Stability Feature Selection using Cluster Representative LASSO

Variable selection in high dimensional regression problems with strongly correlated variables or with near linear dependence among few variables remains one of the most important issues. We propose to cluster the variables first and then do stability feature selection using Lasso for cluster representatives. The first step involves generation of groups based on some criterion and the second step mainly performs group selection with controlling the number of false positives. Thus, our primary emphasis is on controlling type-I error for group variable selection in high-dimensional regression setting. We illustrate the method using simulated and pseudo-real data, and we show that the proposed method finds an optimal and consistent solution.