Whitening_Lasso: Whitening Lasso

In WLasso: Variable Selection for Highly Correlated Predictors

Description

The function implements the approach described in the paper Zhu et al. (2020) given in the references.

Usage

Whitening_Lasso(X, Y, Sigma, gamma = 0.95, maxsteps = 2000)

Arguments

X	Design matrix of the linear model.
Y	Response variable of the linear model.
Sigma	Correlation matrix of the rows of the design matrix. If not specified, the function Sigma_Estimation will be used to estimate this matrix.
gamma	Parameter γ defined in the paper Zhu et al. (2020) given in the references. Its default value is 0.95.
maxsteps	Integer specifying the maximum number of steps for the generalized Lasso algorithm. Its default value is 2000.

Value

Returns a list with the following components

lambda	different values of the parameter λ considered.
beta	matrix of the estimations of β for all the λ considered.
trans_mat	tranformation matrix which is the inverse of the square root of the estimation of the correlation matrix of the rows of the design matrix X.
beta.min	estimation of β which minimize the MSE.
mse	MSE for all the λ considered.

Author(s)

Wencan Zhu [aut, cre], Celine Levy-Leduc [ctb], Nils Ternes [ctb]

References

W. Zhu, C. Levy-Leduc, N. Ternes. "A variable selection approach for highly correlated predictors in high-dimensional genomic data". arXiv:2007.10768.

Examples

data(X)
data(Y)
Sigma_est <- Sigma_Estimation(X)$mat
res_wlasso <- Whitening_Lasso(X=X, Y=Y, Sigma=Sigma_est, maxsteps=100, gamma=0.9)
beta_est <- res_wlasso$beta

WLasso documentation built on Aug. 13, 2020, 5:06 p.m.