{"paper":{"title":"Properly Learning Poisson Binomial Distributions in Almost Polynomial Time","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.ST","stat.TH"],"primary_cat":"cs.DS","authors_text":"Alistair Stewart, Daniel M. Kane, Ilias Diakonikolas","submitted_at":"2015-11-12T20:47:37Z","abstract_excerpt":"We give an algorithm for properly learning Poisson binomial distributions. A Poisson binomial distribution (PBD) of order $n$ is the discrete probability distribution of the sum of $n$ mutually independent Bernoulli random variables. Given $\\widetilde{O}(1/\\epsilon^2)$ samples from an unknown PBD $\\mathbf{p}$, our algorithm runs in time $(1/\\epsilon)^{O(\\log \\log (1/\\epsilon))}$, and outputs a hypothesis PBD that is $\\epsilon$-close to $\\mathbf{p}$ in total variation distance. The previously best known running time for properly learning PBDs was $(1/\\epsilon)^{O(\\log(1/\\epsilon))}$.\n  As one o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.04066","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"}