{"paper":{"title":"Pairwise Multi-marginal Optimal Transport and Embedding for Earth Mover's Distance","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC","math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Cheuk Ting Li, Venkat Anantharam","submitted_at":"2019-08-04T19:09:09Z","abstract_excerpt":"We investigate the problem of pairwise multi-marginal optimal transport, that is, given a collection of probability distributions $\\{P_\\alpha\\}$ on a Polish space $\\mathcal{X}$, to find a coupling $\\{X_\\alpha\\}$, $X_\\alpha\\sim P_\\alpha$, such that $\\mathbf{E}[c(X_\\alpha,X_\\beta)]\\le r\\inf_{X\\sim P_\\alpha,Y\\sim P_\\beta}\\mathbf{E}[c(X,Y)]$ for all $\\alpha,\\beta$, where $c$ is a cost function and $r\\ge1$. In other words, every pair $(X_\\alpha,X_\\beta)$ has an expected cost at most a factor of $r$ from its lowest possible value. This can be regarded as a locality sensitive hash function for probab"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.01388","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/1908.01388/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"}