The analysis of modern high-dimensional inference problems is often framed in terms of detection thresholds, computational-to-statistical gaps, and phase transitions. In this talk, I will describe two scenarios where these properties can be described succinctly using ideas from approximate inference, information theory, and statistical physics. The first part of the talk focuses on random linear estimation problems that arise in channel coding, linear regression, and compressed sensing. I will describe the correspondence between a computationally efficient algorithm (approximate message passing) and the information-theoretic limits. The second part of the talk will focus on the problem of community detection with multiple correlated networks. I will present recent theoretical work showing that the ability to detect different types of community structure can be characterized in terms of the matrix of effective signal-to-noise ratios. I will also discuss some recent methodological approaches inspired by this theory.

Bio: 

Galen Reeves joined the faculty at Duke University in Fall 2013, and is currently an Assistant 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.