Valid, sparse, and stable explanations in graph neural networks

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With the ever-increasing popularity and applications of graph neural networks, several proposals have been made to explain and understand the decisions of a graph neural network. Explanations for graph neural networks differ in principle from other input settings. It is important to attribute the decision to input features and other related instances connected by the graph structure. We find that the previous explanation generation approaches that maximize the mutual information between the label distribution produced by the model and the explanation to be restrictive. Specifically, existing approaches do not enforce explanations to be valid, sparse, or robust to input perturbations. In this paper, we lay down some of the fundamental principles that an explanation method for graph neural networks should follow and introduce a metric RDT-Fidelity as a measure of the explanation's effectiveness. We propose a novel approach Zorro based on the principles from rate-distortion theory that uses a simple combinatorial procedure to optimize for RDT-Fidelity. Extensive experiments on real and synthetic datasets reveal that Zorro produces sparser, stable, and more faithful explanations than existing graph neural network explanation approaches.