Generalized Elastic Net Regression

• Activity Number: 191
• Type: Contributed
• Date/Time: Monday, August 5, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Geoffroy Mouret*+ and Jean-Jules Brault and Vahid Partovi Nia
• Companies: Ecole Polytechnique de Montreal and Ecole Polytechnique de Montreal and École Polytechnique Montréal
• Keywords: elastic net ; fitted values ; generalized lasso ; least angle regression ; variable selection

Abstract

This work presents a variation of the elastic net penalization method. We propose applying a combined l1 and l2 norm penalization on a linear combination of regression parameters. This approach is an alternative to the l1-penalization for variable selection, but takes care of the correlation between the linear combination of parameters. We devise a path algorithm fitting method similar to the one proposed for the least angle regression. Furthermore, a one-shot estimation technique of l2 regularization parameter is proposed as an alternative to cross-validation. A simulation study is conducted to check the validity of the new technique.