"title":"Estimating convergence of markov chains with l-lag couplings.Advances in neural information processing systems, 32, 2019","work_id":"e604119b-7365-4b2b-98fa-5d2b4af1ae95","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1998,"title":"General methods for monitoring convergence of iterative simulations.Journal of computational and graphical statistics, 7(4):434–455, 1998","work_id":"0142c83a-1763-4050-97d9-3822e1a47301","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2025,"title":"A coupling-based approach to f-divergences diagnostics for markov chain monte carlo.arXiv preprint arXiv:2510.07559, 2025","work_id":"7c4ca0bb-e7de-409e-a53a-a22607eba396","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2025,"title":"Coupling without communi- cation and drafter-invariant speculative decoding","work_id":"72c1ef01-9d86-40ed-8b59-2c45ff68ebba","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":29,"snapshot_sha256":"5381f48e6a7fc5aaf43e51e262a3acddf7b0c36a5d77544ac5ff3c16990d0342","internal_anchors":1},"formal_canon":{"evidence_count":2,"snapshot_sha256":"af774157885fce277b8851c63a1f15f1547ee5c08103bd80fcc275cfc3f7e52e"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}