Probing GNN Explainers: A Rigorous Theoretical and Empirical Analysis of GNN Explanation Methods.

As Graph Neural Networks (GNNs) are increasingly employed in real-world applications, it becomes critical to ensure that the stakeholders understand the rationale behind their predictions. While several GNN explanation methods have been proposed recently, there has been little to no work on theoretically analyzing the behavior of these methods or systematically evaluating their effectiveness. Here, we introduce the first axiomatic framework for theoretically analyzing, evaluating, and comparing state-of-the-art GNN explanation methods. We outline and formalize the key desirable properties that all GNN explanation methods should satisfy in order to generate reliable explanations, namely, faithfulness, stability, and fairness. We leverage these properties to present the first ever theoretical analysis of the effectiveness of state-of-the-art GNN explanation methods. Our analysis establishes upper bounds on all the aforementioned properties for popular GNN explanation methods. We also leverage our framework to empirically evaluate these methods on multiple real-world datasets from diverse domains. Our empirical results demonstrate that some popular GNN explanation methods (e.g., gradient-based methods) perform no better than a random baseline and that methods which leverage the graph structure are more effective than those that solely rely on the node features.