  Best subset of groups selection (BSGS) is the process of selecting a small
part of non-overlapping groups to achieve the best interpretability on the
response variable. It has attracted increasing attention and has far-reaching
applications in practice. However, due to the computational intractability of
BSGS in high-dimensional settings, developing efficient algorithms for solving
BSGS remains a research hotspot. In this paper,we propose a group-splicing
algorithm that iteratively detects the relevant groups and excludes the
irrelevant ones. Moreover, coupled with a novel group information criterion, we
develop an adaptive algorithm to determine the optimal model size. Under mild
conditions, it is certifiable that our algorithm can identify the optimal
subset of groups in polynomial time with high probability. Finally, we
demonstrate the efficiency and accuracy of our methods by comparing them with
several state-of-the-art algorithms on both synthetic and real-world datasets.
