High-Dimensional Screening Using Multiple Grouping of Variables
|Event Date:||April 25, 2013|
|Speaker Affiliation:||Rice University|
|Sponsor:||communications, Networking, Signal & Image Processing|
|Contact Name:||Professor Charles Bouman
|Contact Phone:||(765) 494-0340
Screening is the problem of finding a superset of the set of non-zero entries in an unknown p-dimensional vector b given n noisy observations. Naturally, we want this superset to be as small as possible. We propose a novel framework for screening, which we refer to as Multiple Grouping (MuG), that groups variables, performs variable selection over the groups, and repeats this process multiple number of times to estimate a sequence of sets that contains the non-zero entries in b. Screening is done by taking an intersection of all these estimated sets. The MuG framework can be used in conjunction with any group based variable selection algorithm. In the high-dimensional setting, where p >> n, we show that when MuG is used with the group Lasso estimator, screening can be consistently performed without using any tuning parameter. Our numerical simulations clearly show the merits of using the MuG framework in practice.
Divyanshu is a postdoctoral researcher at Rice University funded by an Institute for Mathematics and its Applications (IMA) postdoctoral fellowship. He received the B.S. degree in Electrical Engineering and Mathematics from The University of Texas at Austin in 2006, and M.S. and Ph.D. degrees in Electrical and Computer Engineering from Carnegie Mellon University in 2009 and 2011, respectively. His research interests include statistical signal processing, probability and stochastic processes, information theory, graphical models, and machine learning.