Structured Proportional Jump Processes
Abstract
Learning the association between observed
variables and future trajectories of continuoustime
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.