# On the Selection Stability of Stability Selection and Its Applications

arXiv: https://arxiv.org/abs/2411.09097 · HTML: https://mlsanity.com/paper/2411.09097/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 27 references that are in the map.
- First posted on arXiv 14 Nov 2024.

## Builds on (most cited first, 4 of 4)

- [High-Dimensional Inference: Confidence Intervals, p-Values and R-Software hdi](https://mlsanity.com/paper/1408.4026/) (2014)
- [Automated calibration for stability selection in penalised regression and graphical models](https://mlsanity.com/paper/2106.02521/) (2021)
- [Stability Approach to Regularization Selection for Reduced-Rank Regression](https://mlsanity.com/paper/2207.00924/) (2022)
- [Determining number of factors under stability considerations](https://mlsanity.com/paper/2409.07617/) (2024)

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

- [Stability Selection via Variable Decorrelation](https://mlsanity.com/paper/2505.20864/) (2025)
- [A Stable Lasso](https://mlsanity.com/paper/2511.02306/) (2025)

## Abstract (arXiv)

Stability selection is a widely adopted resampling-based framework for high-dimensional variable selection. This paper seeks to broaden the use of an established stability estimator to evaluate the overall stability of the stability selection results, moving beyond single-variable analysis. We suggest that the stability estimator offers two advantages: it can serve as a reference to reflect the robustness of the results obtained, and it can help identify a Pareto optimal regularization value to improve stability. By determining the regularization value, we calibrate key stability selection parameters, namely, the decision-making threshold and the expected number of falsely selected variables, within established theoretical bounds. In addition, the convergence of stability values over successive sub-samples sheds light on the required number of sub-samples addressing a notable gap in prior studies. The textttstabplot R package is developed to facilitate the use of the methodology featured in this paper.