113 citations · 638 across the 37 of their papers we have counts for
14 papers · 1 filter
Gauss-Newton drifting extends natural gradient descent
Théo Dumont, Théo Lacombe, François-Xavier Vialard
Drifting methods have recently been introduced as a promising new paradigm for training generative models, and have attracted a lot of attention so far. In this work, we focus on h…
On the existence of Monge maps for the Gromov-Wasserstein problem
Théo Dumont, Théo Lacombe, François-Xavier Vialard
The Gromov--Wasserstein problem is a non-convex optimization problem over the polytope of transportation plans between two probability measures supported on two spaces, each equipp…
Toric Geometry of Entropic Regularization
Bernd Sturmfels, Simon Telen, François-Xavier Vialard +1
Entropic regularization is a method for large-scale linear programming. Geometrically, one traces intersections of the feasible polytope with scaled toric varieties, starting at th…
Faster Unbalanced Optimal Transport: Translation invariant Sinkhorn and 1-D Frank-Wolfe
Thibault Séjourné, François-Xavier Vialard, Gabriel Peyré
Unbalanced optimal transport (UOT) extends optimal transport (OT) to take into account mass variations to compare distributions. This is crucial to make OT successful in ML applica…
The Unbalanced Gromov Wasserstein Distance: Conic Formulation and Relaxation
Thibault Séjourné, François-Xavier Vialard, Gabriel Peyré
Comparing metric measure spaces (i.e. a metric space endowed with aprobability distribution) is at the heart of many machine learning problems. The most popular distance between su…
Faster Wasserstein Distance Estimation with the Sinkhorn Divergence
Lenaic Chizat, Pierre Roussillon, Flavien Léger +2
The squared Wasserstein distance is a natural quantity to compare probability distributions in a non-parametric setting. This quantity is usually estimated with the plug-in estimat…
Sinkhorn Divergences for Unbalanced Optimal Transport
Thibault Séjourné, Jean Feydy, François-Xavier Vialard +2
Optimal transport induces the Earth Mover's (Wasserstein) distance between probability distributions, a geometric divergence that is relevant to a wide range of problems. Over the…
Second order models for optimal transport and cubic splines on the Wasserstein space
Jean-David Benamou, Thomas Gallouët, François-Xavier Vialard
On the space of probability densities, we extend the Wasserstein geodesics to the case of higher-order interpolation such as cubic spline interpolation. After presenting the natura…
Scaling Algorithms for Unbalanced Transport Problems
Lenaic Chizat, Gabriel Peyré, Bernhard Schmitzer +1
This article introduces a new class of fast algorithms to approximate variational problems involving unbalanced optimal transport. While classical optimal transport considers only…
Riemannian cubics on the group of diffeomorphisms and the Fisher-Rao metric
Rabah Tahraoui, François-Xavier Vialard
We study a second-order variational problem on the group of diffeomorphisms of the interval [0, 1] endowed with a right-invariant Sobolev metric of order 2, which consists in the m…
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…
Geodesics on Shape Spaces with Bounded Variation and Sobolev Metrics
G. Nardi, G. Peyré, F. -X. Vialard
This paper studies the space of planar curves endowed with the Finsler metric over its tangent space of displacement vector fields. Such a space is of interest for ap…
Invariant higher-order variational problems II
François Gay-Balmaz, Darryl D. Holm, David M. Meier +2
Motivated by applications in computational anatomy, we consider a second-order problem in the calculus of variations on object manifolds that are acted upon by Lie groups of smooth…
Shape Splines and Stochastic Shape Evolutions: A Second Order Point of View
Alain Trouvé, François-Xavier Vialard
This article presents a new mathematical framework to perform statistical analysis on time-indexed sequences of 2D or 3D shapes. At the core of this statistical analysis is the tas…