Fitting L1-Penalized Models by Weighted Maximum Frequency

• Activity Number: 609
• Type: Contributed
• Date/Time: Wednesday, August 12, 2015 : 2:00 PM to 3:50 PM
• Sponsor: Biometrics Section
• Author(s): Hongmei Liu* and J. Sunil Rao
• Companies: University of Miami and University of Miami
• Keywords: Model selection ; L1 penalized regression ; Lasso ; Elastic net ; Bootstrap

Abstract

We provide a unified framework for fitting various L1 penalized regression estimators including the lasso, adaptive lasso, elastic net and fused lasso. By using the trace paths for each estimator, we focus on finding the maximum frequency (MF) sub models at each dimension based on a bootstrap approximation, and prove consistency of selection. To improve finite sample performance, we develop a weighted maximum frequency (WMF) estimator which adjusts the MF for differences in the size of the model space at each dimension. We then prove consistency under the orthogonal design for the WMF. Detailed simulation studies are conducted, and a leukemia gene expression microarray study is analyzed to demonstrate the usefulness of the methodology.