# Safe Screening Rules for Group SLOPE

arXiv: https://arxiv.org/abs/2506.09451 · HTML: https://mlsanity.com/paper/2506.09451/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 43 references that are in the map.
- First posted on arXiv 11 Jun 2025.

## Builds on (most cited first, 20 of 20)

- [The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks](https://mlsanity.com/paper/1803.03635/) (2018)
- [Learning both Weights and Connections for Efficient Neural Networks](https://mlsanity.com/paper/1506.02626/) (2015)
- [A Proximal Stochastic Gradient Method with Progressive Variance Reduction](https://mlsanity.com/paper/1403.4699/) (2014)
- [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)
- [Auto-Train-Once: Controller Network Guided Automatic Network Pruning from Scratch](https://mlsanity.com/paper/2403.14729/) (2024)
- [Simultaneous Safe Screening of Features and Samples in Doubly Sparse Modeling](https://mlsanity.com/paper/1602.02485/) (2016)
- [Screening Tests for Lasso Problems](https://mlsanity.com/paper/1405.4897/) (2014)
- [A Safe Screening Rule for Sparse Logistic Regression](https://mlsanity.com/paper/1307.4145/) (2013)
- [An Accelerated Doubly Stochastic Gradient Method with Faster Explicit Model Identification](https://mlsanity.com/paper/2208.06058/) (2022)
- [Group SLOPE - adaptive selection of groups of predictors](https://mlsanity.com/paper/1610.04960/) (2016)
- [Dynamic Screening: Accelerating First-Order Algorithms for the Lasso and Group-Lasso](https://mlsanity.com/paper/1412.4080/) (2014)
- [Screening Rules for Lasso with Non-Convex Sparse Regularizers](https://mlsanity.com/paper/1902.06125/) (2019)
- [GAP Safe Screening Rules for Sparse-Group-Lasso](https://mlsanity.com/paper/1602.06225/) (2016)
- [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)
- [All-in-One Tuning and Structural Pruning for Domain-Specific LLMs](https://mlsanity.com/paper/2412.14426/) (2024)
- [Strong Screening Rules for Group-based SLOPE Models](https://mlsanity.com/paper/2405.15357/) (2024)
- [Safe Screening Rules for Group OWL Models](https://mlsanity.com/paper/2504.03152/) (2025)

## Abstract (arXiv)

Variable selection is a challenging problem in high-dimensional sparse learning, especially when group structures exist. Group SLOPE performs well for the adaptive selection of groups of predictors. However, the block non-separable group effects in Group SLOPE make existing methods either invalid or inefficient. Consequently, Group SLOPE tends to incur significant computational costs and memory usage in practical high-dimensional scenarios. To overcome this issue, we introduce a safe screening rule tailored for the Group SLOPE model, which efficiently identifies inactive groups with zero coefficients by addressing the block non-separable group effects. By excluding these inactive groups during training, we achieve considerable gains in computational efficiency and memory usage. Importantly, the proposed screening rule can be seamlessly integrated into existing solvers for both batch and stochastic algorithms. Theoretically, we establish that our screening rule can be safely employed with existing optimization algorithms, ensuring the same results as the original approaches. Experimental results confirm that our method effectively detects inactive feature groups and significantly boosts computational efficiency without compromising accuracy.