Rice: Unconventional Wisdom
Colloquium
Electrical and Computer Engineering
Computational and Applied Mathematics
Digital Signal Processing
Speaker: Mark Davenport
Assistant Professor, School of Electrical and Computer Engineering
Georgia Institute of Technology

  One-bit matrix completion
Monday, October 7, 2013
3:00 PM  to 4:00 PM
1064  Duncan Hall
Rice University
6100 Main St
Houston, Texas, USA

In this talk I will describe a theory of matrix completion for the extreme case of noisy 1-bit observations. Instead of observing a subset of the real-valued entries of a matrix M, we obtain a small number of binary (1-bit) measurements generated according to a probability distribution determined by the real-valued entries of M. The central question I will discuss is whether or not it is possible to obtain an accurate estimate of M from this data. In general this would seem impossible, but we show that the maximum likelihood estimate under a suitable constraint returns an accurate estimate of M under certain natural conditions. If the log-likelihood is a concave function (e.g., the logistic or probit observation models), then we can obtain this estimate by optimizing a convex program. I will conclude by discussing several applications of these techniques.


Biography of Mark Davenport:
Mark A. Davenport is an Assistant Professor with the School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA. Prior to this, he spent 2010-2012 as an NSF Mathematical Sciences Postdoctoral Research Fellow in the Department of Statistics at Stanford University and as a visitor with the Laboratoire Jacques-Louis Lions at the Université Pierre et Marie Curie. He received the B.S.E.E., M.S., and Ph.D. degrees in electrical and computer engineering in 2004, 2007, and 2010, all from Rice University. His research interests include compressive sensing, low-rank matrix recovery, nonlinear approximation, and the application of low-dimensional signal models in signal processing and machine learning. In 2007 Dr. Davenport shared the Hershel M. Rich Invention Award from Rice University for his work on the single-pixel camera and compressive sensing. In 2011, he was awarded the Ralph Budd Award for the best engineering thesis from Rice University.


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