Regularization and variable selection via the elastic net

H Zou, T Hastie - Journal of the Royal Statistical Society Series …, 2005 - academic.oup.com
Journal of the Royal Statistical Society Series B: Statistical …, 2005academic.oup.com
We propose the elastic net, a new regularization and variable selection method. Real world
data and a simulation study show that the elastic net often outperforms the lasso, while
enjoying a similar sparsity of representation. In addition, the elastic net encourages a
grouping effect, where strongly correlated predictors tend to be in or out of the model
together. The elastic net is particularly useful when the number of predictors (p) is much
bigger than the number of observations (n). By contrast, the lasso is not a very satisfactory …
Summary
We propose the elastic net, a new regularization and variable selection method. Real world data and a simulation study show that the elastic net often outperforms the lasso, while enjoying a similar sparsity of representation. In addition, the elastic net encourages a grouping effect, where strongly correlated predictors tend to be in or out of the model together. The elastic net is particularly useful when the number of predictors (p) is much bigger than the number of observations (n). By contrast, the lasso is not a very satisfactory variable selection method in the pn case. An algorithm called LARS-EN is proposed for computing elastic net regularization paths efficiently, much like algorithm LARS does for the lasso.
Oxford University Press