  In Graph Neural Networks (GNNs), the graph structure is incorporated into the
learning of node representations. This complex structure makes explaining GNNs'
predictions become much more challenging. In this paper, we propose
PGM-Explainer, a Probabilistic Graphical Model (PGM) model-agnostic explainer
for GNNs. Given a prediction to be explained, PGM-Explainer identifies crucial
graph components and generates an explanation in form of a PGM approximating
that prediction. Different from existing explainers for GNNs where the
explanations are drawn from a set of linear functions of explained features,
PGM-Explainer is able to demonstrate the dependencies of explained features in
form of conditional probabilities. Our theoretical analysis shows that the PGM
generated by PGM-Explainer includes the Markov-blanket of the target
prediction, i.e. including all its statistical information. We also show that
the explanation returned by PGM-Explainer contains the same set of independence
statements in the perfect map. Our experiments on both synthetic and real-world
datasets show that PGM-Explainer achieves better performance than existing
explainers in many benchmark tasks.
