113 citations · 638 across the 37 of their papers we have counts for
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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…
Unbalanced Optimal Transport, from Theory to Numerics
Thibault Séjourné, Gabriel Peyré, François-Xavier Vialard
Optimal Transport (OT) has recently emerged as a central tool in data sciences to compare in a geometrically faithful way point clouds and more generally probability distributions.…
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…