  Algorithmic fairness has received increased attention in socially sensitive
domains. While rich literature on mean fairness has been established, research
on quantile fairness remains sparse but vital. To fulfill great needs and
advocate the significance of quantile fairness, we propose a novel framework to
learn a real-valued quantile function under the fairness requirement of
Demographic Parity with respect to sensitive attributes, such as race or
gender, and thereby derive a reliable fair prediction interval. Using optimal
transport and functional synchronization techniques, we establish theoretical
guarantees of distribution-free coverage and exact fairness for the induced
prediction interval constructed by fair quantiles. A hands-on pipeline is
provided to incorporate flexible quantile regressions with an efficient
fairness adjustment post-processing algorithm. We demonstrate the superior
empirical performance of this approach on several benchmark datasets. Our
results show the model's ability to uncover the mechanism underlying the
fairness-accuracy trade-off in a wide range of societal and medical
applications.
