{"paper":{"title":"Near-Optimal Closeness Testing of Discrete Histogram Distributions","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":"Daniel M. Kane, Ilias Diakonikolas, Vladimir Nikishkin","submitted_at":"2017-03-06T15:03:55Z","abstract_excerpt":"We investigate the problem of testing the equivalence between two discrete histograms. A {\\em $k$-histogram} over $[n]$ is a probability distribution that is piecewise constant over some set of $k$ intervals over $[n]$. Histograms have been extensively studied in computer science and statistics. Given a set of samples from two $k$-histogram distributions $p, q$ over $[n]$, we want to distinguish (with high probability) between the cases that $p = q$ and $\\|p-q\\|_1 \\geq \\epsilon$. The main contribution of this paper is a new algorithm for this testing problem and a nearly matching information-t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.01913","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"}