{"paper":{"title":"A Polynomial Time Algorithm for Maximum Likelihood Estimation of Multivariate Log-concave Densities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Alistair Stewart, Anastasios Sidiropoulos, Ilias Diakonikolas","submitted_at":"2018-12-13T17:09:21Z","abstract_excerpt":"We study the problem of computing the maximum likelihood estimator (MLE) of multivariate log-concave densities. Our main result is the first computationally efficient algorithm for this problem. In more detail, we give an algorithm that, on input a set of $n$ points in $\\mathbb{R}^d$ and an accuracy parameter $\\epsilon>0$, it runs in time $\\text{poly}(n, d, 1/\\epsilon)$, and outputs a log-concave density that with high probability maximizes the log-likelihood up to an additive $\\epsilon$. Our approach relies on a natural convex optimization formulation of the underlying problem that can be eff"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.05524","kind":"arxiv","version":1},"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"}