On Regularization for Explaining Graph Neural Networks: An Information Theory Perspective

This work studies the explainability of graph neural networks (GNNs), which is important for the credibility of GNNs in practical usage. Existing mask-based explanation methods mostly follow the two-phase paradigm to interpret a prediction:
feature attribution
and
selection
. However, another important component — regularization, which is crucial to facilitate the above paradigm-has been seldom studied. Regularization is pivotal in mask-based methods, serving to refine explanatory subgraphs through constraints imposed on mask values. Hence, in this work, we endevour to explore the role of regularization in GNNs explainability. As theoretical groundwork inspired by Graph Information Bottleneck (GIB), we first introduce an innovative principle, GIB tailored for explainability, termed GIBE. GIBE serves to consolidate existing mask-based explanation methods by establishing a unified optimization objective for both feature attribution and selection processes. Then, based on GIBE, our main findings can be summarized as: 1) regularization is essentially pursuing the balance between two phases, 2) its optimal coefficient is proportional to the sparsity of explanations, 3) existing methods imply an implicit regularization effect of stochastic mechanism, and 4) its contradictory effects on two phases are responsible for the out-of-distribution (OOD) issue in post-hoc explainability. Based on these findings, we propose two common optimization methods, which can bolster the performance of the current explanation methods via sparsity-adaptive and OOD-resistant regularization schemes. Extensive empirical studies validate our findings and proposed methods.