# Scalable Holistic Linear Regression

## TL;DR

This paper introduces a scalable holistic linear regression algorithm that models significance and multicollinearity as lazy constraints, significantly improving scalability and accuracy over previous methods.

## Contribution

The paper presents a novel theory and algorithm that enhance scalability and performance of holistic linear regression by modeling key conditions as lazy constraints.

## Key findings

- Scales with thousands of samples, outperforming previous methods.
- Improves accuracy and reduces false detection rate.
- Reduces computational time significantly.

## Abstract

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.