EnMSP: An Elastic-net Multi-step Screening Procedure for High-dimensional Regression

To improve the estimation efficiency of high-dimensional regression problems, penalized regularization is routinely used. However, accurately estimating the model is still challenging when there are correlated effects that irrelevant variables are strongly correlated with relevant variables. In this paper, we propose the Elastic-net Multi-step Screening Procedure (EnMSP), an iterative algorithm designed to recover sparse linear models in correlated data. EnMSP uses a small repeated penalty strategy to identify truly relevant covariates in a few iterations. Specifically, in each iteration, EnMSP enhances the adaptive lasso method by adding a weighted l2 penalty, which improves the selection of relevant variables. The method is shown to select the true model and achieve the l2-norm error bound under certain conditions. Numerical comparisons and applications demonstrate the effectiveness of EnMSP