# Within Group Variable Selection through the Exclusive Lasso

arXiv: https://arxiv.org/abs/1505.07517 · HTML: https://mlsanity.com/paper/1505.07517/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 May 2015.

## Built on by (most cited first, 5 of 5)

- [Autoencoding Random Forests](https://mlsanity.com/paper/2505.21441/) (2025)
- [Exclusive Group Lasso for Structured Variable Selection](https://mlsanity.com/paper/2108.10284/) (2021)
- [Cluster Regularization via a Hierarchical Feature Regression](https://mlsanity.com/paper/2107.04831/) (2021)
- [The non-overlapping statistical approximation to overlapping group lasso](https://mlsanity.com/paper/2211.09221/) (2022)
- [Time-to-event prediction for grouped variables using Exclusive Lasso](https://mlsanity.com/paper/2504.01520/) (2025)

## Abstract (arXiv)

Many data sets consist of variables with an inherent group structure. The problem of group selection has been well studied, but in this paper, we seek to do the opposite: our goal is to select at least one variable from each group in the context of predictive regression modeling. This problem is NP-hard, but we study the tightest convex relaxation: a composite penalty that is a combination of the ℓ1 and ℓ2 norms. Our so-called Exclusive Lasso method performs structured variable selection by ensuring that at least one variable is selected from each group. We study our method's statistical properties and develop computationally scalable algorithms for fitting the Exclusive Lasso. We study the effectiveness of our method via simulations as well as using NMR spectroscopy data. Here, we use the Exclusive Lasso to select the appropriate chemical shift from a dictionary of possible chemical shifts for each molecule in the biological sample.