13 citations · 16 across the 7 of their papers we have counts for
7 papers
Regularized Moment Measures
Alex Delalande, Sara Farinelli
In the work "Dealing with moment measures via entropy and optimal transport", Santambrogio provided an optimal transport approach to study existence of solutions for the moment mea…
Sharper Exponential Convergence Rates for Sinkhorn's Algorithm in Continuous Settings
Lénaïc Chizat, Alex Delalande, Tomas Vaškevičius
We study the convergence rate of Sinkhorn's algorithm for solving entropy-regularized optimal transport problems when at least one of the probability measures, , admits a densit…
Quantitative Stability of the Pushforward Operation by an Optimal Transport Map
Guillaume Carlier, Alex Delalande, Quentin Mérigot
We study the quantitative stability of the mapping that to a measure associates its pushforward measure by a fixed (non-smooth) optimal transport map. We exhibit a tight Hölder-beh…
Quantitative Stability of Barycenters in the Wasserstein Space
Guillaume Carlier, Alex Delalande, Quentin Merigot
Wasserstein barycenters define averages of probability measures in a geometrically meaningful way. Their use is increasingly popular in applied fields, such as image, geometry or l…
Nearly Tight Convergence Bounds for Semi-discrete Entropic Optimal Transport
Alex Delalande
We derive nearly tight and non-asymptotic convergence bounds for solutions of entropic semi-discrete optimal transport. These bounds quantify the stability of the dual solutions of…
Quantitative Stability of Optimal Transport Maps under Variations of the Target Measure
Alex Delalande, Quentin Merigot
This work studies the quantitative stability of the quadratic optimal transport map between a fixed probability density and a probability measure on R^d , which we denote T…
Quantitative stability of optimal transport maps and linearization of the 2-Wasserstein space
Quentin Mérigot, Alex Delalande, Frédéric Chazal
This work studies an explicit embedding of the set of probability measures into a Hilbert space, defined using optimal transport maps from a reference probability density. This emb…