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Distributional Limit Theory for Optimal Transport
Eustasio del Barrio, Alberto González-Sanz, Jean-Michel Loubes +1
The paper surveys recent theoretical results on the statistical behavior of empirical optimal transport quantities, such as plans, maps, and costs, and discusses how to construct c…
An improved central limit theorem for the empirical sliced Wasserstein distance
David RodrÃguez-VÃtores, Eustasio del Barrio, Jean-Michel Loubes
Wasserstein distances are widely used in modern data analysis but pose significant computational and statistical challenges in high dimensions. The sliced Wasserstein distance alle…
Sample Complexity of Quadratically Regularized Optimal Transport
Alberto González-Sanz, Eustasio del Barrio, Marcel Nutz
It is well known that optimal transport suffers from the curse of dimensionality: when the prescribed marginals are approximated by i.i.d. samples, the convergence of the empirical…