  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.
