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 …
Measure estimation on manifolds: an optimal transport approach
V Divol - Probability Theory and Related Fields, 2022 - Springer
Assume that we observe iid points lying close to some unknown d-dimensional C k
submanifold M in a possibly high-dimensional space. We study the problem of …
submanifold M in a possibly high-dimensional space. We study the problem of …
Universally consistent estimation of the reach
The reach of a set M⊂ R d, also known as condition number when M is a manifold, was
introduced by Federer in 1959. The reach is a central concept in geometric measure theory …
introduced by Federer in 1959. The reach is a central concept in geometric measure theory …
Computable Bounds for the Reach and r-Convexity of Subsets of
R Cotsakis - Discrete & Computational Geometry, 2025 - 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 …
Estimating the convex hull of the image of a set with smooth boundary: error bounds and applications
We study the problem of estimating the convex hull of the image f (X)⊂ R n of a compact set
X⊂ R m with smooth boundary through a smooth function f: R m→ R n. Assuming that f is a …
X⊂ R m with smooth boundary through a smooth function f: R m→ R n. Assuming that f is a …
Minimax boundary estimation and estimation with boundary
E Aamari, C Aaron, C Levrard - Bernoulli, 2023 - projecteuclid.org
Minimax boundary estimation and estimation with boundary Page 1 Bernoulli 29(4), 2023,
3334–3368 https://doi.org/10.3150/23-BEJ1585 Minimax boundary estimation and estimation …
3334–3368 https://doi.org/10.3150/23-BEJ1585 Minimax boundary estimation and estimation …
Minimax adaptive estimation in manifold inference
V Divol - Electronic Journal of Statistics, 2021 - projecteuclid.org
We focus on the problem of manifold estimation: given a set of observations sampled close
to some unknown submanifold M, one wants to recover information about the geometry of M …
to some unknown submanifold M, one wants to recover information about the geometry of M …
Topologically penalized regression on manifolds
We study a regression problem on a compact manifold M. In order to take advantage of the
underlying geometry and topology of the data, the regression task is performed on the basis …
underlying geometry and topology of the data, the regression task is performed on the basis …
Effective theory building and manifold learning
DPW Freeborn - Synthese, 2025 - Springer
Manifold learning and effective model building are generally viewed as fundamentally
different types of procedure. After all, in one we build a simplified model of the data, in the …
different types of procedure. After all, in one we build a simplified model of the data, in the …