# Semi-analytic approximate stability selection for correlated data in generalized linear models

arXiv: https://arxiv.org/abs/2003.08670 · HTML: https://mlsanity.com/paper/2003.08670/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Mar 2020.

## Built on by (most cited first, 2 of 2)

- [QCM-SGM+: Improved Quantized Compressed Sensing With Score-Based Generative Models](https://mlsanity.com/paper/2302.00919/) (2023)
- [A replica analysis of under-bagging](https://mlsanity.com/paper/2404.09779/) (2024)

## Abstract (arXiv)

We consider the variable selection problem of generalized linear models (GLMs). Stability selection (SS) is a promising method proposed for solving this problem. Although SS provides practical variable selection criteria, it is computationally demanding because it needs to fit GLMs to many re-sampled datasets. We propose a novel approximate inference algorithm that can conduct SS without the repeated fitting. The algorithm is based on the replica method of statistical mechanics and vector approximate message passing of information theory. For datasets characterized by rotation-invariant matrix ensembles, we derive state evolution equations that macroscopically describe the dynamics of the proposed algorithm. We also show that their fixed points are consistent with the replica symmetric solution obtained by the replica method. Numerical experiments indicate that the algorithm exhibits fast convergence and high approximation accuracy for both synthetic and real-world data.