  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.
