Non-Convex Optimization and Structured Signal Recovery
In the past couple of decades, non-smooth convex optimization has emerged as a powerful tool for the recovery of structured signals (sparse, low rank, finite constellation, etc.) from possibly noisy measurements in a variety of applications in statistics, signal processing and machine learning. While the algorithms (basis pursuit, LASSO, etc.) are often fairly well established, rigorous frameworks for the exact analysis of the performance of such methods are only just emerging. The talk will introduce and describe a fairly general theory for how to determine the performance (minimum number of measurements, mean-square-error, probability-of-error, etc.) of such methods for various measurement ensembles (Gaussian, Haar, etc.). The framework enables one to assess the performance of these methods before actual implementation and allows one to optimally choose parameters such as regularizer coefficients, number of measurements, etc. The theory subsumes earlier results as special cases. It builds on an inconspicuous 1962 lemma of Slepian (for comparing Gaussian processes), as well as on a non-trivial generalization due to Gordon in 1988, and produces concepts from convex geometry (such as Gaussian widths and Moreau envelopes) in a very natural way. The talk will also consider extensions to certain non-Gaussian settings and their applications in massive MIMO, one-bit compressed sensing, graphical LASSO, and phase retrieval.
Babak Hassibi is the inaugural Mose and Lillian S. Bohn Professor of Electrical Engineering at the California Institute of Technology, where he has been since 2001, From 2011 to 2016 he was the Gordon M Binder/Amgen Professor of Electrical Engineering and during 2008-2015 he was Executive Officer of Electrical Engineering, as well as Associate Director of Information Science and Technology. Prior to Caltech, he was a Member of the Technical Staff in the Mathematical Sciences Research Center at Bell Laboratories, Murray Hill, NJ. He obtained his PhD degree from Stanford University in 1996 and his BS degree from the University of Tehran in 1989. His research interests span various aspects of information theory, communications, signal processing, control and machine learning. He is an ISI highly cited author in Computer Science and, among other awards, is the recipient of the US Presidential Early Career Award for Scientists and Engineers (PECASE) and the David and Lucille Packard Fellowship in Science and Engineering.