{"paper":{"title":"Optimal transport map estimation in general function spaces","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["stat.ML","stat.TH"],"primary_cat":"math.ST","authors_text":"Aram-Alexandre Pooladian, Jonathan Niles-Weed, Vincent Divol","submitted_at":"2022-12-07T15:42:11Z","abstract_excerpt":"We study the problem of estimating a function $T$ given independent samples from a distribution $P$ and from the pushforward distribution $T_\\sharp P$. This setting is motivated by applications in the sciences, where $T$ represents the evolution of a physical system over time, and in machine learning, where, for example, $T$ may represent a transformation learned by a deep neural network trained for a generative modeling task. To ensure identifiability, we assume that $T = \\nabla \\varphi_0$ is the gradient of a convex function, in which case $T$ is known as an \\emph{optimal transport map}. Pri"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.03722","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/2212.03722/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"}