{"paper":{"title":"Decomposing Probability Marginals Beyond Affine Requirements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Jannik Matuschke","submitted_at":"2023-11-06T18:53:01Z","abstract_excerpt":"Consider the triplet $(E, \\mathcal{P}, \\pi)$, where $E$ is a finite ground set, $\\mathcal{P} \\subseteq 2^E$ is a collection of subsets of $E$ and $\\pi : \\mathcal{P} \\rightarrow [0,1]$ is a requirement function. Given a vector of marginals $\\rho \\in [0, 1]^E$, our goal is to find a distribution for a random subset $S \\subseteq E$ such that $\\operatorname{Pr}[e \\in S] = \\rho_e$ for all $e \\in E$ and $\\operatorname{Pr}[P \\cap S \\neq \\emptyset] \\geq \\pi_P$ for all $P \\in \\mathcal{P}$, or to determine that no such distribution exists.\n  Generalizing results of Dahan, Amin, and Jaillet, we devise a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.03346","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2311.03346/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}