# A Stable Lasso

arXiv: https://arxiv.org/abs/2511.02306 · HTML: https://mlsanity.com/paper/2511.02306/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 51 references that are in the map.
- First posted on arXiv 4 Nov 2025.

## Builds on (most cited first, 13 of 13)

- [Bagging Provides Assumption-free Stability](https://mlsanity.com/paper/2301.12600/) (2023)
- [High-dimensional Ordinary Least-squares Projection for Screening Variables](https://mlsanity.com/paper/1506.01782/) (2015)
- [Pretraining and the Lasso](https://mlsanity.com/paper/2401.12911/) (2024)
- [Independently Interpretable Lasso: A New Regularizer for Sparse Regression with Uncorrelated Variables](https://mlsanity.com/paper/1711.01796/) (2017)
- [Sparse-group SLOPE: adaptive bi-level selection with FDR-control](https://mlsanity.com/paper/2305.09467/) (2023)
- [Cluster Stability Selection](https://mlsanity.com/paper/2201.00494/) (2022)
- [Univariate-Guided Sparse Regression](https://mlsanity.com/paper/2501.18360/) (2025)
- [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)
- [A Metropolized adaptive subspace algorithm for high-dimensional Bayesian variable selection](https://mlsanity.com/paper/2105.01039/) (2021)
- [Stability Selection via Variable Decorrelation](https://mlsanity.com/paper/2505.20864/) (2025)

## Abstract (arXiv)

The Lasso has been widely used as a method for variable selection, valued for its simplicity and empirical performance. However, Lasso's selection stability deteriorates in the presence of correlated predictors. Several approaches have been developed to mitigate this limitation. In this paper, we provide a brief review of existing approaches, highlighting their limitations. We then propose a simple technique to improve the selection stability of Lasso by integrating a weighting scheme into the Lasso penalty function, where the weights are defined as an increasing function of a correlation-adjusted ranking that reflects the predictive power of predictors. Empirical evaluations on both simulated and real-world datasets demonstrate the efficacy of the proposed method. Additional numerical results demonstrate the effectiveness of the proposed approach in stabilizing other regularization-based selection methods, indicating its potential as a general-purpose solution.