| enet {lqa} | R Documentation |
Elastic Net Penalty
Description
Object of the penalty to handle the elastic net (enet) penalty (Zou \& Hastie, 2005)
Usage
enet (lambda = NULL, ...)
Arguments
lambda |
two-dimensional tuning parameter. The first component corresponds to the regularization parameter |
... |
further arguments. |
Details
The elastic net penalty has been introduced in the linear model context by Zou \& Hastie (2005). The elastic net enables simultaneous automatic variable selection and continuous shrinkage. Furthermore, contrary to the lasso it can select groups of correlated variables. This is related to the so called grouping effect, where strongly correlated regressors tend to be in or out of the model together.
The elastic net penalty
P_{\lambda}^{en} (\boldsymbol{\beta}) = \lambda_1 \sum_{i=1}^p |\beta_i| + \lambda_2 \sum_{i=1}^p \beta_i^2, \quad \lambda =
(\lambda_1, \lambda_2)
is a linear combination of the lasso penalty and the ridge penalty. Therefore the penalty covers these both as extreme cases.
Value
An object of the class penalty. This is a list with elements
penalty |
character: the penalty name. |
lambda |
double: the (nonnegative) tuning parameter. |
getpenmat |
function: computes the diagonal penalty matrix. |
Author(s)
Jan Ulbricht
References
Zou, H. \& T. Hastie (2005) Regularization and variable selection via the elastic net. Journal of the Royal Statistical Society B 67, 301–320.