More recently, Newton-type methods using sparsified Hessian matrices have demonstrated promising results on OT computation, but there still remain a lot of unresolved open questions.

Using these smoothed rank andsort operators, we propose differentiable proxies for the classification 0/1 loss as well as for the quantileregressionloss.

This paper introduces anew onlineestimator ofentropy-regularized OTdistances between twosucharbitrary distributions.

Transportation cost is an attractive similarity measure between probability distributions due to its many useful theoretical properties. However, solving optimal transport exactly can be prohibitively expensive. Therefore, there has been significant effort towards the design of scalable approximation algorithms.

Optimal Transport (OT) distances are now routinely used as loss functions in ML tasks.

Many problems in computational sciences require to compare probability measures or histograms.