Abstract: The optimal transport (OT) problem seeks the most efficient way to transport a distribution of mass from one configuration to another, minimizing the cost associated with the transportation process. This framework has found diverse applications in machine learning due to its ability to define meaningful distances, known as Wasserstein distances, between probability distributions. However, Wasserstein distances can be computationally expensive, particularly in high-dimensional settings. In this seminar, we will introduce a new class of OT-based metrics designed to address these computational challenges. These metrics maintain the desirable properties of the Wasserstein distance while offering significant improvements in efficiency, making them more suitable for large-scale applications.