366 citations · 1.8k across the 46 of their papers we have counts for
52 papers
Wasserstein Control of Mirror Langevin Monte Carlo
Kelvin Shuangjian Zhang, Gabriel Peyré, Jalal Fadili +1
Discretized Langevin diffusions are efficient Monte Carlo methods for sampling from high dimensional target densities that are log-Lipschitz-smooth and (strongly) log-concave. In p…
Geometric Losses for Distributional Learning
Arthur Mensch, Mathieu Blondel, Gabriel Peyré
Building upon recent advances in entropy-regularized optimal transport, and upon Fenchel duality between measures and continuous functions , we propose a generalization of the logi…
Universal Invariant and Equivariant Graph Neural Networks
Nicolas Keriven, Gabriel Peyré
Graph Neural Networks (GNN) come in many flavors, but should always be either invariant (permutation of the nodes of the input graph does not affect the output) or equivariant (per…
Semi-dual Regularized Optimal Transport
Marco Cuturi, Gabriel Peyré
Variational problems that involve Wasserstein distances and more generally optimal transport (OT) theory are playing an increasingly important role in data sciences. Such problems…
Stochastic Deep Networks
Gwendoline de Bie, Gabriel Peyré, Marco Cuturi
Machine learning is increasingly targeting areas where input data cannot be accurately described by a single vector, but can be modeled instead using the more flexible concept of r…
Interpolating between Optimal Transport and MMD using Sinkhorn Divergences
Jean Feydy, Thibault Séjourné, François-Xavier Vialard +3
Comparing probability distributions is a fundamental problem in data sciences. Simple norms and divergences such as the total variation and the relative entropy only compare densit…
Support Localization and the Fisher Metric for off-the-grid Sparse Regularization
Clarice Poon, Nicolas Keriven, Gabriel Peyré
Sparse regularization is a central technique for both machine learning (to achieve supervised features selection or unsupervised mixture learning) and imaging sciences (to achieve…
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…
Model Consistency for Learning with Mirror-Stratifiable Regularizers
Jalal Fadili, Guillaume Garrigos, Jérome Malick +1
Low-complexity non-smooth convex regularizers are routinely used to impose some structure (such as sparsity or low-rank) on the coefficients for linear predictors in supervised lea…
Computational Optimal Transport
Gabriel Peyré, Marco Cuturi
Optimal transport (OT) theory can be informally described using the words of the French mathematician Gaspard Monge (1746-1818): A worker with a shovel in hand has to move a large…
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…
Multi-dimensional Sparse Super-resolution
Clarice Poon, Gabriel Peyré
This paper studies sparse super-resolution in arbitrary dimensions. More precisely, it develops a theoretical analysis of support recovery for the so-called BLASSO method, which is…
Wasserstein Dictionary Learning: Optimal Transport-based unsupervised non-linear dictionary learning
Morgan A. Schmitz, Matthieu Heitz, Nicolas Bonneel +5
This paper introduces a new nonlinear dictionary learning method for histograms in the probability simplex. The method leverages optimal transport theory, in the sense that our aim…
Sensitivity Analysis for Mirror-Stratifiable Convex Functions
Jalal Fadili, Jérôme Malick, Gabriel Peyré
This paper provides a set of sensitivity analysis and activity identification results for a class of convex functions with a strong geometric structure, that we coined "mirror-stra…
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…
Learning Generative Models with Sinkhorn Divergences
Aude Genevay, Gabriel Peyré, Marco Cuturi
The ability to compare two degenerate probability distributions (i.e. two probability distributions supported on two distinct low-dimensional manifolds living in a much higher-dime…
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…
Sparse Support Recovery with Non-smooth Loss Functions
Kévin Degraux, Gabriel Peyré, Jalal M. Fadili +1
In this paper, we study the support recovery guarantees of underdetermined sparse regression using the -norm as a regularizer and a non-smooth loss function for data fideli…
Bayesian Modeling of Motion Perception using Dynamical Stochastic Textures
Jonathan Vacher, Andrew Isaac Meso, Laurent U. Perrinet +1
A common practice to account for psychophysical biases in vision is to frame them as consequences of a dynamic process relying on optimal inference with respect to a generative mod…
A Multi-step Inertial Forward--Backward Splitting Method for Non-convex Optimization
Jingwei Liang, Jalal Fadili, Gabriel Peyré
In this paper, we propose a multi-step inertial Forward--Backward splitting algorithm for minimizing the sum of two non-necessarily convex functions, one of which is proper lower s…
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…
Convergence of Entropic Schemes for Optimal Transport and Gradient Flows
Guillaume Carlier, Vincent Duval, Gabriel Peyré +1
Replacing positivity constraints by an entropy barrier is popular to approximate solutions of linear programs. In the special case of the optimal transport problem, this technique…
Biologically Inspired Dynamic Textures for Probing Motion Perception
Jonathan Vacher, Andrew Meso, Laurent U Perrinet +1
Perception is often described as a predictive process based on an optimal inference with respect to a generative model. We study here the principled construction of a generative mo…
Unbalanced Optimal Transport: Dynamic and Kantorovich Formulation
Lenaic Chizat, Gabriel Peyré, Bernhard Schmitzer +1
This article presents a new class of distances between arbitrary nonnegative Radon measures inspired by optimal transport. These distances are defined by two equivalent alternative…