Structured proportional jump processes

Learning the association between observed variables and future trajectories of continuous-time stochastic processes is a fundamental task in dynamic modeling. Often the dynamics are non-homogeneous and involve a large number of interacting components. We introduce a conditional probabilistic model that captures such dynamics, while maintaining scalability and providing an explicit way to express the interrelation between the system components. The principal idea is a factorization of the model into two distinct elements: one depends only on time and the other depends on the system configuration. We developed a learning procedure, given either full or point observations, and tested it on simulated data. We applied the proposed modeling scheme to study large cohorts of diabetes and HIV patients, and demonstrate that the factorization helps shed light on the dynamics of these diseases.