MIT Stochastics & Statistics Seminar Series: Rina Foygel Barber
October 30, 2015 | 11:00 am-12:00 pm | 32-141

Title: MOCCA: a primal/dual algorithm for nonconvex composite functions with applications to CT imaging

Abstract: Many optimization problems arising in high-dimensional statistics decompose naturally into a sum of several terms, where the individual terms are relatively simple but the composite objective function can only be optimized with iterative algorithms. Specifically, we are interested in optimization problems of the form F(Kx) + G(x), where K is a fixed linear transformation, while F and G are functions that may be nonconvex and/or nondifferentiable. In particular, if either of the terms are nonconvex, existing alternating minimization techniques may fail to converge; other types of existing approaches may instead be unable to handle nondifferentiability. We propose the MOCCA (mirrored convex/concave) algorithm, a primal/dual optimization approach that takes local convex approximation to each term at every iteration. Inspired by optimization problems arising in computed tomography (CT) imaging, this algorithm can handle a range of nonconvex composite optimization problems, and offers theoretical guarantees for convergence when the overall problem is approximately convex (that is, any concavity in one term is balanced out by convexity in the other term). Empirical results show fast convergence for several structured signal recovery problems.

Bio: Rina Foygel Barber is an Assistant Professor of Statistics at the University of Chicago. She received her PhD in Statistics from the University of Chicago in 2012, then was a NSF Postdoctoral Fellow at Stanford University in 2012-2013 before joining the faculty at Chicago in January 2014. Her research in high-dimensional statistics focuses on model selection, false discovery rate control, sparse and low rank modeling, and applications to medical imaging.

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