Learning Fair Graph Representations via Probability of Necessity and Sufficiency

Graph Neural Networks (GNNs) excel at modeling graph data but often amplify biases tied to sensitive attributes like gender and race. Existing causality-based methods use isolated interventions on graph topology or features, yet struggle to produce representations that balance predictive power with fairness. This leads to two issues: (1) weak predictive power, where representations miss critical task-relevant features, and (2) bias amplification, where representations encode sensitive attributes, causing unfair outcomes. To address these issues, we introduce the Probability of Necessity and Sufficiency (PNS), where necessity ensures representations capture only essential features for predictions, and sufficiency guarantees these features are adequate without relying on sensitive attributes. We propose FairSNR, a fairness-aware graph representation learning framework that introduces constraints based on the PNS. Specifically, FairSNR leverages PNS to guide the learning of fair representations from graph data. In particular, FairSNR employs an encoder to learn node representations with high PNS for downstream tasks. To compute and optimize PNS, FairSNR introduces an intervenor that learns to generate the most challenging counterfactual interventions on the representations, thereby enhancing the model’s causal stability even under worst-case scenarios. Finally, a discriminator is trained to detect and mitigate sensitive information leakage in the learned representations, effectively disentangling sensitive biases from task-relevant features. Experiments on real-world graph datasets demonstrate that FairSNR outperforms existing state-of-the-art (SOTA) methods in both fairness and utility.