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 …

The ability to compare two degenerate probability distributions, that is two distributions
supported on low-dimensional manifolds in much higher-dimensional spaces, is a crucial …

The Wasserstein distance between two probability measures on a metric space is a
measure of closeness with applications in statistics, probability, and machine learning. In …

Optimal transport (OT) and maximum mean discrepancies (MMD) are now routinely used in
machine learning to compare probability measures. We focus in this paper on Sinkhorn …

Optimal transport (OT) defines a powerful framework to compare probability distributions in a
geometrically faithful way. However, the practical impact of OT is still limited because of its …

We develop a computationally tractable method for estimating the optimal map between two
distributions over $\mathbb {R}^ d $ with rigorous finite-sample guarantees. Leveraging an …

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

In 1931--1932, Erwin Schrödinger studied a hot gas Gedankenexperiment (an instance of
large deviations of the empirical distribution). Schrödinger's problem represents an early …

This text develops mathematical foundations for entropic optimal transport and Sinkhorn's
algorithm in a self-contained yet general way. It is a revised version of lecture notes from a …

Scaling algorithms for entropic transport-type problems have become a very popular
numerical method, encompassing Wasserstein barycenters, multimarginal problems …