Recently, Optimal Transport has been proposed as a probabilistic framework in Machine
Learning for comparing and manipulating probability distributions. This is rooted in its rich …

Optimal transport (OT) methods seek a transformation map (or plan) between two probability
measures, such that the transformation has the minimum transportation cost. Such a …

Sliced Wasserstein distances preserve properties of classic Wasserstein distances while
being more scalable for computation and estimation in high dimensions. The goal of this …

Sliced-Wasserstein distance (SW) and its variant, Max Sliced-Wasserstein distance (Max-
SW), have been used widely in the recent years due to their fast computation and scalability …

Many variants of the Wasserstein distance have been introduced to reduce its original
computational burden. In particular the Sliced-Wasserstein distance (SW), which leverages …

The Wasserstein distance has become increasingly important in machine learning and deep
learning. Despite its popularity, the Wasserstein distance is hard to approximate because of …

Optimal transport (OT) distances are increasingly used as loss functions for statistical
inference, notably in the learning of generative models or supervised learning. Yet, the …

Quantifying dependence between high-dimensional random variables is central to statistical
learning and inference. Two classical methods are canonical correlation analysis (CCA) …

We study distributionally robust optimization (DRO) with Sinkhorn distance--a variant of
Wasserstein distance based on entropic regularization. We derive convex programming …

The conventional sliced Wasserstein is defined between two probability measures that have
realizations as\textit {vectors}. When comparing two probability measures over images …