In the past couple of decades, convex optimization has emerged as a powerful practical tool for the recovery of structured signals from high-dimensional noisy measurements in a variety of applications in signal processing, wireless-communication, machine-learning etc. In this talk, I will present recent theoretical developments for how to determine the performance (minimum number of measurements, mean-squared-error, bit-error-rate, etc.) of these inference methods. First, I will describe a new framework that leads to precise error analysis, thus shedding light on the relative performance of different algorithms and allowing fine-tuning the involved parameters. Next, I will discuss recent extensions of the theory to generalized linear models, which include the problems of quantized compressed sensing and of phase-retrieval.
Christos Thrampoulidis is an Assistant Professor in the ECE Department at UC Santa Barbara. His research interests include signal processing, optimization, high-dimensional statistics, and machine learning. Before joining UCSB, Dr. Thrampoulidis was a Postdoctoral Researcher at MIT. He received his M.Sc. and Ph.D. degrees in Electrical Engineering from Caltech in 2012 and 2016, respectively, and his Diploma of electrical and computer engineering from the University of Patras in Greece in 2011. He is a recipient of the 2014 Qualcomm Innovation Fellowship, and, of the 2011 Andreas Mentzelopoulos Scholarship.