Optimal transport (OT) theory can be informally described using the words of the French
mathematician Gaspard Monge (1746–1818): A worker with a shovel in hand has to move a …

This article reviews the use of first order convex optimization schemes to solve the
discretized dynamic optimal transport problem, initially proposed by Benamou and Brenier …

Optimal transport has recently been reintroduced to the machine learning community thanks
in part to novel efficient optimization procedures allowing for medium to large scale …

Computing optimal transport distances such as the earth mover's distance is a fundamental
problem in machine learning, statistics, and computer vision. Despite the recent introduction …

Estimating individual treatment effects from observational data is challenging due to
treatment selection bias. Prevalent methods mainly mitigate this issue by aligning different …

Domain adaptation is one of the most challenging tasks of modern data analytics. If the
adaptation is done correctly, models built on a specific data representation become more …

This paper details a general numerical framework to approximate solutions to linear
programs related to optimal transport. The general idea is to introduce an entropic …

This paper introduces a new class of algorithms for optimization problems involving optimal
transportation over geometric domains. Our main contribution is to show that optimal …

We investigate the parameterization of deep neural networks that by design satisfy the
continuity equation, a fundamental conservation law. This is enabled by the observation that …

This article introduces a new class of fast algorithms to approximate variational problems
involving unbalanced optimal transport. While classical optimal transport considers only …