Sparse PCA, Geometric optimization and SURE

Abstract:

The large data volumes now occurring in econometrics, finance and other areas have shown up inadequacies in traditional modeling and analysis methods. VAR models have too many parameters; traditional asymptotics is unreliable since one wants not only the number of observations to approach infinity but also the number of variables to approach infinity; and finally model selection methods fail. There has thus recently been renewed interest in traditional dimension reduction methods such as factor analysis, PCA and more recently sparse modeling methods. In this talk we develop a method of automatically zeroing out (large numbers of) whole variables in PCA by non-smooth penalized optimization. The orthogonality constraints in PCA force the optimization to be on a Stiefel manifold and we discuss a geodesic steepest descent method for carrying this out. We then consider the problem of rank selection in PCA when the number of variables is of similar order to the number of observations. We develop a new selection criterion based on SURE and compare it with more traditional criteria.

About the speaker: Victor Solo is Professor at the School of Electrical Engineering, The University of New South Wales. His research interests are: Systems, Signal Processing and Control, Ill-Conditioned Inverse Problems, Econometrics, Time Series and System Identification, Medical Imaging and Computer Vision, and Neural Coding and Point Processes.