# Screening Tests for Lasso Problems

arXiv: https://arxiv.org/abs/1405.4897 · HTML: https://mlsanity.com/paper/1405.4897/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 May 2014.

## Built on by (most cited first, 15 of 15)

- [Expanding boundaries of Gap Safe screening](https://mlsanity.com/paper/2102.10846/) (2021)
- [Safe rules for the identification of zeros in the solutions of the SLOPE problem](https://mlsanity.com/paper/2110.11784/) (2021)
- [Dynamic Sasvi: Strong Safe Screening for Norm-Regularized Least Squares](https://mlsanity.com/paper/2102.04108/) (2021)
- [Generalized Low-Rank Update: Model Parameter Bounds for Low-Rank Training Data Modifications](https://mlsanity.com/paper/2306.12670/) (2023)
- [Screening for Sparse Online Learning](https://mlsanity.com/paper/2101.06982/) (2021)
- [Beyond GAP screening for Lasso by exploiting new dual cutting half-spaces with supplementary material](https://mlsanity.com/paper/2203.00987/) (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)
- [Low Rank Multi-Dictionary Selection at Scale](https://mlsanity.com/paper/2406.06960/) (2024)
- [Safe Screening Rules for Group OWL Models](https://mlsanity.com/paper/2504.03152/) (2025)
- [Safe Distributionally Robust Feature Selection under Covariate Shift](https://mlsanity.com/paper/2603.16062/) (2026)
- [Safe Screening for Unbalanced Optimal Transport](https://mlsanity.com/paper/2307.00247/) (2023)
- [Fast Screening Rules for Optimal Design via Quadratic Lasso Reformulation](https://mlsanity.com/paper/2310.08939/) (2023)
- [Safe Screening Rules for Group SLOPE](https://mlsanity.com/paper/2506.09451/) (2025)
- [AT-SKM-Net: An Accelerated Trainable Sampling Kaczmarz-Motzkin Framework for Linear Hard-Constraint Feasibility on Dynamic Graphs](https://mlsanity.com/paper/2609.30088/) (2026)

## Abstract (arXiv)

This paper is a survey of dictionary screening for the lasso problem. The lasso problem seeks a sparse linear combination of the columns of a dictionary to best match a given target vector. This sparse representation has proven useful in a variety of subsequent processing and decision tasks. For a given target vector, dictionary screening quickly identifies a subset of dictionary columns that will receive zero weight in a solution of the corresponding lasso problem. These columns can be removed from the dictionary prior to solving the lasso problem without impacting the optimality of the solution obtained. This has two potential advantages: it reduces the size of the dictionary, allowing the lasso problem to be solved with less resources, and it may speed up obtaining a solution. Using a geometrically intuitive framework, we provide basic insights for understanding useful lasso screening tests and their limitations. We also provide illustrative numerical studies on several datasets.