Despite recent progress in Graph Neural Networks (GNNs), explaining predictions made by GNNs remains a challenging open problem. The leading method mainly addresses the local explanations (i.e., important subgraph structure and node features) to interpret why a GNN model makes the prediction for a single instance, e.g. a node or a graph. As a result, the explanation generated is painstakingly customized for each instance. The unique explanation interpreting each instance independently is not sufficient to provide a global understanding of the learned GNN model, leading to the lack of generalizability and hindering it from being used in the inductive setting. Besides, as it is designed for explaining a single instance, it is challenging to explain a set of instances naturally (e.g., graphs of a given class). In this study, we address these key challenges and propose PGExplainer, a parameterized explainer for GNNs. PGExplainer adopts a deep neural network to parameterize the generation process of explanations, which enables PGExplainer a natural approach to multi-instance explanations. Compared to the existing work, PGExplainer has a better generalization power and can be utilized in an inductive setting easily. Experiments on both synthetic and real-life datasets show highly competitive performance with up to 24.7\% relative improvement in AUC on explaining graph classification over the leading baseline.

Weaknesses: The work has a certain tendency to misrepresent the literature for the sake of highlighting the originality and impact of this paper. I do not particularly appreciate this type of approach to a scientific paper. More specifically, I strongly invite the Authors to reconsider the following aspects: - Multi-instance Vs Single-Instance: much of the introduction and motivation of the paper is devoted to stating that multi-instance interpretability is the only desired interpretation one would like to have. This is false, if only for a very practical aspect: general data protection regulations require the right of explanation on the "single" prediction. The one that pertains the single individual and the single decision that has been automatically taken by a computational model. Than is single instance explainability and it is very important to develop methodologies and methods for it.

The authors agree that the paper addresses an important problem and provides really strong empirical results. There was some discussion regarding the novelty of the approach; given that this is a crowded area, the reviewers strongly encourage the authors to clarify and appropriately place the proposed ideas amongst the related work. Additionally, the reviewers ask the authors to ensure reproducibility of the work, and avoid the characterization of their work as "global explanations".

Despite recent progress in Graph Neural Networks (GNNs), explaining predictions made by GNNs remains a challenging open problem. The leading method mainly addresses the local explanations (i.e., important subgraph structure and node features) to interpret why a GNN model makes the prediction for a single instance, e.g. a node or a graph. As a result, the explanation generated is painstakingly customized for each instance. The unique explanation interpreting each instance independently is not sufficient to provide a global understanding of the learned GNN model, leading to the lack of generalizability and hindering it from being used in the inductive setting. Besides, as it is designed for explaining a single instance, it is challenging to explain a set of instances naturally (e.g., graphs of a given class).