# Localized Lasso for High-Dimensional Regression

arXiv: https://arxiv.org/abs/1603.06743 · HTML: https://mlsanity.com/paper/1603.06743/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Mar 2016.

## Built on by (most cited first, 11 of 11)

- [Locally Sparse Neural Networks for Tabular Biomedical Data](https://mlsanity.com/paper/2106.06468/) (2021)
- [Explaining Time Series via Contrastive and Locally Sparse Perturbations](https://mlsanity.com/paper/2401.08552/) (2024)
- [ProtoGate: Prototype-based Neural Networks with Global-to-local Feature Selection for Tabular Biomedical Data](https://mlsanity.com/paper/2306.12330/) (2023)
- [Meta-strategy for Learning Tuning Parameters with Guarantees](https://mlsanity.com/paper/2102.02504/) (2021)
- [The Contextual Lasso: Sparse Linear Models via Deep Neural Networks](https://mlsanity.com/paper/2302.00878/) (2023)
- [Multi-Task Learning Regression via Convex Clustering](https://mlsanity.com/paper/2304.13342/) (2023)
- [Exclusive Group Lasso for Structured Variable Selection](https://mlsanity.com/paper/2108.10284/) (2021)
- [A Bayesian approach to multi-task learning with network lasso](https://mlsanity.com/paper/2110.09040/) (2021)
- [Multi-task learning via robust regularized clustering with non-convex group penalties](https://mlsanity.com/paper/2404.03250/) (2024)
- [MetaSD: A Unified Framework for Scalable Downscaling of Meteorological Variables in Diverse Situations](https://mlsanity.com/paper/2404.17611/) (2024)
- [Genetics-Driven Personalized Disease Progression Model](https://mlsanity.com/paper/2503.00028/) (2025)

## Abstract (arXiv)

We introduce the localized Lasso, which is suited for learning models that are both interpretable and have a high predictive power in problems with high dimensionality d and small sample size n. More specifically, we consider a function defined by local sparse models, one at each data point. We introduce sample-wise network regularization to borrow strength across the models, and sample-wise exclusive group sparsity (a.k.a., ℓ1,2 norm) to introduce diversity into the choice of feature sets in the local models. The local models are interpretable in terms of similarity of their sparsity patterns. The cost function is convex, and thus has a globally optimal solution. Moreover, we propose a simple yet efficient iterative least-squares based optimization procedure for the localized Lasso, which does not need a tuning parameter, and is guaranteed to converge to a globally optimal solution. The solution is empirically shown to outperform alternatives for both simulated and genomic personalized medicine data.