18 citations · 75 across the 20 of their papers we have counts for
22 papers
Extending the Wasserstein metric to positive measures
Hugo Leblanc, Thibaut Le Gouic, Jacques Liandrat +1
We define a metric in the space of positive finite positive measures that extends the 2-Wasserstein metric, i.e. its restriction to the set of probability measures is the 2-Wassers…
Bures-Wasserstein Barycenters and Low-Rank Matrix Recovery
Tyler Maunu, Thibaut Le Gouic, Philippe Rigollet
We revisit the problem of recovering a low-rank positive semidefinite matrix from rank-one projections using tools from optimal transport. More specifically, we show that a variati…
An algorithmic solution to the Blotto game using multi-marginal couplings
Vianney Perchet, Philippe Rigollet, Thibaut Le Gouic
We describe an efficient algorithm to compute solutions for the general two-player Blotto game on n battlefields with heterogeneous values. While explicit constructions for such so…
A probabilistic model for fast-to-evaluate 2D crack path prediction in heterogeneous materials
Kathleen Pele, Jean Baccou, Loïc Daridon +4
This paper is devoted to the construction of a new fast-to-evaluate model for the prediction of 2D crack paths in concrete-like microstructures. The model generates piecewise linea…
The query complexity of sampling from strongly log-concave distributions in one dimension
Sinho Chewi, Patrik Gerber, Chen Lu +2
We establish the first tight lower bound of on the query complexity of sampling from the class of strongly log-concave and log-smooth distributions with condition nu…
Rejection sampling from shape-constrained distributions in sublinear time
Sinho Chewi, Patrik Gerber, Chen Lu +2
We consider the task of generating exact samples from a target distribution, known up to normalization, over a finite alphabet. The classical algorithm for this task is rejection s…
Sampling From the Wasserstein Barycenter
Chiheb Daaloul, Thibaut Le Gouic, Jacques Liandrat +1
This work presents an algorithm to sample from the Wasserstein barycenter of absolutely continuous measures. Our method is based on the gradient flow of the multimarginal formulati…
Optimal dimension dependence of the Metropolis-Adjusted Langevin Algorithm
Sinho Chewi, Chen Lu, Kwangjun Ahn +3
Conventional wisdom in the sampling literature, backed by a popular diffusion scaling limit, suggests that the mixing time of the Metropolis-Adjusted Langevin Algorithm (MALA) scal…
Fast and Smooth Interpolation on Wasserstein Space
Sinho Chewi, Julien Clancy, Thibaut Le Gouic +3
We propose a new method for smoothly interpolating probability measures using the geometry of optimal transport. To that end, we reduce this problem to the classical Euclidean sett…
Projection to Fairness in Statistical Learning
Thibaut Le Gouic, Jean-Michel Loubes, Philippe Rigollet
In the context of regression, we consider the fundamental question of making an estimator fair while preserving its prediction accuracy as much as possible. To that end, we define…
SVGD as a kernelized Wasserstein gradient flow of the chi-squared divergence
Sinho Chewi, Thibaut Le Gouic, Chen Lu +2
Stein Variational Gradient Descent (SVGD), a popular sampling algorithm, is often described as the kernelized gradient flow for the Kullback-Leibler divergence in the geometry of o…
Exponential ergodicity of mirror-Langevin diffusions
Sinho Chewi, Thibaut Le Gouic, Chen Lu +3
Motivated by the problem of sampling from ill-conditioned log-concave distributions, we give a clean non-asymptotic convergence analysis of mirror-Langevin diffusions as introduced…
Fast convergence of empirical barycenters in Alexandrov spaces and the Wasserstein space
Thibaut Le Gouic, Quentin Paris, Philippe Rigollet +1
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,…
A note on flatness of non separable tangent cone
Thibaut Le Gouic
Given a probability measure P on an Alexandrov space S with curvature bounded below, we prove that the support of the pushforward of P on the tangent cone at its (exponential) bary…
Convergence rates for empirical barycenters in metric spaces: curvature, convexity and extendible geodesics
Adil Ahidar-Coutrix, Thibaut Le Gouic, Quentin Paris
This paper provides rates of convergence for empirical (generalised) barycenters on compact geodesic metric spaces under general conditions using empirical processes techniques. Ou…
A notion of stability for k-means clustering
Thibaut Le Gouic, Quentin Paris
In this paper, we define and study a new notion of stability for the -means clustering scheme building upon the notion of quantization of a probability measure. We connect this…
Unconstrained and Curvature-Constrained Shortest-Path Distances and their Approximation
Ery Arias-Castro, Thibaut Le Gouic
We study shortest paths and their distances on a subset of a Euclidean space, and their approximation by their equivalents in a neighborhood graph defined on a sample from that sub…
Mass localization
Thibaut Le Gouic
For a given class of closed sets of a measured metric space , we want to find the smallest element of the class such that , f…
Existence and Consistency of Wasserstein Barycenters
Thibaut Le Gouic, Jean-Michel Loubes
In this paper, based on the Fr{é}chet mean, we define a notion of barycenter corresponding to a usual notion of statistical mean. We prove the existence of Wasserstein barycenters…
Recovering metric from full ordinal information
Thibaut Le Gouic
Given a geodesic space (E, d), we show that full ordinal knowledge on the metric d-i.e. knowledge of the function D d : (w, x, y, z) 1 d(w,x)d(y,z) , determines…
Distribution's template estimate with Wasserstein metrics
Emmanuel Boissard, Thibaut Le Gouic, Jean-Michel Loubes
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 t…
On the mean speed of convergence of empirical and occupation measures in Wasserstein distance
Emmanuel Boissard, Thibaut Le Gouic
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…