{"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/truncated-log-concave-sampling-with","title":"Truncated Log-concave Sampling with Reflective Hamiltonian Monte Carlo","arxiv_id":"2102.13068","date":"2021-02-25","proceeding":null,"authors":["Apostolos Chalkis","Vissarion Fisikopoulos","Marios Papachristou","Elias Tsigaridas"],"abstract":"We introduce Reflective Hamiltonian Monte Carlo (ReHMC), an HMC-based algorithm, to sample from a log-concave distribution restricted to a convex body. We prove that, starting from a warm start, the walk mixes to a log-concave target distribution $\\pi(x) \\propto e^{-f(x)}$, where $f$ is $L$-smooth and $m$-strongly-convex, within accuracy $\\varepsilon$ after $\\widetilde O(\\kappa d^2 \\ell^2 \\log (1 / \\varepsilon))$ steps for a well-rounded convex body where $\\kappa = L / m$ is the condition number of the negative log-density, $d$ is the dimension, $\\ell$ is an upper bound on the number of reflections, and $\\varepsilon$ is the accuracy parameter. We also developed an efficient open source implementation of ReHMC and we performed an experimental study on various high-dimensional data-sets. The experiments suggest that ReHMC outperfroms Hit-and-Run and Coordinate-Hit-and-Run regarding the time it needs to produce an independent sample and introduces practical truncated sampling in thousands of dimensions.","url_abs":"https://arxiv.org/abs/2102.13068v3","url_pdf":"https://arxiv.org/pdf/2102.13068v3.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":"abstracts"},"code_links":[{"paper_slug":"truncated-log-concave-sampling-with","repo_url":"https://github.com/GeomScale/volume_approximation","is_official":1,"mentioned_in_paper":0,"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}