{"paper":{"title":"A Size-Free CLT for Poisson Multinomials and its Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.GT","cs.LG","math.PR","math.ST","stat.TH"],"primary_cat":"cs.DS","authors_text":"Anindya De, Christos Tzamos, Constantinos Daskalakis, Gautam Kamath","submitted_at":"2015-11-11T20:27:33Z","abstract_excerpt":"An $(n,k)$-Poisson Multinomial Distribution (PMD) is the distribution of the sum of $n$ independent random vectors supported on the set ${\\cal B}_k=\\{e_1,\\ldots,e_k\\}$ of standard basis vectors in $\\mathbb{R}^k$. We show that any $(n,k)$-PMD is ${\\rm poly}\\left({k\\over \\sigma}\\right)$-close in total variation distance to the (appropriately discretized) multi-dimensional Gaussian with the same first two moments, removing the dependence on $n$ from the Central Limit Theorem of Valiant and Valiant. Interestingly, our CLT is obtained by bootstrapping the Valiant-Valiant CLT itself through the stru"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.03641","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"}