Fair quantile regression
This addresses fairness in quantile regression for applications like healthcare, but it is incremental as it builds on existing methods with a specific adjustment.
The paper tackles the problem of unfair quantile regression when a protected attribute is unavailable during model fitting, proposing an adjustment procedure on a heldout sample to achieve fairness. The result is a fair estimator that balances target quantiles, demonstrated on a dataset of 200,000 live births to characterize birth weight dependence on demographic attributes.
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.