# Best-Subset Selection in Generalized Linear Models: A Fast and Consistent Algorithm via Splicing Technique

arXiv: https://arxiv.org/abs/2308.00251 · HTML: https://mlsanity.com/paper/2308.00251/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 50 references that are in the map.
- First posted on arXiv 1 Aug 2023.

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

- [Learning Sparse Classifiers: Continuous and Mixed Integer Optimization Perspectives](https://mlsanity.com/paper/2001.06471/) (2020)
- [abess: A Fast Best Subset Selection Library in Python and R](https://mlsanity.com/paper/2110.09697/) (2021)
- [Tuning parameter selection in high dimensional penalized likelihood](https://mlsanity.com/paper/1605.03321/) (2016)
- [Regularization Methods for High-Dimensional Instrumental Variables Regression With an Application to Genetical Genomics](https://mlsanity.com/paper/1304.7829/) (2013)
- [Global and Quadratic Convergence of Newton Hard-Thresholding Pursuit](https://mlsanity.com/paper/1901.02763/) (2019)
- [Estimation and Inference for High Dimensional Generalized Linear Models: A Splitting and Smoothing Approach](https://mlsanity.com/paper/1903.04408/) (2019)
- [On Quadratic Convergence of DC Proximal Newton Algorithm for Nonconvex Sparse Learning in High Dimensions](https://mlsanity.com/paper/1706.06066/) (2017)

## Built on by (most cited first, 3 of 3)

- [Foundations of Top-k Decoding For Language Models](https://mlsanity.com/paper/2505.19371/) (2025)
- [skscope: Fast Sparsity-Constrained Optimization in Python](https://mlsanity.com/paper/2403.18540/) (2024)
- [A Consistent and Scalable Algorithm for Best Subset Selection in Single Index Models](https://mlsanity.com/paper/2309.06230/) (2023)

## Abstract (arXiv)

In high-dimensional generalized linear models, it is crucial to identify a sparse model that adequately accounts for response variation. Although the best subset section has been widely regarded as the Holy Grail of problems of this type, achieving either computational efficiency or statistical guarantees is challenging. In this article, we intend to surmount this obstacle by utilizing a fast algorithm to select the best subset with high certainty. We proposed and illustrated an algorithm for best subset recovery in regularity conditions. Under mild conditions, the computational complexity of our algorithm scales polynomially with sample size and dimension. In addition to demonstrating the statistical properties of our method, extensive numerical experiments reveal that it outperforms existing methods for variable selection and coefficient estimation. The runtime analysis shows that our implementation achieves approximately a fourfold speedup compared to popular variable selection toolkits like glmnet and ncvreg.