Graph Neural Networks (GNNs) have been a powerful tool for node classification tasks in complex networks. However, their decision-making processes remain a black-box to users, making it challenging to understand the reasoning behind their predictions. Counterfactual explanations (CFE) have shown promise in enhancing the interpretability of machine learning models. Prior approaches to compute CFE for GNNS often are learning-based approaches that require training additional graphs. In this paper, we propose a semivalue-based, non-learning approach to generate CFE for node classification tasks, eliminating the need for any additional training. Our results reveals that computing Banzhaf values requires lower sample complexity in identifying the counterfactual explanations compared to other popular methods such as computing Shapley values. Our empirical evidence indicates computing Banzhaf values can achieve up to a fourfold speed up compared to Shapley values. We also design a thresholding method for computing Banzhaf values and show theoretical and empirical results on its robustness in noisy environments, making it superior to Shapley values. Furthermore, the thresholded Banzhaf values are shown to enhance efficiency without compromising the quality (i.e., fidelity) in the explanations in three popular graph datasets.
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