{"paper":{"title":"Learning $k$-Modal Distributions via Testing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.ST","stat.TH"],"primary_cat":"cs.DS","authors_text":"Constantinos Daskalakis, Ilias Diakonikolas, Rocco A. Servedio","submitted_at":"2011-07-13T23:26:53Z","abstract_excerpt":"A $k$-modal probability distribution over the discrete domain $\\{1,...,n\\}$ is one whose histogram has at most $k$ \"peaks\" and \"valleys.\" Such distributions are natural generalizations of monotone ($k=0$) and unimodal ($k=1$) probability distributions, which have been intensively studied in probability theory and statistics.\n  In this paper we consider the problem of \\emph{learning} (i.e., performing density estimation of) an unknown $k$-modal distribution with respect to the $L_1$ distance. The learning algorithm is given access to independent samples drawn from an unknown $k$-modal distribut"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.2700","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":""},"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"}