3 citations · 6 across the 5 of their papers we have counts for
5 papers · 1 filter
A theory of stratification learning
Eddie Aamari, Clément Berenfeld
Given i.i.d. sample from a stratified mixture of immersed manifolds of different dimensions, we study the minimax estimation of the underlying stratified structure. We provide a co…
Theoretical Foundations of Ordinal Multidimensional Scaling, Including Internal and External Unfolding
Ery Arias-Castro, Clément Berenfeld, Daniel Kane
We provide a comprehensive theory of multiple variants of ordinal multidimensional scaling,including internal unfolding and external unfolding. We first follow Shepard (1966) and w…
Optimal Reach Estimation and Metric Learning
Eddie Aamari, Clément Berenfeld, Clément Levrard
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 -dimensional…
Estimating a density near an unknown manifold: a Bayesian nonparametric approach
Clément Berenfeld, Paul Rosa, Judith Rousseau
We study the Bayesian density estimation of data living in the offset of an unknown submanifold of the Euclidean space. In this perspective, we introduce a new notion of anisotropi…
The Coreness and H-Index of Random Geometric Graphs
Eddie Aamari, Ery Arias-Castro, Clément Berenfeld
In network analysis, a measure of node centrality provides a scale indicating how central a node is within a network. The coreness is a popular notion of centrality that accounts f…