WLasso (version 1.0)

Whitening_Lasso: Whitening Lasso

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 \(\gamma\) 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 \(\lambda\) considered.

beta

matrix of the estimations of \(\beta\) for all the \(\lambda\) 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 \(\beta\) which minimize the MSE.

mse

MSE for all the \(\lambda\) considered.

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

# NOT RUN {
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
# }