{"paper":{"title":"Fourier-Based Testing for Families of Distributions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.DM","math.PR","math.ST","stat.TH"],"primary_cat":"cs.DS","authors_text":"Alistair Stewart, Cl\\'ement L. Canonne, Ilias Diakonikolas","submitted_at":"2017-06-18T22:28:20Z","abstract_excerpt":"We study the general problem of testing whether an unknown distribution belongs to a specified family of distributions. More specifically, given a distribution family $\\mathcal{P}$ and sample access to an unknown discrete distribution $\\mathbf{P}$, we want to distinguish (with high probability) between the case that $\\mathbf{P} \\in \\mathcal{P}$ and the case that $\\mathbf{P}$ is $\\epsilon$-far, in total variation distance, from every distribution in $\\mathcal{P}$. This is the prototypical hypothesis testing problem that has received significant attention in statistics and, more recently, in the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.05738","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":""},"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"}