## Regularization and variable selection via the elastic net.(English)Zbl 1069.62054

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

### MSC:

 62J05 Linear regression; mixed models 65C60 Computational problems in statistics (MSC2010)

### Software:

ElemStatLearn; lars
Full Text:

### References:

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