{"paper":{"title":"An Efficient Algorithm for High-Dimensional Log-Concave Maximum Likelihood","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["stat.CO"],"primary_cat":"cs.DS","authors_text":"Brian Axelrod, Gregory Valiant","submitted_at":"2018-11-08T01:04:51Z","abstract_excerpt":"The log-concave maximum likelihood estimator (MLE) problem answers: for a set of points $X_1,...X_n \\in \\mathbb R^d$, which log-concave density maximizes their likelihood? We present a characterization of the log-concave MLE that leads to an algorithm with runtime $poly(n,d, \\frac 1 \\epsilon,r)$ to compute a log-concave distribution whose log-likelihood is at most $\\epsilon$ less than that of the MLE, and $r$ is parameter of the problem that is bounded by the $\\ell_2$ norm of the vector of log-likelihoods the MLE evaluated at $X_1,...,X_n$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.03204","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"}