Unsupervised Hierarchical Graph Representation Learning with Variational Bayes

Hierarchical graph representation learning is an emerging subject owing to the increasingly popular adoption of graph neural networks in machine learning and applications. Loosely speaking, work under this umbrella falls into two categories: (a) use a predefined graph hierarchy to perform pooling; and (b) learn the hierarchy for a given graph through differentiable parameterization of the coarsening process. These approaches are supervised; a predictive task with ground-truth labels is used to drive the learning. In this work, we propose an unsupervised approach, \textsc{BayesPool}, with the use of variational Bayes. It produces graph representations given a predefined hierarchy. Rather than relying on labels, the training signal comes from the evidence lower bound of encoding a graph and decoding the subsequent one in the hierarchy. Node features are treated latent in this variational machinery, so that they are produced as a byproduct and are used in downstream tasks. We demonstrate a comprehensive set of experiments to show the usefulness of the learned representation in the context of graph classification.