Thomas Bonis

activity

20142026

most citedStein's method for normal approximation in Wasserstein distances with application to the multivariate Central Limit Theorem

36 citations · 36 across the 7 of their papers we have counts for

collaborators

9 papers

math.ST2026

Optimal score function estimation via derivatives constraints

Thomas Bonis, Thanh Mai Pham Ngoc, Viet Chi Tran

We provide a statistical theory explaining why empirical score matching can achieve minimax optimal performance for diffusion generative models when the data distribution is suppor…

math.PR2024

Random walks on simplicial complexes

Thomas Bonis, Laurent Decreusefond, Viet Chi Tran +1

The notion of Laplacian of a graph can be generalized to simplicial complexes and hypergraphs, and contains information on the topology of these structures. Even for a graph, the c…

math.PR2023

Improved rates of convergence for the multivariate Central Limit Theorem in Wasserstein distance

Thomas Bonis

We provide new bounds for the rate of convergence of the multivariate Central Limit Theorem in Wasserstein distances of order $p \geq 2$ . In particular, we obtain what we conjectur…

cs.CG2022

Topological phase estimation method for reparameterized periodic functions

Thomas Bonis, Frédéric Chazal, Bertrand Michel +1

We consider a signal composed of several periods of a periodic function, of which we observe a noisy reparametrisation. The phase estimation problem consists of finding that repara…

math.PR2022

Stein's method for steady-state diffusion approximation in Wasserstein distance

Thomas Bonis

We provide a general steady-state diffusion approximation result which bounds the Wasserstein distance between the reversible measure $μ$ of a diffusion process and the measure $ν$ …

math.PR2019★ 36 cited

Stein's method for normal approximation in Wasserstein distances with application to the multivariate Central Limit Theorem

Thomas Bonis

We use Stein's method to bound the Wasserstein distance of order $2$ between a measure $ν$ and the Gaussian measure using a stochastic process $(X_{t})_{t \geq 0}$ such that $X_{t}$ is…

stat.CO2016

Guarantees in Wasserstein Distance for the Langevin Monte Carlo Algorithm

Thomas Bonis

We study the problem of sampling from a distribution $\target$ using the Langevin Monte Carlo algorithm and provide rate of convergences for this algorithm in terms of Wasserstein…

math.PR2015

Rates in the Central Limit Theorem and diffusion approximation via Stein's Method

Thomas Bonis

We present a way to use Stein's method in order to bound the Wasserstein distance of order $2$ between two measures $ν$ and $μ$ supported on $R^{d}$ such that $μ$ is the rev…

stat.ML2014

A Fuzzy Clustering Algorithm for the Mode Seeking Framework

Thomas Bonis, Steve Oudot

In this paper, we propose a new fuzzy clustering algorithm based on the mode-seeking framework. Given a dataset in $R^{d}$ , we define regions of high density that we call cl…