{"paper":{"title":"Testing Closeness of Multivariate Distributions via Ramsey Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","cs.LG","math.IT","math.ST","stat.ML","stat.TH"],"primary_cat":"cs.DS","authors_text":"Daniel M. Kane, Ilias Diakonikolas, Sihan Liu","submitted_at":"2023-11-22T04:34:09Z","abstract_excerpt":"We investigate the statistical task of closeness (or equivalence) testing for multidimensional distributions. Specifically, given sample access to two unknown distributions $\\mathbf p, \\mathbf q$ on $\\mathbb R^d$, we want to distinguish between the case that $\\mathbf p=\\mathbf q$ versus $\\|\\mathbf p-\\mathbf q\\|_{A_k} > \\epsilon$, where $\\|\\mathbf p-\\mathbf q\\|_{A_k}$ denotes the generalized ${A}_k$ distance between $\\mathbf p$ and $\\mathbf q$ -- measuring the maximum discrepancy between the distributions over any collection of $k$ disjoint, axis-aligned rectangles. Our main result is the first"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.13154","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2311.13154/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"}