{"paper":{"title":"Testing Shape Restrictions of Discrete Distributions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","math.PR","math.ST","stat.TH"],"primary_cat":"cs.DS","authors_text":"Cl\\'ement L. Canonne, Ilias Diakonikolas, Ronitt Rubinfeld, Themis Gouleakis","submitted_at":"2015-07-13T19:22:41Z","abstract_excerpt":"We study the question of testing structured properties (classes) of discrete distributions. Specifically, given sample access to an arbitrary distribution $D$ over $[n]$ and a property $\\mathcal{P}$, the goal is to distinguish between $D\\in\\mathcal{P}$ and $\\ell_1(D,\\mathcal{P})>\\varepsilon$. We develop a general algorithm for this question, which applies to a large range of \"shape-constrained\" properties, including monotone, log-concave, $t$-modal, piecewise-polynomial, and Poisson Binomial distributions. Moreover, for all cases considered, our algorithm has near-optimal sample complexity wit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.03558","kind":"arxiv","version":3},"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"}