Interdisciplinary Science Seminar

Speaker: Yue M. Lu, Harvard University

Title: Exploring and Exploiting the Universality Phenomena in High-Dimensional Estimation and Learning

Abstract: Universality is a fascinating high-dimensional phenomenon. It points to the existence of universal laws that govern the macroscopic behavior of wide classes of large and complex systems, despite their differences in microscopic details. The notion of universality originated in statistical mechanics, especially in the study of phase transitions. Similar phenomena have been observed in probability theory, dynamical systems, random matrix theory, and number theory.
In this talk, I will present some recent progresses in rigorously understanding and exploiting the universality phenomena in the context of statistical estimation and learning on high-dimensional data. Examples include spectral methods for high-dimensional projection pursuit, statistical learning based on kernel and random feature models, and approximate message passing algorithms on highly structured, strongly correlated, and even (nearly) deterministic data matrices. Together, they demonstrate the robustness and wide applicability of the universality phenomena.

Bio: Yue M. Lu attended the University of Illinois at Urbana-Champaign, where he received the M.Sc. degree in mathematics and the Ph.D. degree in electrical engineering, both in 2007.  He is currently Gordon McKay Professor of Electrical Engineering and of Applied Mathematics at Harvard University. He is also fortunate to have held visiting appointments at Duke University in 2016 and at the École Normale Supérieure (ENS) in 2019. His research interests include the mathematical foundations of statistical signal processing and machine learning in high dimensions.