{"paper":{"title":"Algorithms for mean-field variational inference via polyhedral optimization in the Wasserstein space","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG","math.OC","stat.TH"],"primary_cat":"math.ST","authors_text":"Aram-Alexandre Pooladian, Sinho Chewi, Yiheng Jiang","submitted_at":"2023-12-05T16:02:04Z","abstract_excerpt":"We develop a theory of finite-dimensional polyhedral subsets over the Wasserstein space and optimization of functionals over them via first-order methods. Our main application is to the problem of mean-field variational inference, which seeks to approximate a distribution $\\pi$ over $\\mathbb{R}^d$ by a product measure $\\pi^\\star$. When $\\pi$ is strongly log-concave and log-smooth, we provide (1) approximation rates certifying that $\\pi^\\star$ is close to the minimizer $\\pi^\\star_\\diamond$ of the KL divergence over a \\emph{polyhedral} set $\\mathcal{P}_\\diamond$, and (2) an algorithm for minimiz"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.02849","kind":"arxiv","version":4},"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/2312.02849/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"}