# Dual Feature Reduction for the Sparse-group Lasso and its Adaptive Variant

arXiv: https://arxiv.org/abs/2405.17094 · HTML: https://mlsanity.com/paper/2405.17094/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 59 references that are in the map.
- First posted on arXiv 27 May 2024.

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

- [LassoNet: A Neural Network with Feature Sparsity](https://mlsanity.com/paper/1907.12207/) (2019)
- [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)
- [Simultaneous Safe Screening of Features and Samples in Doubly Sparse Modeling](https://mlsanity.com/paper/1602.02485/) (2016)
- [GAP Safe screening rules for sparse multi-task and multi-class models](https://mlsanity.com/paper/1506.03736/) (2015)
- [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)
- [Dynamic Screening: Accelerating First-Order Algorithms for the Lasso and Group-Lasso](https://mlsanity.com/paper/1412.4080/) (2014)
- [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)
- [The Contextual Lasso: Sparse Linear Models via Deep Neural Networks](https://mlsanity.com/paper/2302.00878/) (2023)
- [Scaling Up Sparse Support Vector Machines by Simultaneous Feature and Sample Reduction](https://mlsanity.com/paper/1607.06996/) (2016)
- [Adaptive sparse group LASSO in quantile regression](https://mlsanity.com/paper/1911.01081/) (2019)
- [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)
- [The Hessian Screening Rule](https://mlsanity.com/paper/2104.13026/) (2021)
- [A scalable hierarchical lasso for gene-environment interactions](https://mlsanity.com/paper/2103.13510/) (2021)
- [Strong Screening Rules for Group-based SLOPE Models](https://mlsanity.com/paper/2405.15357/) (2024)
- [Machine Learning Methods in the Computational Biology of Cancer](https://mlsanity.com/paper/1402.5728/) (2014)
- [Analytic solution and stationary phase approximation for the Bayesian lasso and elastic net](https://mlsanity.com/paper/1709.08535/) (2017)

## Abstract (arXiv)

The sparse-group lasso performs both variable and group selection, simultaneously using the strengths of the lasso and group lasso. It has found widespread use in genetics, a field that regularly involves the analysis of high-dimensional data, due to its sparse-group penalty, which allows it to utilize grouping information. However, the sparse-group lasso can be computationally expensive, due to the added shrinkage complexity, and its additional hyperparameter that needs tuning. This paper presents a novel feature reduction method, Dual Feature Reduction (DFR), that uses strong screening rules for the sparse-group lasso and the adaptive sparse-group lasso to reduce their input space before optimization, without affecting solution optimality. DFR applies two layers of screening through the application of dual norms and subdifferentials. Through synthetic and real data studies, it is shown that DFR drastically reduces the computational cost under many different scenarios.