{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/parallel-computations-for-metropolis-markov","title":"Parallel computations for Metropolis Markov chains with Picard maps","arxiv_id":"2506.09762","date":"2025-06-11","proceeding":null,"authors":["Sebastiano Grazzi","Giacomo Zanella"],"abstract":"We develop parallel algorithms for simulating zeroth-order (aka gradient-free) Metropolis Markov chains based on the Picard map. For Random Walk Metropolis Markov chains targeting log-concave distributions $\\pi$ on $\\mathbb{R}^d$, our algorithm generates samples close to $\\pi$ in $\\mathcal{O}(\\sqrt{d})$ parallel iterations with $\\mathcal{O}(\\sqrt{d})$ processors, therefore speeding up the convergence of the corresponding sequential implementation by a factor $\\sqrt{d}$. Furthermore, a modification of our algorithm generates samples from an approximate measure $ \\pi_r$ in $\\mathcal{O}(1)$ parallel iterations and $\\mathcal{O}(d)$ processors. We empirically assess the performance of the proposed algorithms in high-dimensional regression problems, an epidemic model where the gradient is unavailable and a real-word application in precision medicine. Our algorithms are straightforward to implement and may constitute a useful tool for practitioners seeking to sample from a prescribed distribution $\\pi$ using only point-wise evaluations of $\\log\\pi$ and parallel computing.","url_abs":"https://arxiv.org/abs/2506.09762v1","url_pdf":"https://arxiv.org/pdf/2506.09762v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"parallel-computations-for-metropolis-markov","repo_url":"https://github.com/sebagraz/parallelmh","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}