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 …

Optimal Transport (OT) has recently emerged as a central tool in data sciences to compare
in a geometrically faithful way point clouds and more generally probability distributions. The …

Solving transport problems, ie finding a map transporting one given distribution to another,
has numerous applications in machine learning. Novel mass transport methods motivated …

Many decision problems in science, engineering, and economics are affected by uncertain
parameters whose distribution is only indirectly observable through samples. The goal of …

Simulation-free methods for training continuous-time generative models construct probability
paths that go between noise distributions and individual data samples. Recent works, such …

We consider the problem of estimating the optimal transport map between two probability
distributions, $ P $ and $ Q $ in $\mathbb {R}^ d $, on the basis of iid samples. All existing …

Estimation of Wasserstein distances in the Spiked Transport Model Page 1 Bernoulli 28(4),
2022, 2663–2688 https://doi.org/10.3150/21-BEJ1433 Estimation of Wasserstein distances …

This work investigates the use of robust optimal transport (OT) for shape matching.
Specifically, we show that recent OT solvers improve both optimization-based and deep …

Classification is a fundamental problem in machine learning, and considerable efforts have
been recently devoted to the demanding long-tailed setting due to its prevalence in nature …

The supplementary materials contain more background on convex functions, wavelets and
empirical processes, as well as tools to prove lower bounds, alternative assumptions based …