Comparing probability distributions is a fundamental problem in data sciences. Simple
norms and divergences such as the total variation and the relative entropy only compare …

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 …

Wasserstein distance plays increasingly important roles in machine learning, stochastic
programming and image processing. Major efforts have been under way to address its high …

Abstract Generative Adversarial Networks (GANs) are one of the most practical methods for
learning data distributions. A popular GAN formulation is based on the use of Wasserstein …

Comparing metric measure spaces (ie a metric space endowed with a probability
distribution) is at the heart of many machine learning problems. The most popular distance …

This paper addresses the problem of Unbalanced Optimal Transport (UOT) in which the
marginal conditions are relaxed (using weighted penalties in lieu of equality) and no …

This paper presents a unified framework for smooth convex regularization of discrete optimal
transport problems. In this context, the regularized optimal transport turns out to be …

We study the use of amortized optimization to predict optimal transport (OT) maps from the
input measures, which we call Meta OT. This helps repeatedly solve similar OT problems …

Trajectory inference aims at recovering the dynamics of a population from snapshots of its
temporal marginals. To solve this task, a min-entropy estimator relative to the Wiener …

Optimal Transport (OT) is a mathematical framework that first emerged in the eighteenth
century and has led to a plethora of methods for answering many theoretical and applied …