{"paper":{"title":"Collision-based Testers are Optimal for Uniformity and Closeness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","cs.LG","math.IT","math.ST","stat.TH"],"primary_cat":"cs.DS","authors_text":"Eric Price, Ilias Diakonikolas, John Peebles, Themis Gouleakis","submitted_at":"2016-11-11T03:59:24Z","abstract_excerpt":"We study the fundamental problems of (i) uniformity testing of a discrete distribution, and (ii) closeness testing between two discrete distributions with bounded $\\ell_2$-norm. These problems have been extensively studied in distribution testing and sample-optimal estimators are known for them~\\cite{Paninski:08, CDVV14, VV14, DKN:15}.\n  In this work, we show that the original collision-based testers proposed for these problems ~\\cite{GRdist:00, BFR+:00} are sample-optimal, up to constant factors. Previous analyses showed sample complexity upper bounds for these testers that are optimal as a f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.03579","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"}