# Safe Screening for Logistic Regression with ℓ0-ℓ2 Regularization

arXiv: https://arxiv.org/abs/2202.00467 · HTML: https://mlsanity.com/paper/2202.00467/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 29 references that are in the map.
- First posted on arXiv 1 Feb 2022.

## Builds on (most cited first, 10 of 10)

- [Best Subset Selection via a Modern Optimization Lens](https://mlsanity.com/paper/1507.03133/) (2015)
- [Fast Best Subset Selection: Coordinate Descent and Local Combinatorial Optimization Algorithms](https://mlsanity.com/paper/1803.01454/) (2018)
- [Sparse High-Dimensional Regression: Exact Scalable Algorithms and Phase Transitions](https://mlsanity.com/paper/1709.10029/) (2017)
- [Gap Safe screening rules for sparsity enforcing penalties](https://mlsanity.com/paper/1611.05780/) (2016)
- [Mind the duality gap: safer rules for the Lasso](https://mlsanity.com/paper/1505.03410/) (2015)
- [Learning Sparse Classifiers: Continuous and Mixed Integer Optimization Perspectives](https://mlsanity.com/paper/2001.06471/) (2020)
- [A Safe Screening Rule for Sparse Logistic Regression](https://mlsanity.com/paper/1307.4145/) (2013)
- [Safe Screening With Variational Inequalities and Its Application to LASSO](https://mlsanity.com/paper/1307.7577/) (2013)
- [Sparse and Smooth Signal Estimation: Convexification of L0 Formulations](https://mlsanity.com/paper/1811.02655/) (2018)
- [Expanding boundaries of Gap Safe screening](https://mlsanity.com/paper/2102.10846/) (2021)

## Built on by (most cited first, 6 of 6)

- [PMLBmini: A Tabular Classification Benchmark Suite for Data-Scarce Applications](https://mlsanity.com/paper/2409.01635/) (2024)
- [Cost-Sensitive Best Subset Selection for Logistic Regression: A Mixed-Integer Conic Optimization Perspective](https://mlsanity.com/paper/2310.05464/) (2023)
- [Constrained Optimization of Rank-One Functions with Indicator Variables](https://mlsanity.com/paper/2303.18158/) (2023)
- [Fair and Accurate Regression: Strong Formulations and Algorithms](https://mlsanity.com/paper/2412.17116/) (2024)
- [BackboneLearn: A Library for Scaling Mixed-Integer Optimization-Based Machine Learning](https://mlsanity.com/paper/2311.13695/) (2023)
- [A Generic Branch-and-Bound Algorithm for ℓ0-Penalized Problems with Supplementary Material](https://mlsanity.com/paper/2506.03974/) (2025)

## Abstract (arXiv)

In logistic regression, it is often desirable to utilize regularization to promote sparse solutions, particularly for problems with a large number of features compared to available labels. In this paper, we present screening rules that safely remove features from logistic regression with ℓ0-ℓ2 regularization before solving the problem. The proposed safe screening rules are based on lower bounds from the Fenchel dual of strong conic relaxations of the logistic regression problem. Numerical experiments with real and synthetic data suggest that a high percentage of the features can be effectively and safely removed apriori, leading to substantial speed-up in the computations.