{"paper":{"title":"The Price of Tolerance in Distribution Testing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT","math.PR","math.ST","stat.ML","stat.TH"],"primary_cat":"cs.DS","authors_text":"Ayush Jain, Cl\\'ement L. Canonne, Gautam Kamath, Jerry Li","submitted_at":"2021-06-25T03:59:42Z","abstract_excerpt":"We revisit the problem of tolerant distribution testing. That is, given samples from an unknown distribution $p$ over $\\{1, \\dots, n\\}$, is it $\\varepsilon_1$-close to or $\\varepsilon_2$-far from a reference distribution $q$ (in total variation distance)? Despite significant interest over the past decade, this problem is well understood only in the extreme cases. In the noiseless setting (i.e., $\\varepsilon_1 = 0$) the sample complexity is $\\Theta(\\sqrt{n})$, strongly sublinear in the domain size. At the other end of the spectrum, when $\\varepsilon_1 = \\varepsilon_2/2$, the sample complexity j"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.13414","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2106.13414/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}