  Graph neural networks are increasingly becoming the framework of choice for
graph-based machine learning. In this paper, we propose a new graph neural
network architecture that substitutes classical message passing with an
analysis of the local distribution of node features. To this end, we extract
the distribution of features in the egonet for each local neighbourhood and
compare them against a set of learned label distributions by taking the
histogram intersection kernel. The similarity information is then propagated to
other nodes in the network, effectively creating a message passing-like
mechanism where the message is determined by the ensemble of the features. We
perform an ablation study to evaluate the network's performance under different
choices of its hyper-parameters. Finally, we test our model on standard graph
classification and regression benchmarks, and we find that it outperforms
widely used alternative approaches, including both graph kernels and graph
neural networks.
