University Universality in High-Dimensional Sensing and Learning Systems
- Sponsor
- Minh Do, Ph.D.
- Speaker
- Yue M. Lu, Ph.D.
- Contact
- Minh Do, Ph.D.
- minhdo@illinois.edu
- Views
- 25
- Originating Calendar
- Illinois ECE Distinguished Colloquium Series
Abstract:
Modern sensing and learning systems operate in regimes where the ambient dimension, sample size, and number of parameters all grow large. In such high-dimensional settings, an interesting probabilistic phenomenon can arise: certain macroscopic performance metrics become largely insensitive to microscopic details. This phenomenon, known as universality, reveals that certain high-dimensional systems obey asymptotic statistical laws that transcend specific models and design choices. In this talk, I will present recent progress on the theoretical understanding of universality in high-dimensional estimation and learning. I will discuss semi-random and nearly deterministic sensing systems whose asymptotic behavior matches that of idealized random models, and describe an equivalence principle for nonlinear random matrices that enables sharp asymptotic characterizations of a wide range of kernel and random feature methods.These results suggest that high dimensionality is not merely a complication to be managed, but a source of emergent probabilistic regularity that can inform the analysis and design of modern sensing and learning systems.
Bio:
Yue M. Lu is the Gordon McKay Professor of Electrical Engineering and of Applied Mathematics at the Harvard John A. Paulson School of Engineering and Applied Sciences, with an affiliate appointment in the Department of Statistics. Since 2024, he has also held the title of Harvard College Professor. A proud alumnus of Illinois ECE, he received both his M.Sc. in Mathematics and his Ph.D. in Electrical Engineering from the University of Illinois at Urbana-Champaign in 2007.His research lies at the interface of signal processing, statistics, and applied probability, with an emphasis on randomness and structure in high-dimensional systems. He develops probabilistic methods to characterize fundamental limits in estimation and learning, drawing on tools from high-dimensional probability and random matrix theory. He is an IEEE Fellow (Class of 2024) and a recipient of the 2015 ECE Illinois Young Alumni Achievement Award.