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Regularization and variable selection via theelastic netHui Zou and Trevor HastieStanford University, USA[Received December 2003. Final revision September 2004]Summary. We propose the elastic net, a new regularization and variable selection method. Realworld data and a simulation study show that the elastic net often outperforms the lasso, whileenjoying a similar sparsity of representation. In addition, the elastic net encourages a groupingeffect, where strongly correlated predictors tend to be in or out of the model together.The elasticnet is particularly useful when the number of predictors (p) is much bigger than the number ofobservations (n). By contrast, the lasso is not a very satisfactory variable selection method in thepn case. An algorithm called LARS-EN is proposed for computing elastic net regularizationpaths efficiently, much like algorithm LARS does for the lasso.Keywords: Grouping effect; LARS algorithm; Lasso; Penalization; pn problem; Variableselection1. Introduction and motivationWe consider the usual linear regression model: given p predictors x1,..., xp, the response y ispredicted byˆβ0 +x1ˆβ1 +... +xpˆˆ βp: .1/y=A model fitting procedure produces the vector of

Author

Hui Zou,Trevor Hastie

Published

2005

Language

EN