6 papers
Difference of Convex Programming in the Wasserstein Space with Applications to MMD Optimization
Clément Bonet, Pierre-Cyril Aubin-Frankowski, Youssef Mroueh
Optimizing functionals over the space of probability measures is now ubiquitous in machine learning. A widely used approach is to perform the optimization directly over the Wassers…
Busemann Functions in the Wasserstein Space: Existence, Closed-Forms, and Applications to Slicing
Clément Bonet, Elsa Cazelles, Lucas Drumetz +1
The Busemann function has recently found much interest in a variety of geometric machine learning problems, as it naturally defines projections onto geodesic rays of Riemannian man…
Flowing Datasets with Wasserstein over Wasserstein Gradient Flows
Clément Bonet, Christophe Vauthier, Anna Korba
Many applications in machine learning involve data represented as probability distributions. The emergence of such data requires radically novel techniques to design tractable grad…
DDEQs: Distributional Deep Equilibrium Models through Wasserstein Gradient Flows
Jonathan Geuter, Clément Bonet, Anna Korba +1
Deep Equilibrium Models (DEQs) are a class of implicit neural networks that solve for a fixed point of a neural network in their forward pass. Traditionally, DEQs take sequences as…
Slicing Unbalanced Optimal Transport
Clément Bonet, Kimia Nadjahi, Thibault Séjourné +2
Optimal transport (OT) is a powerful framework to compare probability measures, a fundamental task in many statistical and machine learning problems. Substantial advances have been…
Mirror and Preconditioned Gradient Descent in Wasserstein Space
Clément Bonet, Théo Uscidda, Adam David +2
As the problem of minimizing functionals on the Wasserstein space encompasses many applications in machine learning, different optimization algorithms on have receiv…