{"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/quantitative-stability-of-optimal-transport","title":"Quantitative stability of optimal transport maps and linearization of the 2-Wasserstein space","arxiv_id":"1910.05954","date":"2019-10-14","proceeding":null,"authors":["Quentin Mérigot","Alex Delalande","Frédéric Chazal"],"abstract":"This work studies an explicit embedding of the set of probability measures into a Hilbert space, defined using optimal transport maps from a reference probability density. This embedding linearizes to some extent the 2-Wasserstein space, and enables the direct use of generic supervised and unsupervised learning algorithms on measure data. Our main result is that the embedding is (bi-)H\\\"older continuous, when the reference density is uniform over a convex set, and can be equivalently phrased as a dimension-independent H\\\"older-stability results for optimal transport maps.","url_abs":"https://arxiv.org/abs/1910.05954v1","url_pdf":"https://arxiv.org/pdf/1910.05954v1.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":"quantitative-stability-of-optimal-transport","repo_url":"https://github.com/AlxDel/stability_ot_maps_and_linearization_wasserstein_space","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1910.05954","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}