{"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/transport-monte-carlo","title":"Transport Monte Carlo: High-Accuracy Posterior Approximation via Random Transport","arxiv_id":"1907.10448","date":"2019-07-24","proceeding":null,"authors":["Leo L. Duan"],"abstract":"In Bayesian applications, there is a huge interest in rapid and accurate estimation of the posterior distribution, particularly for high dimensional or hierarchical models. In this article, we propose to use optimization to solve for a joint distribution (random transport plan) between two random variables, $\\theta$ from the posterior distribution and $\\beta$ from the simple multivariate uniform. Specifically, we obtain an approximate estimate of the conditional distribution $\\Pi(\\beta\\mid \\theta)$ as an infinite mixture of simple location-scale changes; applying the Bayes' theorem, $\\Pi(\\theta\\mid\\beta)$ can be sampled as one of the reversed transforms from the uniform, with the weight proportional to the posterior density/mass function. This produces independent random samples with high approximation accuracy, as well as nice theoretic guarantees. Our method shows compelling advantages in performance and accuracy, compared to the state-of-the-art Markov chain Monte Carlo and approximations such as variational Bayes and normalizing flow. We illustrate this approach via several challenging applications, such as sampling from multi-modal distribution, estimating sparse signals in high dimension, and soft-thresholding of a graph with a prior on the degrees.","url_abs":"https://arxiv.org/abs/1907.10448v6","url_pdf":"https://arxiv.org/pdf/1907.10448v6.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":"transport-monte-carlo","repo_url":"https://github.com/leoduan/TransportMonteCarlo","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"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}