# Stability Selection via Variable Decorrelation

arXiv: https://arxiv.org/abs/2505.20864 · HTML: https://mlsanity.com/paper/2505.20864/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 64 references that are in the map.
- First posted on arXiv 27 May 2025.

## Builds on (most cited first, 17 of 17)

- [Deep Stable Learning for Out-Of-Distribution Generalization](https://mlsanity.com/paper/2104.07876/) (2021)
- [Stable Learning via Sample Reweighting](https://mlsanity.com/paper/1911.12580/) (2019)
- [Correlation and variable importance in random forests](https://mlsanity.com/paper/1310.5726/) (2013)
- [Stabilizing Variable Selection and Regression](https://mlsanity.com/paper/1911.01850/) (2019)
- [Bagging Provides Assumption-free Stability](https://mlsanity.com/paper/2301.12600/) (2023)
- [High-Dimensional Inference: Confidence Intervals, p-Values and R-Software hdi](https://mlsanity.com/paper/1408.4026/) (2014)
- [High-dimensional Ordinary Least-squares Projection for Screening Variables](https://mlsanity.com/paper/1506.01782/) (2015)
- [Forward Stability and Model Path Selection](https://mlsanity.com/paper/2103.03462/) (2021)
- [Independently Interpretable Lasso: A New Regularizer for Sparse Regression with Uncorrelated Variables](https://mlsanity.com/paper/1711.01796/) (2017)
- [Ultra-marginal Feature Importance: Learning from Data with Causal Guarantees](https://mlsanity.com/paper/2204.09938/) (2022)
- [Cluster Stability Selection](https://mlsanity.com/paper/2201.00494/) (2022)
- [Univariate-Guided Sparse Regression](https://mlsanity.com/paper/2501.18360/) (2025)
- [Automated calibration for stability selection in penalised regression and graphical models](https://mlsanity.com/paper/2106.02521/) (2021)
- [Air-HOLP: Adaptive Regularized Feature Screening for High Dimensional Correlated Data](https://mlsanity.com/paper/2408.13000/) (2024)
- [Bayesian Stability Selection and Inference on Selection Probabilities](https://mlsanity.com/paper/2410.21914/) (2024)
- [On the Selection Stability of Stability Selection and Its Applications](https://mlsanity.com/paper/2411.09097/) (2024)
- [Ridge partial correlation screening for ultrahigh-dimensional data](https://mlsanity.com/paper/2504.19393/) (2025)

## Built on by (most cited first, 1 of 1)

- [A Stable Lasso](https://mlsanity.com/paper/2511.02306/) (2025)

## Abstract (arXiv)

The Lasso is a prominent algorithm for variable selection. However, its instability in the presence of correlated variables in the high-dimensional setting is well-documented. Although previous research has attempted to address this issue by modifying the Lasso loss function, this paper introduces an approach that simplifies the data processed by Lasso. We propose that decorrelating variables before applying the Lasso improves the stability of variable selection regardless of the direction of correlation among predictors. Furthermore, we highlight that the irrepresentable condition, which ensures consistency for the Lasso, is satisfied after variable decorrelation under two assumptions. In addition, by noting that the instability of the Lasso is not limited to high-dimensional settings, we demonstrate the effectiveness of the proposed approach for low-dimensional data. Finally, we present empirical results that indicate the efficacy of the proposed method across different variable selection techniques, highlighting its potential for broader application. The DVS R package is developed to facilitate the implementation of the methodology proposed in this paper.