Abstract:
Optimal transport (OT) has been attracting much research attention in various fields recently, including in particular machine learning, statistics, and computer vision.
This talk will consist of two parts. In the first part, we will give an overview of the mathematical formulation of OT and some of its applications in machine learning and computer vision. In the second part, we will discuss the entropic regularization of OT, which is an approach to alleviate the generally heavy computational demand of the exact OT problem. Our focus will be on the setting of Gaussian measures and Gaussian processes, where
the corresponding distances and divergences admit closed form expressions. In particular, we show that entropic regularized Wasserstein distance satisfies many favorable theoretical properties in comparison with the exact Wasserstein distance, including dimension-independent sample complexity, among others. The mathematical formulation will be illustrated with numerical experiments on Gaussian processes.
Referenti: Alessandra Di Pierro - Vittorio Murino
