# Scalable Holistic Linear Regression

arXiv: https://arxiv.org/abs/1902.03272 · HTML: https://mlsanity.com/paper/1902.03272/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Feb 2019.

## Built on by (most cited first, 6 of 6)

- [Learning Sparse Nonlinear Dynamics via Mixed-Integer Optimization](https://mlsanity.com/paper/2206.00176/) (2022)
- [Holistic Generalized Linear Models](https://mlsanity.com/paper/2205.15447/) (2022)
- [Feature subset selection for kernel SVM classification via mixed-integer optimization](https://mlsanity.com/paper/2205.14325/) (2022)
- [A distribution-free mixed-integer optimization approach to hierarchical modelling of clustered and longitudinal data](https://mlsanity.com/paper/2302.03157/) (2023)
- [Automated Model Selection for Generalized Linear Models](https://mlsanity.com/paper/2404.16560/) (2024)
- [Buffered AUC maximization for scoring systems via mixed-integer optimization](https://mlsanity.com/paper/2601.05544/) (2026)

## Abstract (arXiv)

We propose a new scalable algorithm for holistic linear regression building on Bertsimas & King (2016). Specifically, we develop new theory to model significance and multicollinearity as lazy constraints rather than checking the conditions iteratively. The resulting algorithm scales with the number of samples n in the 10,000s, compared to the low 100s in the previous framework. Computational results on real and synthetic datasets show it greatly improves from previous algorithms in accuracy, false detection rate, computational time and scalability.