# Screening Rules for Lasso with Non-Convex Sparse Regularizers

arXiv: https://arxiv.org/abs/1902.06125 · HTML: https://mlsanity.com/paper/1902.06125/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Feb 2019.

## Built on by (most cited first, 11 of 11)

- [Beyond L1: Faster and Better Sparse Models with skglm](https://mlsanity.com/paper/2204.07826/) (2022)
- [Distributed Contrastive Learning for Medical Image Segmentation](https://mlsanity.com/paper/2208.03808/) (2022)
- [An Accelerated Doubly Stochastic Gradient Method with Faster Explicit Model Identification](https://mlsanity.com/paper/2208.06058/) (2022)
- [Efficient Model Selection for Predictive Pattern Mining Model by Safe Pattern Pruning](https://mlsanity.com/paper/2306.13561/) (2023)
- [Feature Selection from Differentially Private Correlations](https://mlsanity.com/paper/2408.10862/) (2024)
- [Distributed Dynamic Safe Screening Algorithms for Sparse Regularization](https://mlsanity.com/paper/2204.10981/) (2022)
- [Safe Screening Rules for Group OWL Models](https://mlsanity.com/paper/2504.03152/) (2025)
- [Screening for a Reweighted Penalized Conditional Gradient Method](https://mlsanity.com/paper/2107.01106/) (2021)
- [A Screening Strategy for Structured Optimization Involving Nonconvex ℓq,p Regularization](https://mlsanity.com/paper/2208.02161/) (2022)
- [Safe Screening Rules for Group SLOPE](https://mlsanity.com/paper/2506.09451/) (2025)
- [Simpler Methods Work Better for L1 Penalized Logistic Models and Large Datasets](https://mlsanity.com/paper/2609.23995/) (2026)

## Abstract (arXiv)

Leveraging on the convexity of the Lasso problem , screening rules help in accelerating solvers by discarding irrelevant variables, during the optimization process. However, because they provide better theoretical guarantees in identifying relevant variables, several non-convex regularizers for the Lasso have been proposed in the literature. This work is the first that introduces a screening rule strategy into a non-convex Lasso solver. The approach we propose is based on a iterative majorization-minimization (MM) strategy that includes a screening rule in the inner solver and a condition for propagating screened variables between iterations of MM. In addition to improve efficiency of solvers, we also provide guarantees that the inner solver is able to identify the zeros components of its critical point in finite time. Our experimental analysis illustrates the significant computational gain brought by the new screening rule compared to classical coordinate-descent or proximal gradient descent methods.