Certifiably Polynomial Algorithm for Best Group Subset Selection

Best group subset selection aims to choose a small part of non-overlapping groups to achieve the best interpretability on the response variable. It is practically attractive for group variable selection; however, due to the computational intractability in high dimensionality setting, it doesn't catch enough attention. To fill the blank of efficient algorithms for best group subset selection, in this paper, we propose a group-splicing algorithm that iteratively detects effective groups and excludes the helpless ones. Moreover, coupled with a novel Bayesian group information criterion, an adaptive algorithm is developed to determine the true group subset size. It is certifiable that our algorithms enable identifying the optimal group subset in polynomial time under mild conditions. We demonstrate the efficiency and accuracy of our proposal by comparing state-of-the-art algorithms on both synthetic and real-world datasets.