crossvalidation {smoothedLasso}

Perform cross validation to select the regularization parameter.

Description

Perform cross validation to select the regularization parameter.

Usage

crossvalidation(auxfun, X, y, param, K = 10)

Arguments

auxfun

A complete fitting function which takes as arguments a data matrix X, a response vector y, and some parameter p (to be tuned), and returns the estimator (betavector) (minimizer) of the regression operator under investigation.

X

The design matrix.

y

The response vector.

param

A vector of regularization parameters which are to be evaluated via cross validation.

K

The number of folds for cross validation (should divide the number of rows of X). The default is 10.

Value

A vector of average errors over all folds. The entries in the returned vector correspond to the entries in the vector param in the same order.

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.

Tibshirani, R. (2013). Model selection and validation 1: Cross-validation. https://www.stat.cmu.edu/~ryantibs/datamining/lectures/18-val1.pdf

Examples

library(smoothedLasso)
n <- 1000
p <- 100
betavector <- runif(p)
X <- matrix(runif(n*p),nrow=n,ncol=p)
y <- X %*% betavector
auxfun <- function(X,y,lambda) {
		temp <- standardLasso(X,y,lambda)
	obj <- function(z) objFunction(z,temp$u,temp$v,temp$w)
		objgrad <- function(z) objFunctionGradient(z,temp$w,temp$du,temp$dv,temp$dw)
	return(minimizeFunction(p,obj,objgrad))
}
lambdaVector <- seq(0,1,by=0.1)
print(crossvalidation(auxfun,X,y,lambdaVector,10))