Optimal Reach Estimation and Metric Learning - Université Paris Cité Accéder directement au contenu
Article Dans Une Revue Annals of Statistics Année : 2023

Optimal Reach Estimation and Metric Learning

Résumé

We 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 $\mathcal{C}^k$-smooth submanifold of $\mathbb{R}^D$ , 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.
Fichier principal
Vignette du fichier
Optimal Reach Estimation and Metric Learning.pdf (1.15 Mo) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03722236 , version 1 (13-07-2022)

Identifiants

Citer

Eddie Aamari, Clément Berenfeld, Clément Levrard. Optimal Reach Estimation and Metric Learning. Annals of Statistics, 2023, ⟨10.1214/23-AOS2281⟩. ⟨hal-03722236⟩
80 Consultations
49 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More