Optimal Transport Maps: Theory and Applications

Abstract

PhD Defense:

Over the last few years Optimal Transport (OT) has become ubiquitous in data science and machine learning. It can be used in several ways such as quantifying the difference between distributions, learning well- behaved transformations between two shapes, or to model dynamics over time just to name a few of its uses. While these techniques have been widely employed, they are often void of theoretical guarantees or are explicitly known to have poor worst-case performance, especially when working with high-dimensional data (the curse of dimensionality). In this defense we will cover two applications where OT arises as well as a variant of OT, known as the entropy-regularized OT (EOT) problem which can be leveraged to provide positive theoretical performance guarantees. These results are essential for working with OT tools in problems with high-dimensional data, a setting which is become more and more prevalent in data science.

Please join the meeting in JCC 302 or via Zoom: https://tufts.zoom.us/j/95841599881? pwd=nVbeWwCxgsb1FXoKWxYHiQqGan08F4.1