# Conditional Linear Regression

arXiv: https://arxiv.org/abs/1806.02326 · HTML: https://mlsanity.com/paper/1806.02326/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Jun 2018.

## Built on by (most cited first, 4 of 4)

- [Data-Driven Subgroup Identification for Linear Regression](https://mlsanity.com/paper/2305.00195/) (2023)
- [DoGR: Disaggregated Gaussian Regression for Reproducible Analysis of Heterogeneous Data](https://mlsanity.com/paper/2108.13581/) (2021)
- [Conditional Linear Regression for Heterogeneous Covariances](https://mlsanity.com/paper/2111.07834/) (2021)
- [Personalized Prediction By Learning Halfspace Reference Classes Under Well-Behaved Distribution](https://mlsanity.com/paper/2509.15592/) (2025)

## Abstract (arXiv)

Work in machine learning and statistics commonly focuses on building models that capture the vast majority of data, possibly ignoring a segment of the population as outliers. However, there does not often exist a good model on the whole dataset, so we seek to find a small subset where there exists a useful model. We are interested in finding a linear rule capable of achieving more accurate predictions for just a segment of the population. We give an efficient algorithm with theoretical analysis for the conditional linear regression task, which is the joint task of identifying a significant segment of the population, described by a k-DNF, along with its linear regression fit.