Statistical Limits for the Matrix Tensor Product

High-dimensional models involving the products of large random matrices include the spiked matrix models appearing in principle component analysis and the stochastic block model appearing in network analysis. In this talk I will present some recent theoretical work that provides an asymptotically exact characterization of the fundamental limits of inference for a broad class of these models. The first part of the talk will introduce the “matrix tensor product” model and describe some implications of the theory for community detection in correlated networks. The second part will highlight some of the ideas in the analysis, which builds upon ideas from information theory and statistical physics.

The material in this talk is appears in following papers:
Information-Theoretic Limits for the Matrix Tensor Product, Galen Reeves
Mutual Information in Community Detection with Covariate Information and Correlated Networks, Vaishakhi Mayya and Galen Reeves

Galen Reeves joined the faculty at Duke University in Fall 2013, and is currently an Associate Professor with a joint appointment in the Department of Electrical Computer Engineering and the Department of Statistical Science. He completed his PhD in Electrical Engineering and Computer Sciences at the University of California, Berkeley in 2011, and he was a postdoctoral associate in the Departments of Statistics at Stanford University from 2011 to 2013. His research interests include information theory and high-dimensional statistics. He received the NSF CAREER award in 2017.