Graph Mixture Density Networks

We introduce the Graph Mixture Density Network, a new family of machine learning models that can fit multimodal output distributions conditioned on arbitrary input graphs. By combining ideas from mixture models and graph representation learning, we address a broad class of challenging regression problems that rely on structured data. Our main contribution is the design and evaluation of our method on large stochastic epidemic simulations conditioned on random graphs. We show that there is a significant improvement in the likelihood of an epidemic outcome when taking into account both multimodality and structure. In addition, we investigate how to \textit{implicitly} retain structural information in node representations by computing the distance between distributions of adjacent nodes, and the technique is tested on two structure reconstruction tasks with very good accuracy. Graph Mixture Density Networks open appealing research opportunities in the study of structure-dependent phenomena that exhibit non-trivial conditional output distributions.