Whitening Lasso
The function implements the approach described in the paper Zhu et al. (2020) given in the references.
Whitening_Lasso(X, Y, Sigma, gamma = 0.95, maxsteps = 2000)
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 |
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. |
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. |
Wencan Zhu [aut, cre], Celine Levy-Leduc [ctb], Nils Ternes [ctb]
W. Zhu, C. Levy-Leduc, N. Ternes. "A variable selection approach for highly correlated predictors in high-dimensional genomic data". arXiv:2007.10768.
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
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