activity
20192025
most citedQuantitative stability of optimal transport maps and linearization of the 2-Wasserstein space

13 citations · 16 across the 7 of their papers we have counts for

collaborators

7 papers

math.FA2025

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…

math.OC2024

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…

math.OC2024

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…

math.NA2022

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…

cs.AI2021★ 2 cited

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…

math.FA2021★ 1 cited

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…

stat.ML2019★ 13 cited

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…