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hal.structure.identifierCentre de Mathématiques et de Leurs Applications [CMLA]
dc.contributor.authorFeydy, Jean
hal.structure.identifierDépartement de Mathématiques et Applications - ENS Paris [DMA]
dc.contributor.authorSéjourné, Thibault
hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorVialard, François-Xavier
hal.structure.identifierRIKEN Center for Brain Science [Wako] [RIKEN CBS]
dc.contributor.authorAmari, Shun-ichi
hal.structure.identifierCentre de Mathématiques et de Leurs Applications [CMLA]
dc.contributor.authorTrouvé, Alain
HAL ID: 737853
hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorPeyré, Gabriel
HAL ID: 1211
dc.date.accessioned2019-02-18T16:17:30Z
dc.date.available2019-02-18T16:17:30Z
dc.date.issued2018
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/18450
dc.language.isoenen
dc.subjectOptimal Transporten
dc.subjectMMDen
dc.subjectSinkhorn Divergencesen
dc.subject.ddc519en
dc.titleInterpolating between Optimal Transport and MMD using Sinkhorn Divergencesen
dc.typeDocument de travail / Working paper
dc.description.abstractenComparing probability distributions is a fundamental problem in data sciences. Simple norms and divergences such as the total variation and the relative entropy only compare densities in a point-wise manner and fail to capture the geometric nature of the problem. In sharp contrast, Maximum Mean Discrepancies (MMD) and Optimal Transport distances (OT) are two classes of distances between measures that take into account the geometry of the underlying space and metrize the convergence in law. This paper studies the Sinkhorn divergences, a family of geometric divergences that interpolates between MMD and OT. Relying on a new notion of geometric entropy, we provide theoretical guarantees for these divergences: positivity, convexity and metrization of the convergence in law. On the practical side, we detail a numerical scheme that enables the large scale application of these divergences for machine learning: on the GPU, gradients of the Sinkhorn loss can be computed for batches of a million samples.en
dc.identifier.citationpages15en
dc.relation.ispartofseriestitleCahier de recherche CEREMADE, Université Paris-Dauphineen
dc.identifier.urlsitehttps://hal.archives-ouvertes.fr/hal-01898858en
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.identifier.citationdate2018-10
dc.description.ssrncandidatenonen
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.date.updated2019-02-18T10:09:48Z
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