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Home | Seminars and Symposia | Past seminars/symposia: Tuesday, August 14, 2012

DTC Seminar Series

Geodesic convexity and covariance estimation

by

Ami Wiesel
School of Computer Science and Engineering
Hebrew University of Jerusalem, Israel

Tuesday, August 14, 2012
3:00 p.m. reception
3:30 p.m. lecture

401/402 Walter Library

WieselGeodesic convexity is a generalization of classical convexity which guarantees that all local minima of g-convex functions are globally optimal. We consider g-convex functions with positive definite matrix variables, and prove that Kronecker products, and logarithms of determinants are g-convex. We apply these results to two modern covariance estimation problems: robust estimation in scaled Gaussian distributions, and Kronecker structured models. Maximum likelihood estimation in these settings involves non-convex minimizations. We show that these problems are in fact g-convex. This leads to straight forward analysis, allows the use of standard optimization methods and paves the road to various extensions via additional g-convex regularization.

 

Ami Wiesel received the B.Sc. and M.Sc. degrees in electrical engineering from Tel-Aviv University, Tel-Aviv, Israel, in 2000 and 2002, respectively, and the Ph.D. degree in electrical engineering from the Technion-Israel Institute of Technology, Haifa, in 2007. He was a Postdoctoral Fellow with the Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, from 2007 to 2009. Since January 2010, he has been a Faculty Member at the Rachel and Selim Benin School of Computer Science and Engineering at the Hebrew University of Jerusalem, Israel. Dr. Wiesel was a recipient of the Young Author Best Paper Award for a 2006 paper in the IEEE Trans. on Signal Processing and a Student Paper Award for a 2005 Workshop on Signal Processing Advances in Wireless Communications (SPAWC) paper. He was awarded the Weinstein Study Prize in 2002, the Intel Award in 2005, the Viterbi Fellowship in 2005 and 2007, and the Marie Curie Fellowship in 2008.