Addressing Structural Distribution Shift in Explanations for Graph Neural Networks

Graph Neural Networks (GNNs) are essential for processing graph-structured data and have wide applications in critical domains. The increasing use of GNNs in high-stakes scenarios requires robust explainability to ensure trust and transparency in decision-making. A common approach to explaining GNNs is to identify subgraphs, a.k.a. explanations, that significantly influence model predictions. However, this task is challenging due to the distribution shifts from the original training graphs to the explanation subgraphs, a factor that is largely overlooked in the existing research. These shifts arise because GNNs are trained on original graphs, while explanation subgraphs often differ in properties such as the number of nodes or structural patterns. As a result, GNNs may struggle to generalize to explanation subgraphs with a different distribution from its training data. In this paper, we systematically investigate the Out-Of-Distribution (OOD) problem through theoretical analysis and empirical studies. To address this challenge, we first develop a theoretical framework that formalizes the notion of explanation subgraphs through sufficiency and minimality criteria, ensuring both prediction preservation and structural compactness. Our analysis reveals a fundamental distributional disparity between explanation subgraphs and original graphs, leading to a novel concept of proxy graphs proposed in this work. Proxy graphs maintain the essential explanatory information while conforming to the original data distribution through a combination of parametric and non-parametric optimization approaches. Empirical evaluations on diverse datasets show that our method improves the quality and reliability of GNN explanations, advancing the field of GNN explainability.