{"paper":{"title":"Testing probability distributions underlying aggregated data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.PR","math.ST","stat.TH"],"primary_cat":"cs.DS","authors_text":"Cl\\'ement Canonne, Ronitt Rubinfeld","submitted_at":"2014-02-16T20:00:00Z","abstract_excerpt":"In this paper, we analyze and study a hybrid model for testing and learning probability distributions. Here, in addition to samples, the testing algorithm is provided with one of two different types of oracles to the unknown distribution $D$ over $[n]$. More precisely, we define both the dual and cumulative dual access models, in which the algorithm $A$ can both sample from $D$ and respectively, for any $i\\in[n]$,\n  - query the probability mass $D(i)$ (query access); or\n  - get the total mass of $\\{1,\\dots,i\\}$, i.e. $\\sum_{j=1}^i D(j)$ (cumulative access)\n  These two models, by generalizing t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.3835","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"}