# Strong Screening Rules for Group-based SLOPE Models

arXiv: https://arxiv.org/abs/2405.15357 · HTML: https://mlsanity.com/paper/2405.15357/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 80 references that are in the map.
- First posted on arXiv 24 May 2024.

## Builds on (most cited first, 24 of 24)

- [Gap Safe screening rules for sparsity enforcing penalties](https://mlsanity.com/paper/1611.05780/) (2016)
- [SLOPE - Adaptive variable selection via convex optimization](https://mlsanity.com/paper/1407.3824/) (2014)
- [Mind the duality gap: safer rules for the Lasso](https://mlsanity.com/paper/1505.03410/) (2015)
- [Fast OSCAR and OWL Regression via Safe Screening Rules](https://mlsanity.com/paper/2006.16433/) (2020)
- [Simultaneous Safe Screening of Features and Samples in Doubly Sparse Modeling](https://mlsanity.com/paper/1602.02485/) (2016)
- [A Safe Screening Rule for Sparse Logistic Regression](https://mlsanity.com/paper/1307.4145/) (2013)
- [Group SLOPE - adaptive selection of groups of predictors](https://mlsanity.com/paper/1610.04960/) (2016)
- [GAP Safe Screening Rules for Sparse-Group-Lasso](https://mlsanity.com/paper/1602.06225/) (2016)
- [The Geometry of Uniqueness, Sparsity and Clustering in Penalized Estimation](https://mlsanity.com/paper/2004.09106/) (2020)
- [sparsegl: An R Package for Estimating Sparse Group Lasso](https://mlsanity.com/paper/2208.02942/) (2022)
- [The Strong Screening Rule for SLOPE](https://mlsanity.com/paper/2005.03730/) (2020)
- [Two-Layer Feature Reduction for Sparse-Group Lasso via Decomposition of Convex Sets](https://mlsanity.com/paper/1410.4210/) (2014)
- [Adaptive Three Operator Splitting](https://mlsanity.com/paper/1804.02339/) (2018)
- [Safe rules for the identification of zeros in the solutions of the SLOPE problem](https://mlsanity.com/paper/2110.11784/) (2021)
- [A Survey of Numerical Algorithms that can Solve the Lasso Problems](https://mlsanity.com/paper/2303.03576/) (2023)
- [Sparse-group SLOPE: adaptive bi-level selection with FDR-control](https://mlsanity.com/paper/2305.09467/) (2023)
- [Coordinate Descent for SLOPE](https://mlsanity.com/paper/2210.14780/) (2022)
- [Sparse Estimation with Strongly Correlated Variables using Ordered Weighted L1 Regularization](https://mlsanity.com/paper/1409.4005/) (2014)
- [An Exact Solution Path Algorithm for SLOPE and Quasi-Spherical OSCAR](https://mlsanity.com/paper/2010.15511/) (2020)
- [Sparse Graphical Modelling via the Sorted L1-Norm](https://mlsanity.com/paper/2204.10403/) (2022)
- [Hybrid safe-strong rules for efficient optimization in lasso-type problems](https://mlsanity.com/paper/1704.08742/) (2017)
- [ExSIS: Extended Sure Independence Screening for Ultrahigh-dimensional Linear Models](https://mlsanity.com/paper/1708.06077/) (2017)
- [A study on tuning parameter selection for the high-dimensional lasso](https://mlsanity.com/paper/1602.01522/) (2016)
- [High-dimensional robust regression and outliers detection with SLOPE](https://mlsanity.com/paper/1712.02640/) (2017)

## Built on by (most cited first, 2 of 2)

- [Dual Feature Reduction for the Sparse-group Lasso and its Adaptive Variant](https://mlsanity.com/paper/2405.17094/) (2024)
- [Safe Screening Rules for Group SLOPE](https://mlsanity.com/paper/2506.09451/) (2025)

## Abstract (arXiv)

Tuning the regularization parameter in penalized regression models is an expensive task, requiring multiple models to be fit along a path of parameters. Strong screening rules drastically reduce computational costs by lowering the dimensionality of the input prior to fitting. We develop strong screening rules for group-based Sorted L-One Penalized Estimation (SLOPE) models: Group SLOPE and Sparse-group SLOPE. The developed rules are applicable to the wider family of group-based OWL models, including OSCAR. Our experiments on both synthetic and real data show that the screening rules significantly accelerate the fitting process. The screening rules make it accessible for group SLOPE and sparse-group SLOPE to be applied to high-dimensional datasets, particularly those encountered in genetics.