Promoting Fairness in GNNs: A Characterization of Stability

The Lipschitz bound, a technique from robust statistics, can limit the maximum changes in the output concerning the input, taking into account associated irrelevant biased factors. It is an efficient and provable method for examining the output stability of machine learning models without incurring additional computation costs. Recently, Graph Neural Networks (GNNs), which operate on non-Euclidean data, have gained significant attention. However, no previous research has investigated the GNN Lipschitz bounds to shed light on stabilizing model outputs, especially when working on non-Euclidean data with inherent biases. Given the inherent biases in common graph data used for GNN training, it poses a serious challenge to constraining the GNN output perturbations induced by input biases, thereby safeguarding fairness during training. Recently, despite the Lipschitz constant's use in controlling the stability of Euclideanneural networks, the calculation of the precise Lipschitz constant remains elusive for non-Euclidean neural networks like GNNs, especially within fairness contexts. To narrow this gap, we begin with the general GNNs operating on an attributed graph, and formulate a Lipschitz bound to limit the changes in the output regarding biases associated with the input. Additionally, we theoretically analyze how the Lipschitz constant of a GNN model could constrain the output perturbations induced by biases learned from data for fairness training. We experimentally validate the Lipschitz bound's effectiveness in limiting biases of the model output. Finally, from a training dynamics perspective, we demonstrate why the theoretical Lipschitz bound can effectively guide the GNN training to better trade-off between accuracy and fairness.