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

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

We study first order methods to compute the barycenter of a probability distribution $ P $
over the space of probability measures with finite second moment. We develop a framework …

Variational problems that involve Wasserstein distances have been recently proposed to
summarize and learn from probability measures. Despite being conceptually simple, such …

We consider in this paper the dictionary learning problem when the observations are
normalized histograms of features. This problem can be tackled using non-negative matrix …

This article defines a new way to perform intuitive and geometrically faithful regressions on
histogram-valued data. It leverages the theory of optimal transport, and in particular the …

We study first-order optimization algorithms for computing the barycenter of Gaussian
distributions with respect to the optimal transport metric. Although the objective is …

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

We propose a new method to estimate Wasserstein distances and optimal transport plans
between two probability distributions from samples in high dimension. Unlike plug-in rules …