Data depths meet Hamilton-Jacobi equations presented by Ryan Murray
Abstract: One fundamental geometric quantity in robust statistics is known as a depth function, 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 (specifically Tukey/Halfspace depths) with Hamilton-Jacobi equations, a first-order partial differential equation that is fundamental to control theory. These equations provide potential new approaches for theoretical, modeling, and computational aspects of data depths. Connections to convex geometry and a number of related open problems will also be discussed.