# L0Learn: A Scalable Package for Sparse Learning using L0 Regularization

arXiv: https://arxiv.org/abs/2202.04820 · HTML: https://mlsanity.com/paper/2202.04820/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 38 references that are in the map.
- First posted on arXiv 10 Feb 2022.

## Builds on (most cited first, 8 of 8)

- [Best Subset Selection via a Modern Optimization Lens](https://mlsanity.com/paper/1507.03133/) (2015)
- [Fast Best Subset Selection: Coordinate Descent and Local Combinatorial Optimization Algorithms](https://mlsanity.com/paper/1803.01454/) (2018)
- [Sparse Regression at Scale: Branch-and-Bound rooted in First-Order Optimization](https://mlsanity.com/paper/2004.06152/) (2020)
- [Sparse High-Dimensional Regression: Exact Scalable Algorithms and Phase Transitions](https://mlsanity.com/paper/1709.10029/) (2017)
- [Learning Sparse Classifiers: Continuous and Mixed Integer Optimization Perspectives](https://mlsanity.com/paper/2001.06471/) (2020)
- [Subset Selection with Shrinkage: Sparse Linear Modeling when the SNR is low](https://mlsanity.com/paper/1708.03288/) (2017)
- [Grouped Variable Selection with Discrete Optimization: Computational and Statistical Perspectives](https://mlsanity.com/paper/2104.07084/) (2021)
- [Picasso: A Sparse Learning Library for High Dimensional Data Analysis in R and Python](https://mlsanity.com/paper/2006.15261/) (2020)

## Built on by (most cited first, 12 of 12)

- [Foundations of Top-k Decoding For Language Models](https://mlsanity.com/paper/2505.19371/) (2025)
- [Interpretable Generalized Additive Models for Datasets with Missing Values](https://mlsanity.com/paper/2412.02646/) (2024)
- [FIRE: An Optimization Approach for Fast Interpretable Rule Extraction](https://mlsanity.com/paper/2306.07432/) (2023)
- [Outlier detection in regression: conic quadratic formulations](https://mlsanity.com/paper/2307.05975/) (2023)
- [Efficient Cross-Validation for Sparse Linear Regression](https://mlsanity.com/paper/2306.14851/) (2023)
- [BackboneLearn: A Library for Scaling Mixed-Integer Optimization-Based Machine Learning](https://mlsanity.com/paper/2311.13695/) (2023)
- [FAST: An Optimization Framework for Fast Additive Segmentation in Transparent ML](https://mlsanity.com/paper/2402.12630/) (2024)
- [Nash: Neural Adaptive Shrinkage for Structured High-Dimensional Regression](https://mlsanity.com/paper/2505.11143/) (2025)
- [A Generic Branch-and-Bound Algorithm for ℓ0-Penalized Problems with Supplementary Material](https://mlsanity.com/paper/2506.03974/) (2025)
- [El0ps: An Exact L0-regularized Problems Solver](https://mlsanity.com/paper/2506.06373/) (2025)
- [MOSS: Multi-Objective Optimization for Stable Rule Sets](https://mlsanity.com/paper/2506.08030/) (2025)
- [A Flexible Empirical Bayes Approach to Generalized Linear Models, with Applications to Sparse Logistic Regression](https://mlsanity.com/paper/2601.21217/) (2026)

## Abstract (arXiv)

We present L0Learn: an open-source package for sparse linear regression and classification using ℓ0 regularization. L0Learn implements scalable, approximate algorithms, based on coordinate descent and local combinatorial optimization. The package is built using C++ and has user-friendly R and Python interfaces. L0Learn can address problems with millions of features, achieving competitive run times and statistical performance with state-of-the-art sparse learning packages. L0Learn is available on both CRAN and GitHub (https://cran.r-project.org/package=L0Learn and https://github.com/hazimehh/L0Learn).