Fairness-aware Bayes optimal functional classification
Xiaoyu Hu, Gengyu Xue, Zhenhua Lin, Yi Yu
TL;DR
This work addresses fairness-aware binary classification for functional data by leveraging the Radon-Nikodym derivative to derive a δ-fair Bayes-optimal rule via a generalized Neyman–Pearson framework. It introduces Fair-FLDA for Gaussian-process features, providing a plug-in estimator with a calibration variant to guarantee probabilistic disparity control and finite-sample fairness and excess-risk guarantees. The approach recovers standard FLDA as a special case and is validated through simulations and a NHANES real-data application, demonstrating effective disparity control with competitive predictive performance. Overall, it offers a rigorous framework for fairness-aware FDA in infinite-dimensional spaces and a practical, post-processing method for Gaussian-process functional data.
Abstract
Algorithmic fairness has become a central topic in machine learning, and mitigating disparities across different subpopulations has emerged as a rapidly growing research area. In this paper, we systematically study the classification of functional data under fairness constraints, ensuring the disparity level of the classifier is controlled below a pre-specified threshold. We propose a unified framework for fairness-aware functional classification, tackling an infinite-dimensional functional space, addressing key challenges from the absence of density ratios and intractability of posterior probabilities, and discussing unique phenomena in functional classification. We further design a post-processing algorithm, Fair Functional Linear Discriminant Analysis classifier (Fair-FLDA), which targets at homoscedastic Gaussian processes and achieves fairness via group-wise thresholding. Under weak structural assumptions on eigenspace, theoretical guarantees on fairness and excess risk controls are established. As a byproduct, our results cover the excess risk control of the standard FLDA as a special case, which, to the best of our knowledge, is first time seen. Our theoretical findings are complemented by extensive numerical experiments on synthetic and real datasets, highlighting the practicality of our designed algorithm.