The concepts of risk-aversion, chance-constrained optimization, and robust optimization
have developed significantly over the last decade. Statistical learning community has also …

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 …

While efficient distribution learning is no doubt behind the groundbreaking success of
diffusion modeling, its theoretical guarantees are quite limited. In this paper, we provide the …

The squared Wasserstein distance is a natural quantity to compare probability distributions
in a non-parametric setting. This quantity is usually estimated with the plug-in estimator …

Understanding generalization and robustness of machine learning models fundamentally
relies on assuming an appropriate metric on the data space. Identifying such a metric is …

Distributionally robust optimization (DRO) has attracted attention in machine learning due to
its connections to regularization, generalization, and robustness. Existing work has …

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 …

We provide upper bounds of the expected Wasserstein distance between a probability
measure and its empirical version, generalizing recent results for finite dimensional …

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

This paper studies the rates of convergence for learning distributions implicitly with the
adversarial framework and Generative Adversarial Networks (GANs), which subsume …