  Graph-based anomaly detection finds numerous applications in the real-world.
Thus, there exists extensive literature on the topic that has recently shifted
toward deep detection models due to advances in deep learning and graph neural
networks (GNNs). A vast majority of prior work focuses on detecting
node/edge/subgraph anomalies within a single graph, with much less work on
graph-level anomaly detection in a graph database. This work aims to fill two
gaps in the literature: We (1) design GLAM, an end-to-end graph-level anomaly
detection model based on GNNs, and (2) focus on unsupervised model selection,
which is notoriously hard due to lack of any labels, yet especially critical
for deep NN based models with a long list of hyper-parameters. Further, we
propose a new pooling strategy for graph-level embedding, called MMD-pooling,
that is geared toward detecting distribution anomalies which has not been
considered before. Through extensive experiments on 15 real-world datasets, we
show that (i) GLAM outperforms node-level and two-stage (i.e. not end-to-end)
baselines, and (ii) model selection picks a significantly more effective model
than expectation (i.e. average) -- without using any labels -- among candidates
with otherwise large variation in performance.
