We study core-set construction algorithms for the task of Diversity Maximization under fairness/partition constraint.

The widespread deployment of Graph Neural Networks (GNNs) sparks significant interest in their explainability, which plays a vital role in model auditing and ensuring trustworthy graph learning. The objective of GNN explainability is to discern the underlying graph structures that have the most significant impact on model predictions. Ensuring that explanations generated are reliable necessitates consideration of the in-distribution property, particularly due to the vulnerability of GNNs to out-of-distribution data. Unfortunately, prevailing explainability methods tend to constrain the generated explanations to the structure of the original graph, thereby downplaying the significance of the in-distribution property and resulting in explanations that lack reliability. To address these challenges, we propose D4Explainer, a novel approach that provides in-distribution GNN explanations for both counterfactual and model-level explanation scenarios. The proposed D4Explainer incorporates generative graph distribution learning into the optimization objective, which accomplishes two goals: 1) generate a collection of diverse counterfactual graphs that conform to the in-distribution property for a given instance, and 2) identify the most discriminative graph patterns that contribute to a specific class prediction, thus serving as model-level explanations. It is worth mentioning that D4Explainer is the first unified framework that combines both counterfactual and model-level explanations. Empirical evaluations conducted on synthetic and real-world datasets provide compelling evidence of the state-ofthe-art performance achieved by D4Explainer in terms of explanation accuracy, faithfulness, diversity, and robustness.