Student Seminar Series - September 11, 2007
University of Minnesota
School of Statistics
College of Liberal Arts



Adaptive Regularization via the Entire Solution Surface


Seongho Wu


Tuesday, September 11, 2007
2:00 PM,
300 Ford Hall
Minneapolis, East Bank Campus

Refreshments at 1:40 PM
300 Ford Hall

Abstract


Several penalties have been proposed for delivery of good predictive performance in automatic variable selection within the framework of regularization. However, one key assumption is that the true model is sparse. We propose a penalty, a convex combination of the L1 and L∞ norm, that adapts to a variety of situations including sparseness and nonsparseness, grouping and non-grouping. In addition, we introduce a novel homotopy algorithm utilizing subdifferentials for developing regularization solution surfaces involving multiple regularizers. This permits efficient computation and adaptive tuning. The proposed penalty performs grouping and adaptive regularization. Numerical experiments are conducted via simulation. The proposed penalty compares well against popular penalties in simulated and real data.