  Comorbid diseases co-occur and progress via complex temporal patterns that
vary among individuals. In electronic health records we can observe the
different diseases a patient has, but can only infer the temporal relationship
between each co-morbid condition. Learning such temporal patterns from event
data is crucial for understanding disease pathology and predicting prognoses.
To this end, we develop deep diffusion processes (DDP) to model "dynamic
comorbidity networks", i.e., the temporal relationships between comorbid
disease onsets expressed through a dynamic graph. A DDP comprises events
modelled as a multi-dimensional point process, with an intensity function
parameterized by the edges of a dynamic weighted graph. The graph structure is
modulated by a neural network that maps patient history to edge weights,
enabling rich temporal representations for disease trajectories. The DDP
parameters decouple into clinically meaningful components, which enables
serving the dual purpose of accurate risk prediction and intelligible
representation of disease pathology. We illustrate these features in
experiments using cancer registry data.
