{"paper":{"title":"Monge, Bregman and Occam: Interpretable Optimal Transport in High-Dimensions with Feature-Sparse Maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","q-bio.GN"],"primary_cat":"stat.ML","authors_text":"Marco Cuturi, Michal Klein, Pierre Ablin","submitted_at":"2023-02-08T14:02:34Z","abstract_excerpt":"Optimal transport (OT) theory focuses, among all maps $T:\\mathbb{R}^d\\rightarrow \\mathbb{R}^d$ that can morph a probability measure onto another, on those that are the ``thriftiest'', i.e. such that the averaged cost $c(x, T(x))$ between $x$ and its image $T(x)$ be as small as possible. Many computational approaches have been proposed to estimate such Monge maps when $c$ is the $\\ell_2^2$ distance, e.g., using entropic maps [Pooladian'22], or neural networks [Makkuva'20, Korotin'20]. We propose a new model for transport maps, built on a family of translation invariant costs $c(x, y):=h(x-y)$, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.04065","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2302.04065/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"}