Regularization and variable selection via the elastic net

Hui Zou, Trevor Hastie

Research output: Contribution to journalArticlepeer-review


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 p ≫ n case. An algorithm called LARS-EN is proposed for computing elastic net regularization paths efficiently, much like algorithm LARS does for the lasso.

Original languageEnglish (US)
Pages (from-to)301-320
Number of pages20
JournalJournal of the Royal Statistical Society. Series B: Statistical Methodology
Issue number2
StatePublished - 2005
Externally publishedYes


  • Grouping effect
  • LARS algorithm
  • Lasso
  • P ≫ n problem
  • Penalization
  • Variable selection


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