{"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/gibbs-flow-for-approximate-transport-with","title":"Gibbs Flow for Approximate Transport with Applications to Bayesian Computation","arxiv_id":"1509.08787","date":"2015-09-29","proceeding":null,"authors":["Jeremy Heng","Arnaud Doucet","Yvo Pokern"],"abstract":"Let $\\pi_{0}$ and $\\pi_{1}$ be two distributions on the Borel space $(\\mathbb{R}^{d},\\mathcal{B}(\\mathbb{R}^{d}))$. Any measurable function $T:\\mathbb{R}^{d}\\rightarrow\\mathbb{R}^{d}$ such that $Y=T(X)\\sim\\pi_{1}$ if $X\\sim\\pi_{0}$ is called a transport map from $\\pi_{0}$ to $\\pi_{1}$. For any $\\pi_{0}$ and $\\pi_{1}$, if one could obtain an analytical expression for a transport map from $\\pi_{0}$ to $\\pi_{1}$, then this could be straightforwardly applied to sample from any distribution. One would map draws from an easy-to-sample distribution $\\pi_{0}$ to the target distribution $\\pi_{1}$ using this transport map. Although it is usually impossible to obtain an explicit transport map for complex target distributions, we show here how to build a tractable approximation of a novel transport map. This is achieved by moving samples from $\\pi_{0}$ using an ordinary differential equation with a velocity field that depends on the full conditional distributions of the target. Even when this ordinary differential equation is time-discretized and the full conditional distributions are numerically approximated, the resulting distribution of mapped samples can be efficiently evaluated and used as a proposal within sequential Monte Carlo samplers. We demonstrate significant gains over state-of-the-art sequential Monte Carlo samplers at a fixed computational complexity on a variety of applications.","url_abs":"https://arxiv.org/abs/1509.08787v2","url_pdf":"https://arxiv.org/pdf/1509.08787v2.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":"gibbs-flow-for-approximate-transport-with","repo_url":"https://github.com/jeremyhengjm/GibbsFlow","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/1509.08787","atlas_url":"https://app.syntology.ai/?focus=1509.08787","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}