Tuesday, July 3, 2012
Many natural and man-made signals exhibit a few degrees of freedom relative to their dimension due to natural parameterizations or constraints. The inherent low-dimensional structure of such signals are mathematically modeled via combinatorial and geometric concepts, such as sparsity, unions-of-subspaces, or spectral sets, and are now revolutionizing the way we address linear inverse problems from incomplete data.
In this talk, we describe a set of structured sparse models for constrained linear inverse problems that feature exact and epsilon-approximate projections in polynomial time. We pay particular attention to the sparsity models based on matroids, multi-knapsack, and clustering as well as spectrally constrained models. We then study sparse projections onto convex sets, such as the (general) simplex, and ell-1,2,inf balls. Finally, we describe a hybrid optimization framework which explicitly leverages these non-convex models along with additional convex constraints to obtain better recovery performance in compressive sensing, learn interpretable sparse densities from finite samples, and improved sparse Markowitzs portfolios with better return/cost performance.
Prof. Volkan Cevher
Volkan Cevher received his BSc degree (valedictorian) in Electrical Engineering from Bilkent University in 1999, and his PhD degree in Electrical and Computer Engineering from Georgia Institute of Technology in 2005. He held research scientist positions at University of Maryland, College Park during 2006-2007 and at Rice University during 2008-2009. Currently, he is an assistant professor at Swiss Federal Institute of Technology Lausanne and a Faculty Fellow at Rice University. His research interests include signal processing theory, machine learning, graphical models, and information theory. Dr. Cevher received a best paper award at SPARS in 2009 and an ERC StG in 2011.