A Splicing Approach to Best Subset of Groups Selection
This addresses the problem of efficient and interpretable group selection in high-dimensional data for researchers and practitioners in statistics and machine learning, representing an incremental improvement with a novel method for a known bottleneck.
The paper tackles the computational intractability of best subset of groups selection (BSGS) in high-dimensional settings by proposing a group-splicing algorithm that iteratively detects relevant groups and excludes irrelevant ones, coupled with a novel group information criterion to determine optimal model size, demonstrating efficiency and accuracy compared to state-of-the-art algorithms on synthetic and real-world datasets.
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.