3 citations · 7 across the 9 of their papers we have counts for
11 papers · 1 filter
Statistical Analysis of Markovian Generative Modeling
Eddie Aamari, Arthur Stéphanovitch
These lecture notes introduce the statistical analysis of continuous-time generative models built from Markov dynamics. We begin with the stochastic-calculus foundations of score-b…
Generalization bounds for score-based generative models: a synthetic proof
Arthur Stéphanovitch, Eddie Aamari, Clément Levrard
We establish minimax convergence rates for score-based generative models (SGMs) under the -Wasserstein distance. Assuming the target density lies in a nonparametric $β…
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…
Wasserstein GANs are Minimax Optimal Distribution Estimators
Arthur Stéphanovitch, Eddie Aamari, Clément Levrard
We provide non asymptotic rates of convergence of the Wasserstein Generative Adversarial networks (WGAN) estimator. We build neural networks classes representing the generators and…
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…
Minimax Boundary Estimation and Estimation with Boundary
Eddie Aamari, Catherine Aaron, Clément Levrard
We derive non-asymptotic minimax bounds for the Hausdorff estimation of -dimensional submanifolds with (possibly) non-empty boundary . The m…
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…
Adversarial Manifold Estimation
Eddie Aamari, Alexander Knop
This paper studies the statistical query (SQ) complexity of estimating -dimensional submanifolds in . We propose a purely geometric algorithm called Manifold Propa…
Estimating the Reach of a Manifold
Eddie Aamari, Jisu Kim, Frédéric Chazal +3
Various problems in manifold estimation make use of a quantity called the reach, denoted by , which is a measure of the regularity of the manifold. This paper is the first in…
Non-Asymptotic Rates for Manifold, Tangent Space, and Curvature Estimation
Eddie Aamari, Clément Levrard
Given an -sample drawn on a submanifold , we derive optimal rates for the estimation of tangent spaces , the second fundamental form , a…
Stability and Minimax Optimality of Tangential Delaunay Complexes for Manifold Reconstruction
Eddie Aamari, Clément Levrard
We consider the problem of optimality in manifold reconstruction. A random sample composed of points close to a $…