5 papers
p-Wasserstein distances on networks and 3D to 1D convergence
Martin Burger, Ariane Fazeny, Gilles Mordant +1
We study transport distances on metric graphs representing gas networks. Starting from the dynamic formulation of the Wasserstein distance, we review extensions to networks, with a…
Estimation of Algebraic Sets: Extending PCA Beyond Linearity
Alberto González-Sanz, Gilles Mordant, Álvaro Samperio +1
An algebraic set is defined as the zero locus of a system of real polynomial equations. In this paper we address the problem of recovering an unknown algebraic set fr…
Infinitesimal behavior of Quadratically Regularized Optimal Transport and its relation with the Porous Medium Equation
Alejandro Garriz-Molina, Alberto González-Sanz, Gilles Mordant
The quadratically regularized optimal transport problem has recently been considered in various applications where the coupling needs to be \emph{sparse}, i.e., the density of the…
Regularised optimal self-transport is approximate Gaussian mixture maximum likelihood
Gilles Mordant
We investigate the link between regularised self-transport problems and maximum likelihood estimation in Gaussian mixture models (GMM). This link suggests that self-transport follo…
Extrema of multinomial assignment process
Mikhail Lifshits, Gilles Mordant
We study the asymptotic behavior of the expectation of the maxima and minima of random assignment process generated by a large matrix with multinomial entries. A variety of results…