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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

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

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

SVGD as a kernelized Wasserstein gradient flow of the chi-squared divergence

- Sinho Chewi, Thibaut Le Gouic, Chen Lu, Tyler Maunu, P. Rigollet
- Mathematics, Computer Science
- NeurIPS
- 3 June 2020

TLDR

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

Projection to Fairness in Statistical Learning.

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

TLDR

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

Exponential ergodicity of mirror-Langevin diffusions

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

TLDR

Optimal dimension dependence of the Metropolis-Adjusted Langevin Algorithm

- Sinho Chewi, Chen Lu, Kwangjun Ahn, X. Cheng, Thibaut Le Gouic, P. Rigollet
- Computer Science, Mathematics
- COLT
- 23 December 2020

TLDR

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, i.e., parametric, rates of convergence for empirical barycenters over a large class of geodesic spaces with curvature bounds in the sense of Alexandrov. More specifically,… Expand

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