A Simple Latent Variable Model for Graph Learning and Inference

We introduce a probabilistic latent variable model for graphs that generalizes both the established graphon and stochastic block models. This naive histogram AHK model is simple and versatile, and we demonstrate its use for disparate tasks including complex predictive inference usually not supported by other approaches, and graph generation. We analyze the tradeoffs entailed by the simplicity of the model, which imposes certain limitations on expressivity on the one hand, but on the other hand leads to robust generalization capabilities to graph sizes different from what was seen in the training data.