{"paper":{"title":"Uniformity Testing over Hypergrids with Subcube Conditioning","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.IT","cs.LG","math.IT","math.PR","math.ST","stat.TH"],"primary_cat":"cs.DS","authors_text":"Cassandra Marcussen, Xi Chen","submitted_at":"2023-02-17T17:29:24Z","abstract_excerpt":"We give an algorithm for testing uniformity of distributions supported on hypergrids $[m_1] \\times \\cdots \\times [m_n]$, which makes $\\smash{\\widetilde{O}(\\text{poly}(m)\\sqrt{n}/\\epsilon^2)}$ many queries to a subcube conditional sampling oracle with $m=\\max_i m_i$. When $m$ is a constant, our algorithm is nearly optimal and strengthens the algorithm of [CCK+21] which has the same query complexity but works for hypercubes $\\{\\pm 1\\}^n$ only.\n  A key technical contribution behind the analysis of our algorithm is a proof of a robust version of Pisier's inequality for functions over hypergrids us"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.09013","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/2302.09013/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"}