Abstract

Optimal transport theory has been introduced two and a half centuries ago, as a means to compare two probability measures. This provides a natural mathematical framework for data based applications in machine learning and data science, as well as in finance. Most applications require some generalizations of the original theory. In this talk, we will briefly introduce the theory of optimal transport, then explore through simple applications its different generalizations. Topics include: Regularized optimal transport, Martingale optimal transport, Barycenter problem and interpolation, and if time permits sample based optimal transport.