Graph-in-Graph (GiG): Learning interpretable latent graphs in non-Euclidean domain for biological and healthcare applications

Graphs are a powerful tool for representing and analyzing unstructured, non-Euclidean data ubiquitous in the healthcare domain. Two prominent examples are molecule property prediction and brain connectome analysis. Importantly, recent works have shown that considering relationships between input data samples have a positive regularizing effect for the downstream task in healthcare applications. These relationships are naturally modeled by a (possibly unknown) graph structure between input samples. In this work, we propose Graph-in-Graph (GiG), a neural network architecture for protein classification and brain imaging applications that exploits the graph representation of the input data samples and their latent relation. We assume an initially unknown latent-graph structure between graph-valued input data and propose to learn end-to-end a parametric model for message passing within and across input graph samples, along with the latent structure connecting the input graphs. Further, we introduce a degree distribution loss that helps regularize the predicted latent relationships structure. This regularization can significantly improve the downstream task. Moreover, the obtained latent graph can represent patient population models or networks of molecule clusters, providing a level of interpretability and knowledge discovery in the input domain of particular value in healthcare.