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

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 …

The ability to compare two degenerate probability distributions, that is two distributions
supported on low-dimensional manifolds in much higher-dimensional spaces, is a crucial …

There is intense interest in applying machine learning to problems of causal inference in
fields such as healthcare, economics and education. In particular, individual-level causal …

A Hilbert space embedding of a distribution—in short, a kernel mean embedding—has
recently emerged as a powerful tool for machine learning and statistical inference. The basic …

Optimal transport (OT) and maximum mean discrepancies (MMD) are now routinely used in
machine learning to compare probability measures. We focus in this paper on Sinkhorn …

Transformers play a central role in the inner workings of large language models. We
develop a mathematical framework for analyzing Transformers based on their interpretation …

Optimal transport (OT) defines a powerful framework to compare probability distributions in a
geometrically faithful way. However, the practical impact of OT is still limited because of its …

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 …

We present a unified framework for deriving PAC-Bayesian generalization bounds. Unlike
most previous literature on this topic, our bounds are anytime-valid (ie, time-uniform) …