5 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 $Î…
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…
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…
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…