Bi-level Variable Selection Methods Based On Lasso

Variable selection is an extremely important part of the statistical modeling. In many engineering and scientific applications, covariates posses a grouping structure. At this time, we need to conduct bi-level selection——both grouped variables selection and individual variable selection in the groups. Many scholars have tried to use penalized regression to deal with this problem:group lasso、group bridge lasso、gMCP、sparse group lasso, and so on. However, these methods exist some limitations:the algorithm of group bridge lasso can’t guarantee that this method converges to the true minimum; the gMCP tends to select too many groups, and so on.In our paper, we proposed two improved methods for the disadvantages of these methods. Firstly, we point out the problems of the sparse group lasso. We proposed two improved method——method one and method two, and gave the corresponding algorithm. To verify the rationality and superiority of the method, we recorded the results of method two, and carried out some comparison and summary with the use of R. The results of my method are satisfactory.