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Optimal Reach Estimation and Metric Learning

hal.structure.identifierLaboratoire de Probabilités, Statistique et Modélisation [LPSM (UMR_8001)]
dc.contributor.authorAamari, Eddie
HAL ID: 181405
ORCID: 0000-0003-4516-3009
hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorBerenfeld, Clément
hal.structure.identifierLaboratoire de Probabilités, Statistique et Modélisation [LPSM (UMR_8001)]
dc.contributor.authorLevrard, Clément
dc.date.accessioned2022-12-09T11:28:39Z
dc.date.available2022-12-09T11:28:39Z
dc.date.issued2022
dc.identifier.urihttps://basepub.dauphine.psl.eu/handle/123456789/23324
dc.language.isoenen
dc.subject.ddc519en
dc.titleOptimal Reach Estimation and Metric Learningen
dc.typeDocument de travail / Working paper
dc.description.abstractenWe study the estimation of the reach, an ubiquitous regularity parameter in manifold estimation and geometric data analysis. Given an i.i.d. sample over an unknown d-dimensional Ck-smooth submanifold of RD , we provide optimal nonasymptotic bounds for the estimation of its reach. We build upon a formulation of the reach in terms of maximal curvature on one hand, and geodesic metric distortion on the other hand. The derived rates are adaptive, with rates depending on whether the reach of M arises from curvature or from a bottleneck structure. In the process, we derive optimal geodesic metric estimation bounds.en
dc.publisher.cityParisen
dc.identifier.citationpages47en
dc.relation.ispartofseriestitleCahier de recherche CEREMADE, Université Paris Dauphine-PSLen
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.identifier.citationdate2022
dc.description.ssrncandidatenon
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.date.updated2022-12-09T11:23:15Z
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