Seminar 2023-29-09

Depth Functions and Their Applications to Classification and Clustering

Giacomo Francisci

Postdoc

Department of Statistics

George Mason University

Date: Friday, September 29, 2023

Time: 11:00 A.M. – 12:00 P.M. Eastern Time

Location: Johnson Center, Room 325 Meeting Room A

Depth functions provide a center-outward order similar to that of the real line and are used to specify medians and quantiles of multivariate distributions. As they do not require any assumption on the underlying distribution, they are widely used in non-parametric statistics and robust methods, for instance, in outlier detection and classification. In the setting of classification, a common issue is that points of zero depth with respect to all classes arise in practice leading to classification challenges. In the first part of the presentation, we address this issue using an extended notion of depth function. We use this idea to study classification for tree-indexed random variables. In the final part of the presentation, we introduce a concept of local depth function and use it to study modal clustering. We also discuss consistency properties of the clustering algorithm.

Giacomo Francisci is a Postdoctoral Research Fellow at the Department of Statistics at GMU, where he works under the supervision of Prof. Vidyashankar. Prior to that, he obtained a Double Degree MSc. in Mathematics at the University of Trento (Italy) and University of Tübingen (Germany). He obtained a Cotutelle PhD. in Mathematics and Statistics at the University of Trento (Italy) and the University of Cantabria (Spain). His research interests are in depth functions and their applications to machine learning, empirical processes, branching processes, and branching random walks.

Nicholas Rios

David Kepplinger