EE Systems Seminar
Empirical Risk Minimization in High-dimensions: Asymptotics, Optimality and Double Descent
ABSTRACT At the heart of contemporary statistical signal processing problems, as well as modern machine-learning practices, lie high-dimensional inference tasks in which the number of unknown parameters is of the same order as (and often larger than) the number of observations.
In this talk, I describe a framework based on Gaussian-process inequalities to sharply characterize the statistical performance of convex empirical risk minimization in high dimensions. By focusing on the simple, yet highly versatile, model of binary linear classification, I will demonstrate that, albeit challenging, sharp results are advantageous over loose order-wise bounds. For instance, they lead to precise answers to the following questions: When are training data linearly separable? Is least-squares bad for binary classification? What is the best convex loss function? Is double descent observed in linear models and how do its features (such as the transition threshold and global minima) depend on the training data and on the learning procedure?
Many of the ideas and technical tools of our work originate from the study of sharp phase-transitions in compressed sensing. Throughout the talk, I will highlight how our results relate to and advance this literature.
BIO Christos Thrampoulidis is an Assistant Professor in the ECE Department at UC Santa Barbara since July 2018. His research interests include statistical signal processing, optimization, and, machine learning. Before joining UCSB, Dr. Thrampoulidis was a Postdoctoral Researcher at the Research Laboratory of Electronics 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.
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