Controlling Wasserstein Distances by Kernel Norms with Application to Compressive Statistical Learning

Comparing probability distributions is at the crux of many machine learning algorithms. Maximum Mean Discrepancies (MMD) and Wasserstein distances are two classes of distances between probability distributions that have attracted abundant attention in past years. This paper establishes some conditions under which the Wasserstein distance can be controlled by MMD norms. Our work is motivated by the compressive statistical learning (CSL) theory, a general framework for resource-efficient large sca...