2 citations · 6 across the 14 of their papers we have counts for
14 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…
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…
Sliced-Wasserstein Distances and Flows on Cartan-Hadamard Manifolds
Clément Bonet, Lucas Drumetz, Nicolas Courty
While many Machine Learning methods were developed or transposed on Riemannian manifolds to tackle data with known non Euclidean geometry, Optimal Transport (OT) methods on such sp…
Leveraging Optimal Transport via Projections on Subspaces for Machine Learning Applications
Clément Bonet
Optimal Transport has received much attention in Machine Learning as it allows to compare probability distributions by exploiting the geometry of the underlying space. However, in…
Fast Optimal Transport through Sliced Wasserstein Generalized Geodesics
Guillaume Mahey, Laetitia Chapel, Gilles Gasso +2
Wasserstein distance (WD) and the associated optimal transport plan have been proven useful in many applications where probability measures are at stake. In this paper, we propose…
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…
Sliced-Wasserstein on Symmetric Positive Definite Matrices for M/EEG Signals
Clément Bonet, Benoît Malézieux, Alain Rakotomamonjy +4
When dealing with electro or magnetoencephalography records, many supervised prediction tasks are solved by working with covariance matrices to summarize the signals. Learning with…
Hyperbolic Sliced-Wasserstein via Geodesic and Horospherical Projections
Clément Bonet, Laetitia Chapel, Lucas Drumetz +1
It has been shown beneficial for many types of data which present an underlying hierarchical structure to be embedded in hyperbolic spaces. Consequently, many tools of machine lear…
Spherical Sliced-Wasserstein
Clément Bonet, Paul Berg, Nicolas Courty +3
Many variants of the Wasserstein distance have been introduced to reduce its original computational burden. In particular the Sliced-Wasserstein distance (SW), which leverages one-…
Subspace Detours Meet Gromov-Wasserstein
Clément Bonet, Nicolas Courty, François Septier +1
In the context of optimal transport methods, the subspace detour approach was recently presented by Muzellec and Cuturi (2019). It consists in building a nearly optimal transport p…
Efficient Gradient Flows in Sliced-Wasserstein Space
Clément Bonet, Nicolas Courty, François Septier +1
Minimizing functionals in the space of probability distributions can be done with Wasserstein gradient flows. To solve them numerically, a possible approach is to rely on the Jorda…