Show simple item record

dc.contributor.authorCarlier, Guillaume
dc.contributor.authorDelalande, Alex
dc.contributor.authorMérigot, Quentin
dc.date.accessioned2023-01-05T12:39:50Z
dc.date.available2023-01-05T12:39:50Z
dc.date.issued2023
dc.identifier.issn0178-8051
dc.identifier.urihttps://basepub.dauphine.psl.eu/handle/123456789/23603
dc.language.isoenen
dc.subjectOptimal transport
dc.subjectBarycenters
dc.subjectQuantitative stability
dc.subject.ddc515en
dc.titleQuantitative Stability of Barycenters in the Wasserstein Space
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenWasserstein barycenters define averages of probability measures in a geometrically meaningful way. Their use is increasingly popular in applied fields, such as image, geometry or language processing. In these fields however, the probability measures of interest are often not accessible in their entirety and the practitioner may have to deal with statistical or computational approximations instead. In this article, we quantify the effect of such approximations on the corresponding barycenters. We show that Wasserstein barycenters depend in a Hölder-continuous way on their marginals under relatively mild assumptions. Our proof relies on recent estimates that quantify the strong convexity of the dual quadratic optimal transport problem and a new result that allows to control the modulus of continuity of the push-forward operation under a (not necessarily smooth) optimal transport map.
dc.publisher.cityParisen
dc.relation.isversionofjnlnameProbability Theory and Related Fields
dc.relation.isversionofjnldate2023
dc.relation.isversionofdoi10.1007/s00440-023-01241-5
dc.identifier.urlsitehttps://hal.science/hal-03781835
dc.relation.isversionofjnlpublisherSpringer
dc.subject.ddclabelAnalyseen
dc.description.ssrncandidatenon
dc.description.halcandidatenon
dc.description.readershiprecherche
dc.description.audienceInternational
dc.relation.Isversionofjnlpeerreviewedoui
dc.date.updated2024-01-30T13:25:10Z


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record