# The Strong Screening Rule for SLOPE

arXiv: https://arxiv.org/abs/2005.03730 · HTML: https://mlsanity.com/paper/2005.03730/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 May 2020.

## Built on by (most cited first, 8 of 8)

- [Safe rules for the identification of zeros in the solutions of the SLOPE problem](https://mlsanity.com/paper/2110.11784/) (2021)
- [Coordinate Descent for SLOPE](https://mlsanity.com/paper/2210.14780/) (2022)
- [Strong Screening Rules for Group-based SLOPE Models](https://mlsanity.com/paper/2405.15357/) (2024)
- [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)
- [Proximal Operators of Sorted Nonconvex Penalties](https://mlsanity.com/paper/2506.15315/) (2025)
- [Efficient Solvers for SLOPE in R, Python, Julia, and C++](https://mlsanity.com/paper/2511.02430/) (2025)
- [Beyond False Discovery Rate: A Stepdown Group SLOPE Approach for Grouped Variable Selection](https://mlsanity.com/paper/2603.00955/) (2026)

## Abstract (arXiv)

Extracting relevant features from data sets where the number of observations (n) is much smaller then the number of predictors (p) is a major challenge in modern statistics. Sorted L-One Penalized Estimation (SLOPE), a generalization of the lasso, is a promising method within this setting. Current numerical procedures for SLOPE, however, lack the efficiency that respective tools for the lasso enjoy, particularly in the context of estimating a complete regularization path. A key component in the efficiency of the lasso is predictor screening rules: rules that allow predictors to be discarded before estimating the model. This is the first paper to establish such a rule for SLOPE. We develop a screening rule for SLOPE by examining its subdifferential and show that this rule is a generalization of the strong rule for the lasso. Our rule is heuristic, which means that it may discard predictors erroneously. We present conditions under which this may happen and show that such situations are rare and easily safeguarded against by a simple check of the optimality conditions. Our numerical experiments show that the rule performs well in practice, leading to improvements by orders of magnitude for data in the p gg n domain, as well as incurring no additional computational overhead when n gg p. We also examine the effect of correlation structures in the design matrix on the rule and discuss algorithmic strategies for employing the rule. Finally, we provide an efficient implementation of the rule in our R package SLOPE.