smoothedLasso (version 1.6)

elasticNet: Auxiliary function which returns the objective, penalty, and dependence structure among regression coefficients of the elastic net.

Description

Auxiliary function which returns the objective, penalty, and dependence structure among regression coefficients of the elastic net.

Usage

elasticNet(X, y, alpha)

Arguments

X

The design matrix.

y

The response vector.

alpha

The regularization parameter of the elastic net.

Value

A list with six functions, precisely the objective $u$, penalty $v$, and dependence structure $w$, as well as their derivatives $du$, $dv$, and $dw$.

References

Zou, H. and Hastie, T. (2005). Regularization and variable selection via the elastic net. J Roy Stat Soc B Met, 67(2):301-320.

Friedman, J., Hastie, T., Tibshirani, R., Narasimhan, B., Tay, K., Simon, N., and Qian, J. (2020). glmnet: Lasso and Elastic-Net Regularized Generalized Linear Models. R-package version 4.0.

Hahn, G., Lutz, S., Laha, N., and Lange, C. (2020). A framework to efficiently smooth L1 penalties for linear regression. bioRxiv:2020.09.17.301788.

Examples

# NOT RUN {
library(smoothedLasso)
n <- 100
p <- 500
betavector <- runif(p)
X <- matrix(runif(n*p),nrow=n,ncol=p)
y <- X %*% betavector
alpha <- 0.5
temp <- elasticNet(X,y,alpha)

# }