{"paper":{"title":"High-dimensional Bayesian inference via the Unadjusted Langevin Algorithm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ME","stat.ML","stat.TH"],"primary_cat":"math.ST","authors_text":"Alain Durmus, Eric Moulines","submitted_at":"2016-05-05T11:42:35Z","abstract_excerpt":"We consider in this paper the problem of sampling a high-dimensional probability distribution $\\pi$ having a density with respect to the Lebesgue measure on $\\mathbb{R}^d$, known up to a normalization constant $x \\mapsto \\pi(x)= \\mathrm{e}^{-U(x)}/\\int_{\\mathbb{R}^d} \\mathrm{e}^{-U(y)} \\mathrm{d} y$. Such problem naturally occurs for example in Bayesian inference and machine learning. Under the assumption that $U$ is continuously differentiable, $\\nabla U$ is globally Lipschitz and $U$ is strongly convex, we obtain non-asymptotic bounds for the convergence to stationarity in Wasserstein distan"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.01559","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":""},"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"}