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Graph neural networks (GNNs) find applications in various domains such as computational biology, natural language processing, and computer security. Owing to their popularity, there is an increasing need to explain GNN predictions since GNNs are black-box machine learning models. One way to address this issue involves usingcounterfactualreasoning where the objective is to alter the GNN prediction by minimal changes in the input graph. Existing methods for counterfactual explanation of GNNs are limited to instance-specificlocalreasoning. This approach has two major limitations of not being able to offer global recourse policies and overloading human cognitive ability with too much information. In this work, we study theglobalexplainability of GNNs through global counterfactual reasoning. Specifically, we want to find asmallset of representative counterfactual graphs that explainsallinput graphs. Toward this goal, we proposeGCFExplainer, a novel algorithm powered byvertex-reinforced random walkson anedit mapof graphs with agreedy summary. Extensive experiments on real graph datasets show that the global explanation fromGCFExplainerprovides important high-level insights of the model behavior and achieves a46.9%gain in recourse coverage, a9.5%reduction in recourse cost compared to the state-of-the-art local counterfactual explainers. We also demonstrate thatGCFExplainergenerates explanations that are more consistent with input dataset characteristics, and is robust under adversarial attacks. In addition,K-GCFExplainer, which incorporates a graph clustering component intoGCFExplainer, is introduced as a more competitive extension for datasets with a clustering structure, leading to superior performance in three out of four datasets in the experiments and better scalability. 

Link prediction is a fundamental problem in graph data. In its most realistic setting, the problem consists of predicting missing or future links between random pairs of nodes from the set of disconnected pairs. Graph Neural Networks (GNNs) have become the predominant framework for link prediction. GNN-based methods treat link prediction as a binary classification problem and handle the extreme class imbalance---real graphs are very sparse---by sampling (uniformly at random) a balanced number of disconnected pairs not only for training but also for evaluation. However, we show that the reported performance of GNNs for link prediction in the balanced setting does not translate to the more realistic imbalanced setting and that simpler topology-based approaches are often better at handling sparsity. These findings motivate Gelato, a similarity-based link-prediction method that applies (1) graph learning based on node attributes to enhance a topological heuristic, (2) a ranking loss for addressing class imbalance, and (3) a negative sampling scheme that efficiently selects hard training pairs via graph partitioning. Experiments show that Gelato outperforms existing GNN-based alternatives. 

Counterfactual explanations of Graph Neural Networks (GNNs) offer a powerful way to understand data that can naturally be represented by a graph structure. Furthermore, in many domains, it is highly desirable to derive data-driven global explanations or rules that can better explain the high-level properties of the models and data in question. However, evaluating global counterfactual explanations is hard in real-world datasets due to a lack of human-annotated ground truth, which limits their use in areas like molecular sciences. Additionally, the increasing scale of these datasets provides a challenge for random search-based methods. In this paper, we develop a novel global explanation model RLHEX for molecular property prediction. It aligns the counterfactual explanations with humandefined principles, making the explanations more interpretable and easy for experts to evaluate. RLHEX includes a VAE-based graph generator to generate global explanations and an adapter to adjust the latent representation space to human-defined principles. Optimized by Proximal Policy Optimization (PPO), the global explanations produced by RLHEX cover 4.12% more input graphs and reduce the distance between the counterfactual explanation set and the input set by 0.47% on average across three molecular datasets. RLHEX provides a flexible framework to incorporate different human-designed principles into the counterfactual explanation generation process, aligning these explanations with domain expertise. The code and data are released at https://github.com/dqwang122/RLHEX.