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Publications Influence

Existence and consistency of Wasserstein barycenters

- Thibaut Le Gouic, Jean-Michel Loubes
- Mathematics
- 12 June 2015

Based on the Fréchet mean, we define a notion of barycenter corresponding to a usual notion of statistical mean. We prove the existence of Wasserstein barycenters of random probabilities defined on a… Expand

73 13- PDF

Distribution's template estimate with Wasserstein metrics

- Emmanuel Boissard, Thibaut Le Gouic, Jean-Michel Loubes
- Mathematics
- 25 November 2011

In this paper we tackle the problem of comparing distributions of random variables and defining a mean pattern between a sample of random events. Using barycenters of measures in the Wasserstein… Expand

59 6- PDF

On the rate of convergence of empirical barycentres in metric spaces: curvature, convexity and extendible geodesics

- Adil Ahidar-Coutrix, Thibaut Le Gouic, Q. Paris
- Mathematics
- 17 June 2019

This paper provides rates of convergence for empirical (generalised) barycenters on compact geodesic metric spaces under general conditions using empirical processes techniques.
Our main assumption… Expand

5 3

Convergence rates for empirical barycenters in metric spaces: curvature, convexity and extendable geodesics

- Adil Ahidar-Coutrix, Thibaut Le Gouic, Q. Paris
- Mathematics
- 7 June 2018

This paper provides rates of convergence for empirical (generalised) barycenters on compact geodesic metric spaces under general conditions using empirical processes techniques. Our main assumption… Expand

14 2- PDF

On the mean speed of convergence of empirical and occupation measures in Wasserstein distance

- Emmanuel Boissard, Thibaut Le Gouic
- Mathematics
- 26 May 2011

In this work, we provide non-asymptotic bounds for the average speed of convergence of the empirical measure in the law of large numbers, in Wasserstein distance. We also consider occupation measures… Expand

52 1- PDF

Exponential ergodicity of mirror-Langevin diffusions

- Sinho Chewi, Thibaut Le Gouic, C. Lu, Tyler Maunu, P. Rigollet, Austin Stromme
- Mathematics, Computer Science
- ArXiv
- 19 May 2020

TLDR

3 1- PDF

Projection to Fairness in Statistical Learning.

- Thibaut Le Gouic, Jean-Michel Loubes, P. Rigollet
- Computer Science, Mathematics
- 24 May 2020

TLDR

3 1- PDF

Fast convergence of empirical barycenters in Alexandrov spaces and the Wasserstein space

- Thibaut Le Gouic, Q. Paris, P. Rigollet, Austin Stromme
- Mathematics
- 2 August 2019

This work establishes fast rates of convergence for empirical barycenters over a large class of geodesic spaces with curvature bounds in the sense of Alexandrov. More specifically, we show that… Expand

5- PDF

Unconstrained and Curvature-Constrained Shortest-Path Distances and Their Approximation

- Ery Arias-Castro, Thibaut Le Gouic
- Mathematics, Computer Science
- Discret. Comput. Geom.
- 28 June 2017

TLDR

4- PDF

"Exact" deviations in Wasserstein distance for empirical and occupation measures

- Emmanuel Boissard, Thibaut Le Gouic
- Mathematics
- 16 March 2011

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