IMA Data Science Seminar: Data depths meet Hamilton-Jacobi equations

The Institute for Mathematics and Its Applications (IMA) Data Science Seminars are a forum for data scientists of IMA academic and industrial partners to discuss and learn about recent developments in the broad area of data science. The seminars take place on Tuesdays from 1:25 p.m. - 2:25 p.m.

This week's speaker, Ryan Murray (North Carolina State University), will be giving a talk titled "Data depths meet Hamilton-Jacobi equations."

You may attend the talk either in person in Walter 402 or registering via Zoom.

Abstract

Widespread application of modern machine learning has increased the need for robust statistical algorithms. One fundamental geometric quantity in robust statistics is known as a data depth, which generalizes the notion of quantiles and medians to multiple dimensions. This talk will discuss recent work (in collaboration with Martin Molina-Fructuoso) which connects certain types of data depths with Hamilton-Jacobi equations, a first-order partial differential equation that is fundamental to control theory. Computational considerations, connections to convex geometry and a number of related open problems will all be discussed.

Biography

Ryan Murray received his Ph.D. in mathematics from Carnegie Mellon University in 2016, and was a Chowla Assistant Professor at Penn State University from 2016-2019. Since 2019 he is an assistant professor at North Carolina State University, department of mathematics.