Fairness-aware Bayes optimal functional classification

2025-05-14

AI Summary

This paper addresses algorithmic fairness in functional data classification, aiming to bound predictive disparity across subpopulations within a pre-specified threshold. To this end, we establish the first theoretical framework that unifies fairness constraints with Bayes optimality in infinite-dimensional function spaces. We propose Fair-FLDA, a post-processing algorithm for functional linear discriminant analysis (FLDA), which achieves risk control via group-adaptive thresholding and feature-space regularization—yielding the first fairness-guaranteed variant of FLDA. Leveraging homoscedastic Gaussian process modeling and infinite-dimensional statistical inference, we prove that Fair-FLDA attains the optimal convergence rate under fairness constraints; its excess risk bound exhibits explicit dependence on key parameters and naturally recovers standard FLDA as a special case. Empirical evaluation on synthetic and real-world functional datasets confirms its effectiveness.

Technology Category

• Machine Learning: Ethics, Bias, and Fairness
• Game Theory and Economic Paradigms: Fair Division
• Computer Vision: Bias, Fairness & Privacy

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Social Networks and Social Media: Fairness and bias in social network and social media analysis
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

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.

Problem

• Classify functional data under fairness constraints
• Address challenges in infinite-dimensional functional space
• Ensure fairness and risk control in classification

Innovation

• Fairness-aware functional classification framework
• Fair-FLDA algorithm with group-wise thresholding
• Theoretical guarantees on fairness and risk