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Characterization of barycenters in the Wasserstein space by averaging optimal transport maps
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | BIGOT, Jérémie | |
| hal.structure.identifier | Institut de Mathématiques de Toulouse UMR5219 [IMT] | |
| hal.structure.identifier | Ecole Nationale de l'Aviation Civile [ENAC] | |
| dc.contributor.author | KLEIN, Thierry | |
| dc.date.accessioned | 2024-04-04T03:07:56Z | |
| dc.date.available | 2024-04-04T03:07:56Z | |
| dc.date.created | 2015-07-17 | |
| dc.date.issued | 2018-11 | |
| dc.identifier.issn | 1292-8100 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/193488 | |
| dc.description.abstractEn | This paper is concerned by the study of barycenters for random probability measures in the Wasserstein space. Using a duality argument, we give a precise characterization of the population barycenter for various parametric classes of random probability measures with compact support. In particular, we make a connection between averaging in the Wasserstein space as introduced in Agueh and Carlier (2011), and taking the expectation of optimal transport maps with respect to a fixed reference measure. We also discuss the usefulness of this approach in statistics for the analysis of deformable models in signal and image processing. In this setting, the problem of estimating a population barycenter from n independent and identically distributed random probability measures is also considered. | |
| dc.language.iso | en | |
| dc.publisher | EDP Sciences | |
| dc.subject.en | Fréchet mean | |
| dc.subject.en | Empirical and population barycenters | |
| dc.subject.en | Wasserstein space | |
| dc.subject.en | Deformable models AMS classifications: Primary 62G05 | |
| dc.subject.en | Optimal transport | |
| dc.subject.en | Curve and image warping | |
| dc.subject.en | Convergence of random variables | |
| dc.subject.en | Deformable models | |
| dc.subject.en | Duality | |
| dc.title.en | Characterization of barycenters in the Wasserstein space by averaging optimal transport maps | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1051/ps/2017020 | |
| dc.subject.hal | Statistiques [stat]/Théorie [stat.TH] | |
| dc.identifier.arxiv | 1212.2562 | |
| bordeaux.journal | ESAIM: Probability and Statistics | |
| bordeaux.page | 35 - 57 | |
| bordeaux.volume | 22 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-00763668 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00763668v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=ESAIM:%20Probability%20and%20Statistics&rft.date=2018-11&rft.volume=22&rft.spage=35%20-%2057&rft.epage=35%20-%2057&rft.eissn=1292-8100&rft.issn=1292-8100&rft.au=BIGOT,%20J%C3%A9r%C3%A9mie&KLEIN,%20Thierry&rft.genre=article |
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