147 citations
Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.
- Centre de Recherche en Mathématiques de la DécisionFR19 papers
- Centre National de la Recherche ScientifiqueFR11 papers
- Institut national de recherche en sciences et technologies du numériqueFR11 papers
- Université Paris Dauphine-PSLFR7 papers
- Département de mathématiques et applicationsFR6 papers
- École Normale Supérieure - PSLFR4 papers
- Laboratoire d'Informatique Gaspard-MongeFR4 papers
- Université Gustave EiffelFR4 papers
- Centre de Mathématiques Appliquées de l'École polytechniqueFR3 papers
- École PolytechniqueFR3 papers
- Laboratoire de Probabilités, Statistique et ModélisationFR3 papers
- Kyoto UniversityJP2 papers
30 papers
A geometric Laplace method
Flavien Léger, François-Xavier Vialard
A classical tool for approximating integrals is the Laplace method. The first-order, as well as the higher-order Laplace formula is most often written in coordinates without any ge…
From geodesic extrapolation to a variational BDF2 scheme for Wasserstein gradient flows
Thomas Gallouët, Andrea Natale, Gabriele Todeschi
We introduce a time discretization for Wasserstein gradient flows based on the classical Backward Differentiation Formula of order two. The main building block of the scheme is the…
Quantitative Stability of Barycenters in the Wasserstein Space
Guillaume Carlier, Alex Delalande, Quentin Merigot
Wasserstein barycenters define averages of probability measures in a geometrically meaningful way. Their use is increasingly popular in applied fields, such as image, geometry or l…
Mass concentration in rescaled first order integral functionals
Antonin Monteil, Paul Pegon
We consider first order local minimization problems of the form under a mass constraint . We prove that the minimal…
Is interpolation benign for random forest regression?
Ludovic Arnould, Claire Boyer, Erwan Scornet
Statistical wisdom suggests that very complex models, interpolating training data, will be poor at predicting unseen examples.Yet, this aphorism has been recently challenged by the…
Regularity theory and geometry of unbalanced optimal transport
Thomas Gallouët, Roberta Ghezzi, François-Xavier Vialard
Using the dual formulation only, we show that the regularity of unbalanced optimal transport also called entropy-transport inherits from the regularity of standard optimal transpor…
Model-based Clustering with Missing Not At Random Data
Aude Sportisse, Matthieu Marbac, Fabien Laporte +4
Model-based unsupervised learning, as any learning task, stalls as soon as missing data occurs. This is even more true when the missing data are informative, or said missing not at…
Parameter tuning and model selection in optimal transport with semi-dual Brenier formulation
Adrien Vacher, François-Xavier Vialard
Over the past few years, numerous computational models have been developed to solve Optimal Transport (OT) in a stochastic setting, where distributions are represented by samples a…
Convergence of a Lagrangian discretization for barotropic fluids and porous media flow
Thomas Gallouët, Quentin Merigot, Andrea Natale
When expressed in Lagrangian variables, the equations of motion for compressible (barotropic) fluids have the structure of a classical Hamiltonian system in which the potential ene…
Towards Off-the-grid Algorithms for Total Variation Regularized Inverse Problems
Yohann de Castro, Vincent Duval, Romain Petit
We introduce an algorithm to solve linear inverse problems regularized with the total (gradient) variation in a gridless manner. Contrary to most existing methods, that produce an…
Stability in Gagliardo-Nirenberg-Sobolev inequalities: flows, regularity and the entropy method
Matteo Bonforte, Jean Dolbeault, Bruno Nazaret +1
The purpose of this work is to establish a quantitative and constructive stability result for a class of subcritical Gagliardo-Nirenberg-Sobolev inequalities which interpolates bet…
Sample Complexity of Sinkhorn divergences
Aude Genevay, Lénaic Chizat, Francis Bach +2
Optimal transport (OT) and maximum mean discrepancies (MMD) are now routinely used in machine learning to compare probability measures. We focus in this paper on \emph{Sinkhorn div…
Generalized compressible flows and solutions of the H(div) geodesic problem
Thomas Gallouët, Andrea Natale, François-Xavier Vialard
We study the geodesic problem on the group of diffeomorphism of a domain MRd, equipped with the H(div) metric. The geodesic equations coincide with the Camassa-Holm equati…
On Representer Theorems and Convex Regularization
Claire Boyer, Antonin Chambolle, Yohann De Castro +3
We establish a general principle which states that regularizing an inverse problem with a convex function yields solutions which are convex combinations of a small number of atoms.…
Stein operators, kernels and discrepancies for multivariate continuous distributions
Guillaume Mijoule, Gesine Reinert, Yvik Swan
In this paper we present a general framework for Stein's method for multivariate continuous distributions. The approach gives a collection of Stein characterisations, among which w…
Regularity of solutions of the Stein equation and rates in the multivariate central limit theorem
Thomas Gallouët, Guillaume Mijoule, Yvik Swan
Consider the multivariate Stein equation , where is a standard -dimensional Gaussian random vector, and let be the solution give…
Embedding Camassa-Holm equations in incompressible Euler
François-Xavier Vialard, Andrea Natale
In this article, we show how to embed the so-called CH2 equations into the geodesic flow of the Hdiv metric in 2D, which, itself, can be embedded in the incompressible Euler equati…
A Low-Rank Approach to Off-The-Grid Sparse Deconvolution
Paul Catala, Vincent Duval, Gabriel Peyré
We propose a new solver for the sparse spikes deconvolution problem over the space of Radon measures. A common approach to off-the-grid deconvolution considers semidefinite (SDP) r…
Minimal convex extensions and finite difference discretization of the quadratic Monge-Kantorovich problem
Jean-David Benamou, Vincent Duval
We present an adaptation of the MA-LBR scheme to the Monge-Amp{è}re equation with second boundary value condition, provided the target is a convex set. This yields a fast adaptive…
Optimal Transport for Diffeomorphic Registration
Jean Feydy, Benjamin Charlier, François-Xavier Vialard +1
This paper introduces the use of unbalanced optimal transport methods as a similarity measure for diffeomorphic matching of imaging data. The similarity measure is a key object in…
A study of the dual problem of the one-dimensional L-infinity optimal transport problem with applications
Luigi De Pascale, Jean Louet
The Monge-Kantorovich problem for the infinite Wasserstein distance presents several peculiarities. Among them the lack of convexity and then of a direct duality. We study in dimen…
The entropic regularization of the Monge problem on the real line
Simone Di Marino, Jean Louet
We study the entropic regularization of the optimal transport problem in dimension 1 when the cost function is the distance c(x, y) = |y -- x|. The selected plan at the limit is, a…
Quantum Optimal Transport for Tensor Field Processing
Gabriel Peyré, Lenaïc Chizat, François-Xavier Vialard +1
This article introduces a new notion of optimal transport (OT) between tensor fields, which are measures whose values are positive semidefinite (PSD) matrices. This "quantum" formu…
Stochastic Optimization for Large-scale Optimal Transport
Genevay Aude, Marco Cuturi, Gabriel Peyré +1
Optimal transport (OT) defines a powerful framework to compare probability distributions in a geometrically faithful way. However, the practical impact of OT is still limited becau…