Exploiting Sparsity: Algorithms and Applications
Monday, November 14, Kemper Hall 1065, 2:10pm-3:00pm
Speaker: Dr. Alyson Fletcher
In many fields, a key challenge is how to best to extract essential features from large amounts of noisy information. Seeking out sparsity, or lower-dimensional representations, has been a longstanding but evolving approach. Driven by burgeoning data sets and advances in computational resources, a recent flurry of interest led to the feasibility of algorithms for adaptive and nonlinear sparse estimation on richer model classes. Current widespread interest stems from the ability to now address complex systems across a spectrum of data-driven applications such as biological imaging, economics, and networking. However much remains unknown: when can sparse structures be extracted, how do current algorithms perform, and how can these methods be improved? In this talk, I present two lines of work toward these goals. First, I describe a general framework based on statistical physics that provides a surprisingly precise characterization of many widely-used algorithms. Secondly, I describe a new broad framework for sparse estimation based on Gaussian approximations of graphical models. I address the problems of neural mapping and receptive field estimation via this methodology.
Alyson Fletcher received the M.S. and Ph.D. in electrical engineering and the M.S. in mathematics from the University of California, Berkeley. She is a recipient of a UC President's Postdoctoral Fellowship, the UC Berkeley EECS Lawler Award, a Luce Foundation fellowship, and an NSF Graduate Fellowship. Her research interests include machine learning, optimization, statistical inference, computational neuroscience, and applications in biological systems.