{"paper":{"title":"On the Structure, Covering, and Learning of Poisson Multinomial Distributions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.PR","math.ST","stat.TH"],"primary_cat":"cs.DS","authors_text":"Christos Tzamos, Constantinos Daskalakis, Gautam Kamath","submitted_at":"2015-04-30T19:53:03Z","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 prove a structural characterization of these distributions, showing that, for all $\\varepsilon >0$, any $(n, k)$-Poisson multinomial random vector is $\\varepsilon$-close, in total variation distance, to the sum of a discretized multidimensional Gaussian and an independent $(\\text{poly}(k/\\varepsilon), k)$-Poisson multinomial random vector. Our structural characterization extends th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.08363","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"}