A Splicing Approach to Best Subset of Groups Selection

TL;DR

This paper introduces a novel group-splicing algorithm for best subset of groups selection, efficiently identifying relevant groups in high-dimensional data with theoretical guarantees and demonstrated superior performance.

Contribution

It proposes a new group-splicing method with an adaptive criterion, providing polynomial-time identification of the optimal group subset with high probability.

Findings

Algorithm achieves high accuracy on synthetic datasets.

Method outperforms existing algorithms on real-world data.

Provides theoretical guarantees for optimal subset recovery.

Abstract

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.