{"paper":{"title":"Truncated Log-concave Sampling with Reflective Hamiltonian Monte Carlo","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"cs.LG","authors_text":"Apostolos Chalkis, Elias Tsigaridas, Marios Papachristou, Vissarion Fisikopoulos","submitted_at":"2021-02-25T18:34:45Z","abstract_excerpt":"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 reflec"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2102.13068","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2102.13068/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}