{"paper":{"title":"$\\ell_p$ Testing and Learning of Discrete Distributions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.ST","stat.TH"],"primary_cat":"cs.DS","authors_text":"Bo Waggoner","submitted_at":"2014-12-07T03:57:29Z","abstract_excerpt":"The classic problems of testing uniformity of and learning a discrete distribution, given access to independent samples from it, are examined under general $\\ell_p$ metrics. The intuitions and results often contrast with the classic $\\ell_1$ case. For $p > 1$, we can learn and test with a number of samples that is independent of the support size of the distribution: With an $\\ell_p$ tolerance $\\epsilon$, $O(\\max\\{ \\sqrt{1/\\epsilon^q}, 1/\\epsilon^2 \\})$ samples suffice for testing uniformity and $O(\\max\\{ 1/\\epsilon^q, 1/\\epsilon^2\\})$ samples suffice for learning, where $q=p/(p-1)$ is the conj"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.2314","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"}