# BackboneLearn: A Library for Scaling Mixed-Integer Optimization-Based Machine Learning

arXiv: https://arxiv.org/abs/2311.13695 · HTML: https://mlsanity.com/paper/2311.13695/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 23 references that are in the map.
- First posted on arXiv 22 Nov 2023.

## Builds on (most cited first, 12 of 12)

- [Finding Neurons in a Haystack: Case Studies with Sparse Probing](https://mlsanity.com/paper/2305.01610/) (2023)
- [Sparse Regression at Scale: Branch-and-Bound rooted in First-Order Optimization](https://mlsanity.com/paper/2004.06152/) (2020)
- [Learning Sparse Nonlinear Dynamics via Mixed-Integer Optimization](https://mlsanity.com/paper/2206.00176/) (2022)
- [Quant-BnB: A Scalable Branch-and-Bound Method for Optimal Decision Trees with Continuous Features](https://mlsanity.com/paper/2206.11844/) (2022)
- [L0Learn: A Scalable Package for Sparse Learning using L0 Regularization](https://mlsanity.com/paper/2202.04820/) (2022)
- [Safe Screening Rules for ℓ0-Regression](https://mlsanity.com/paper/2004.08773/) (2020)
- [The Backbone Method for Ultra-High Dimensional Sparse Machine Learning](https://mlsanity.com/paper/2006.06592/) (2020)
- [Slowly Varying Regression under Sparsity](https://mlsanity.com/paper/2102.10773/) (2021)
- [Safe Screening for Logistic Regression with ℓ0-ℓ2 Regularization](https://mlsanity.com/paper/2202.00467/) (2022)
- [Sparse PCA With Multiple Components](https://mlsanity.com/paper/2209.14790/) (2022)
- [Compressed Sensing: A Discrete Optimization Approach](https://mlsanity.com/paper/2306.04647/) (2023)
- [ODTlearn: A Package for Learning Optimal Decision Trees for Prediction and Prescription](https://mlsanity.com/paper/2307.15691/) (2023)

## Abstract (arXiv)

We present BackboneLearn: an open-source software package and framework for scaling mixed-integer optimization (MIO) problems with indicator variables to high-dimensional problems. This optimization paradigm can naturally be used to formulate fundamental problems in interpretable supervised learning (e.g., sparse regression and decision trees), in unsupervised learning (e.g., clustering), and beyond; BackboneLearn solves the aforementioned problems faster than exact methods and with higher accuracy than commonly used heuristics. The package is built in Python and is user-friendly and easily extensible: users can directly implement a backbone algorithm for their MIO problem at hand. The source code of BackboneLearn is available on GitHub (link: https://github.com/chziakas/backbone_learn).