{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/large-scale-optimal-transport-and-mapping","title":"Large-Scale Optimal Transport and Mapping Estimation","arxiv_id":"1711.02283","date":"2017-11-07","proceeding":null,"authors":["Vivien Seguy","Bharath Bhushan Damodaran","Rémi Flamary","Nicolas Courty","Antoine Rolet","Mathieu Blondel"],"abstract":"This paper presents a novel two-step approach for the fundamental problem of\nlearning an optimal map from one distribution to another. First, we learn an\noptimal transport (OT) plan, which can be thought as a one-to-many map between\nthe two distributions. To that end, we propose a stochastic dual approach of\nregularized OT, and show empirically that it scales better than a recent\nrelated approach when the amount of samples is very large. Second, we estimate\na \\textit{Monge map} as a deep neural network learned by approximating the\nbarycentric projection of the previously-obtained OT plan. This\nparameterization allows generalization of the mapping outside the support of\nthe input measure. We prove two theoretical stability results of regularized OT\nwhich show that our estimations converge to the OT plan and Monge map between\nthe underlying continuous measures. We showcase our proposed approach on two\napplications: domain adaptation and generative modeling.","url_abs":"http://arxiv.org/abs/1711.02283v2","url_pdf":"http://arxiv.org/pdf/1711.02283v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"large-scale-optimal-transport-and-mapping","repo_url":"https://github.com/mikigom/large-scale-OT-mapping-TF","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":{"status":"ok"}},{"paper_slug":"large-scale-optimal-transport-and-mapping","repo_url":"https://github.com/vivienseguy/Large-Scale-OT","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok"}}],"tasks":[{"task_slug":"domain-adaptation","task_name":"Domain Adaptation"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1711.02283","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}