{"paper":{"title":"Minimum--Entropy Couplings and their Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","math.IT"],"primary_cat":"cs.IT","authors_text":"Ferdinando Cicalese, Luisa Gargano, Ugo Vaccaro","submitted_at":"2019-01-19T10:57:21Z","abstract_excerpt":"Given two discrete random variables $X$ and $Y,$ with probability distributions ${\\bf p}=(p_1, \\ldots , p_n)$ and ${\\bf q}=(q_1, \\ldots , q_m)$, respectively, denote by ${\\cal C}({\\bf p}, {\\bf q})$ the set of all couplings of ${\\bf p}$ and ${\\bf q}$, that is, the set of all bivariate probability distributions that have ${\\bf p}$ and ${\\bf q}$ as marginals. In this paper, we study the problem of finding a joint probability distribution in ${\\cal C}({\\bf p}, {\\bf q})$ of \\emph{minimum entropy} (equivalently, a coupling that \\emph{maximizes} the mutual information between $X$ and $Y$), and we dis"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.07530","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"}