### Abstract

- Top of page
- Abstract
- 1. Introduction and motivation
- 2. Naïve elastic net
- 3. Elastic net
- 4. Prostate cancer example
- 5. A simulation study
- 6. Microarray classification and gene selection
- 7. Discussion
- Acknowledgements
- References
- Appendix

**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 *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.