# Exclusive Group Lasso for Structured Variable Selection

arXiv: https://arxiv.org/abs/2108.10284 · HTML: https://mlsanity.com/paper/2108.10284/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 42 references that are in the map.
- First posted on arXiv 23 Aug 2021.

## Builds on (most cited first, 7 of 7)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [The Squared-Error of Generalized LASSO: A Precise Analysis](https://mlsanity.com/paper/1311.0830/) (2013)
- [Localized Lasso for High-Dimensional Regression](https://mlsanity.com/paper/1603.06743/) (2016)
- [Within Group Variable Selection through the Exclusive Lasso](https://mlsanity.com/paper/1505.07517/) (2015)
- [Learning the Structure for Structured Sparsity](https://mlsanity.com/paper/1503.03082/) (2015)
- [A Penalty Function Promoting Sparsity Within and Across Groups](https://mlsanity.com/paper/1603.03650/) (2016)
- [A dual Newton based preconditioned proximal point algorithm for exclusive lasso models](https://mlsanity.com/paper/1902.00151/) (2019)

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

- [Multi-level projection with exponential parallel speedup; Application to sparse auto-encoders neural networks](https://mlsanity.com/paper/2405.02086/) (2024)
- [Time-to-event prediction for grouped variables using Exclusive Lasso](https://mlsanity.com/paper/2504.01520/) (2025)

## Abstract (arXiv)

A structured variable selection problem is considered in which the covariates, divided into predefined groups, activate according to sparse patterns with few nonzero entries per group. Capitalizing on the concept of atomic norm, a composite norm can be properly designed to promote such exclusive group sparsity patterns. The resulting norm lends itself to efficient and flexible regularized optimization algorithms for support recovery, like the proximal algorithm. Moreover, an active set algorithm is proposed that builds the solution by successively including structure atoms into the estimated support. It is also shown that such an algorithm can be tailored to match more rigid structures than plain exclusive group sparsity. Asymptotic consistency analysis (with both the number of parameters as well as the number of groups growing with the observation size) establishes the effectiveness of the proposed solution in terms of signed support recovery under conventional assumptions. Finally, a set of numerical simulations further corroborates the results.