{"paper":{"title":"Learning mixtures of structured distributions over discrete domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","math.ST","stat.TH"],"primary_cat":"cs.LG","authors_text":"Ilias Diakonikolas, Rocco A. Servedio, Siu-on Chan, Xiaorui Sun","submitted_at":"2012-10-02T18:07:13Z","abstract_excerpt":"Let $\\mathfrak{C}$ be a class of probability distributions over the discrete domain $[n] = \\{1,...,n\\}.$ We show that if $\\mathfrak{C}$ satisfies a rather general condition -- essentially, that each distribution in $\\mathfrak{C}$ can be well-approximated by a variable-width histogram with few bins -- then there is a highly efficient (both in terms of running time and sample complexity) algorithm that can learn any mixture of $k$ unknown distributions from $\\mathfrak{C}.$\n  We analyze several natural types of distributions over $[n]$, including log-concave, monotone hazard rate and unimodal dis"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.0864","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"}