Data depths meet Hamilton-Jacobi equations
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.
Ryan Murray received his PhD 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.