objFunctionSmooth {smoothedLasso}

Auxiliary function to define the objective function of the smoothed L1 penalized regression operator.

Description

Auxiliary function to define the objective function of the smoothed L1 penalized regression operator.

Usage

objFunctionSmooth(betavector, u, v, w, mu, entropy = TRUE)

Arguments

betavector

The vector of regression coefficients.

u

The function encoding the objective of the regression operator.

v

The function encoding the penalty of the regression operator.

w

The function encoding the dependence structure among the regression coefficients.

mu

The Nesterov smoothing parameter.

entropy

A boolean switch to select the entropy prox function (default) or the squared error prox function.

Value

The value of the smoothed regression operator for the input betavector.

References

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

library(smoothedLasso)
n <- 100
p <- 500
betavector <- runif(p)
X <- matrix(runif(n*p),nrow=n,ncol=p)
y <- X %*% betavector
lambda <- 1
temp <- standardLasso(X,y,lambda)
print(objFunctionSmooth(betavector,temp$u,temp$v,temp$w,mu=0.1))