ARI GUEST TALK: 13. 5. 2024
Optimal Transport (OT) theory has emerged as a powerful tool across various fields, including machine learning and signal processing analysis. We will start with an overview of OT theory, focusing on the Wasserstein distance for probability measures through Monge’s, Kantorovich’s, and dynamic formulations of the OT problem. We will emphasize why the Wasserstein distance is useful for discriminating distributions. Additionally, we will introduce an "embedding" or "transform" based on OT: the “Linear Optimal Transport Embedding” (LOT), which significantly reduces the computational cost of the Wasserstein distance. Furthermore, we will discuss its 1D version, known as the Cumulative Distribution Transform (CDT). If time permits, we will explore the balanced mass limitation in classical OT, thus delving into Partial Optimal Transport and Unbalanced Optimal Transport.
The talk will cover parts of joint works with A. Aldroubi, Y. Bai, S. Kolouri, I. Medri, S. Thareja, G. Rohde, and the MINT Lab at Vanderbilt University.
About herself: I am an Argentinian mathematician, currently working as a postdoctoral researcher at Vanderbilt University in Nashville, TN, USA. My primary research interests lie in the field of Harmonic Analysis. In recent years, I have been particularly focused on studying Optimal Transport Theory. This fascinating topic has not only allowed me to expand my mathematical expertise but has also provided opportunities to explore its applications and collaborate with experts in Computer Science.