Large-Scale Simulation Evaluation for Model Selection: Lasso and Bayesian Derivatives

• Activity Number: 41
• Type: Contributed
• Date/Time: Sunday, August 1, 2010 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Alan Burton Lenarcic*+ and Edoardo M. Airoldi and Palak Patel
• Companies: Harvard University and Harvard University and Harvard University
• Keywords: LASSO ; Phase Plane ; Bayes EM ; Mixture Models ; Two-Lasso ; Covariance Selection

Abstract

The computer generated images of Donoho and Stodden 2006 revealed an inherent barrier of methods like LASSO to select by plotting median L2 criterion error at a dense grid in space k < n < p. As parallel computing resources become available, dense plots that took months can be generated in minutes, becoming a new standard of judgment of estimators. However, we show that regions of good L2 performance do not necessarily reflect regions of low Type 1 and Type 2 error. When inputs are changed, when signal is deterministic, when negative correlations are allowed, and when noise is increased, LASSO's performance changes significantly. As comparison we develop Two-Lasso estimators, which include LASSO algorithms in an intuitively chosen EM mixture model. We then study several LASSO stopping criteria and extend into covariance graphical network and generalized linear model settings.