A Characteristics-based Approach to Computing Tukey Depths

Martin Molina-Fructuoso (North Carolina State University)

Registration is required to access the Zoom webinar. Martin will also be in person in 402 Walter.

Statistical depths extend the concepts of quantiles and medians to multidimensional data and can be useful to establish a ranking order within data clusters. The Tukey depth is one classical geometric construction of a highly robust statistical depth that has deep connections with convex geometry. Finding the Tukey depth for general measures is a computationally expensive problem, particularly in high dimensions.

In recent work (in collaboration with Ryan Murray) we have shown a link between the Tukey depth of measures with some degree of regularity and a partial differential equation of the Hamilton-Jacobi type. This talk will discuss a strategy based on the characteristics of the differential equation that intends to use this connection to calculate Tukey depths. This approach is inspired by other recent work which attempts to compute solutions to eikonal equations in high dimensions using characteristic-based methods for special classes of initial data.

Martin Molina-Fructuoso graduated from the University of Maryland, College Park with a PhD in Applied Mathematics advised by Profs. Antoine Mellet and Pierre-Emmanuel Jabin. He then joined North Carolina State University as a Postdoctoral Research Scholar where he worked with Prof. Ryan Murray. His interests lie in PDE-based variational methods for problems related to machine learning and in optimal transportation and its applications.