Bridging Fairness and Uncertainty: Theoretical Insights and Practical Strategies for Equalized Coverage in GNNs

Graph Neural Networks (GNNs) have become indispensable tools in many domains, such as social network analysis, financial fraud detection, and drug discovery. Prior research primarily concentrated on improving prediction accuracy while overlooking how reliable the model predictions are. Conformal prediction on graphs emerges as a promising solution, offering statistically sound uncertainty estimates with a pre-defined coverage level. Despite the promising progress, existing works only focus on achieving model coverage guarantees without considering fairness in the coverage within different demographic groups. To bridge the gap between conformal prediction and fair coverage across different groups, we pose the fundamental question: Can fair GNNs enable the uncertainty estimates to be fairly applied across demographic groups? To answer this question, we provide a comprehensive analysis of the uncertainty estimation in fair GNNs employing various strategies. We prove theoretically that fair GNNs can enforce consistent uncertainty bounds across different demographic groups, thereby minimizing bias in uncertainty estimates. Furthermore, we conduct extensive experiments on five commonly used datasets across seven state-of-the-art fair GNN models to validate our theoretical findings. Additionally, based on the theoretical and empirical insights, we identify and analyze the key strategies from various fair GNN models that contribute to ensuring equalized uncertainty estimates. Our work estimates a solid foundation for future exploration of the practical implications and potential adjustments needed to enhance fairness in GNN applications across various domains. For reproducibility, we publish our data and code at https://github.com/wulongfeng/EqualizedCoverage_CP.