Conditional Linear Regression

TL;DR

This paper introduces an efficient algorithm for conditional linear regression, which identifies a significant population segment described by a k-DNF and fits a linear model to improve prediction accuracy within that segment.

Contribution

It presents the first efficient algorithm with theoretical guarantees for the joint task of segment identification and linear model fitting in conditional linear regression.

Findings

Algorithm effectively finds segments with accurate linear models.

Theoretical analysis guarantees performance and efficiency.

Applicable to various data distributions and segment complexities.

Abstract

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.