# A Splicing Approach to Best Subset of Groups Selection

arXiv: https://arxiv.org/abs/2104.12576 · HTML: https://mlsanity.com/paper/2104.12576/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 53 references that are in the map.
- First posted on arXiv 23 Apr 2021.

## Builds on (most cited first, 7 of 7)

- [Best Subset Selection via a Modern Optimization Lens](https://mlsanity.com/paper/1507.03133/) (2015)
- [Sparse Regression at Scale: Branch-and-Bound rooted in First-Order Optimization](https://mlsanity.com/paper/2004.06152/) (2020)
- [Sparse High-Dimensional Regression: Exact Scalable Algorithms and Phase Transitions](https://mlsanity.com/paper/1709.10029/) (2017)
- [Grouped Variable Selection with Discrete Optimization: Computational and Statistical Perspectives](https://mlsanity.com/paper/2104.07084/) (2021)
- [Slowly Varying Regression under Sparsity](https://mlsanity.com/paper/2102.10773/) (2021)
- [Structured Sparse Regression via Greedy Hard-Thresholding](https://mlsanity.com/paper/1602.06042/) (2016)
- [An Interactive Greedy Approach to Group Sparsity in High Dimensions](https://mlsanity.com/paper/1707.02963/) (2017)

## Built on by (most cited first, 4 of 4)

- [abess: A Fast Best Subset Selection Library in Python and R](https://mlsanity.com/paper/2110.09697/) (2021)
- [Holistic Generalized Linear Models](https://mlsanity.com/paper/2205.15447/) (2022)
- [Group selection and shrinkage: Structured sparsity for semiparametric additive models](https://mlsanity.com/paper/2105.12081/) (2021)
- [A Consistent and Scalable Algorithm for Best Subset Selection in Single Index Models](https://mlsanity.com/paper/2309.06230/) (2023)

## Abstract (arXiv)

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.