Fair quantile regression

TL;DR

This paper addresses fairness in quantile regression when protected attributes are unavailable during model fitting, proposing an adjustment method that balances quantile estimates across subpopulations, validated on a large birth dataset.

Contribution

It introduces a novel adjustment procedure for fair quantile regression that ensures balanced estimates across protected groups, supported by empirical process analysis.

Findings

The adjustment improves fairness in quantile estimates across subpopulations.

The method achieves $\

The approach is validated on a large dataset of 200,000 births, demonstrating practical effectiveness.

Abstract

Quantile regression is a tool for learning conditional distributions. In this paper we study quantile regression in the setting where a protected attribute is unavailable when fitting the model. This can lead to "unfair'' quantile estimators for which the effective quantiles are very different for the subpopulations defined by the protected attribute. We propose a procedure for adjusting the estimator on a heldout sample where the protected attribute is available. The main result of the paper is an empirical process analysis showing that the adjustment leads to a fair estimator for which the target quantiles are brought into balance, in a statistical sense that we call $\sqrt{n}$-fairness. We illustrate the ideas and adjustment procedure on a dataset of 200,000 live births, where the objective is to characterize the dependence of the birth weights of the babies on demographic attributes of the birth mother; the protected attribute is the mother's race.