Optimal reach estimation and metric learning
E Aamari, C Berenfeld, C Levrard - The Annals of Statistics, 2023 - projecteuclid.org
Optimal reach estimation and metric learning Page 1 The Annals of Statistics 2023, Vol. 51, No.
3, 1086–1108 https://doi.org/10.1214/23-AOS2281 © Institute of Mathematical Statistics, 2023 …
3, 1086–1108 https://doi.org/10.1214/23-AOS2281 © Institute of Mathematical Statistics, 2023 …
Computable Bounds for the Reach and r-Convexity of Subsets of
R Cotsakis - Discrete & Computational Geometry, 2024 - Springer
The convexity of a set can be generalized to the two weaker notions of positive reach and r-
convexity; both describe the regularity of a set's boundary. For any compact subset of R d …
convexity; both describe the regularity of a set's boundary. For any compact subset of R d …
Tight bounds for the learning of homotopy à la Niyogi, Smale, and Weinberger for subsets of Euclidean spaces and of Riemannian manifolds
In this article we extend and strengthen the seminal work by Niyogi, Smale, and Weinberger
on the learning of the homotopy type from a sample of an underlying space. In their work …
on the learning of the homotopy type from a sample of an underlying space. In their work …
On the notion of polynomial reach: A statistical application
The volume function V (t) of a compact set S∈ R d is just the Lebesgue measure of the set of
points within a distance to S not larger than t. According to some classical results in …
points within a distance to S not larger than t. According to some classical results in …
Statistical inference on unknown manifolds
C Berenfeld - 2022 - theses.hal.science
In high-dimensional statistics, the manifold hypothesis presumes that the data lie near low-
dimensional structures, called manifolds. This assumption helps explain why machine …
dimensional structures, called manifolds. This assumption helps explain why machine …
On standardness and the non-estimability of certain functionals of a set
A Cholaquidis, LM Beatriz - arXiv preprint arXiv:2306.16295, 2023 - arxiv.org
Standardness is a popular assumption in the literature on set estimation. It also appears in
statistical approaches to topological data analysis, where it is common to assume that the …
statistical approaches to topological data analysis, where it is common to assume that the …
Optimal homotopy reconstruction results\a la Niyogi, Smale, and Weinberger
In this article we show that the proof of the homotopy reconstruction result by Niyogi, Smale,
and Weinberger can be streamlined considerably using Federer's work on the reach and …
and Weinberger can be streamlined considerably using Federer's work on the reach and …
Computable bounds for the reach and -convexity of subsets of
R Cotsakis - arXiv preprint arXiv:2212.01013, 2022 - arxiv.org
The convexity of a set can be generalized to the two weaker notions of reach and $ r $-
convexity; both describe the regularity of a set's boundary. For any compact subset of …
convexity; both describe the regularity of a set's boundary. For any compact subset of …
Choosing the parameter of the Fermat distance: navigating geometry and noise
The Fermat distance has been recently established as a useful tool for machine learning
tasks when a natural distance is not directly available to the practitioner or to improve the …
tasks when a natural distance is not directly available to the practitioner or to improve the …
[PDF][PDF] New advances in set estimation
A Cholaquidis - Boletın de Estadıstica e Investigación Operativa BEIO, 2024 - seio.es
Some recent advances in Set Estimation, from 2009 to the present, are discussed. These
include some new findings, improved convergence rates, and new type of sets under study …
include some new findings, improved convergence rates, and new type of sets under study …