# Group SLOPE - adaptive selection of groups of predictors

arXiv: https://arxiv.org/abs/1610.04960 · HTML: https://mlsanity.com/paper/1610.04960/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Oct 2016.

## Built on by (most cited first, 13 of 13)

- [Sparse Neural Additive Model: Interpretable Deep Learning with Feature Selection via Group Sparsity](https://mlsanity.com/paper/2202.12482/) (2022)
- [Composite Feature Selection using Deep Ensembles](https://mlsanity.com/paper/2211.00631/) (2022)
- [Safe rules for the identification of zeros in the solutions of the SLOPE problem](https://mlsanity.com/paper/2110.11784/) (2021)
- [Generalization Error Bounds for Multiclass Sparse Linear Classifiers](https://mlsanity.com/paper/2204.06264/) (2022)
- [Characterizing the SLOPE Trade-off: A Variational Perspective and the Donoho-Tanner Limit](https://mlsanity.com/paper/2105.13302/) (2021)
- [Chi-square and normal inference in high-dimensional multi-task regression](https://mlsanity.com/paper/2107.07828/) (2021)
- [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)
- [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)
- [Sampling Method for Generalized Graph Signals with Pre-selected Vertices via DC Optimization](https://mlsanity.com/paper/2509.14836/) (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)

Sorted L-One Penalized Estimation (SLOPE) is a relatively new convex optimization procedure which allows for adaptive selection of regressors under sparse high dimensional designs. Here we extend the idea of SLOPE to deal with the situation when one aims at selecting whole groups of explanatory variables instead of single regressors. Such groups can be formed by clustering strongly correlated predictors or groups of dummy variables corresponding to different levels of the same qualitative predictor. We formulate the respective convex optimization problem, gSLOPE (group SLOPE), and propose an efficient algorithm for its solution. We also define a notion of the group false discovery rate (gFDR) and provide a choice of the sequence of tuning parameters for gSLOPE so that gFDR is provably controlled at a prespecified level if the groups of variables are orthogonal to each other. Moreover, we prove that the resulting procedure adapts to unknown sparsity and is asymptotically minimax with respect to the estimation of the proportions of variance of the response variable explained by regressors from different groups. We also provide a method for the choice of the regularizing sequence when variables in different groups are not orthogonal but statistically independent and illustrate its good properties with computer simulations. Finally, we illustrate the advantages of gSLOPE in the context of Genome Wide Association Studies. R package grpSLOPE with implementation of our method is available on CRAN.