  Continuous-time Bayesian networks is a natural structured representation
language for multicomponent stochastic processes that evolve continuously over
time. Despite the compact representation, inference in such models is
intractable even in relatively simple structured networks. Here we introduce a
mean field variational approximation in which we use a product of inhomogeneous
Markov processes to approximate a distribution over trajectories. This
variational approach leads to a globally consistent distribution, which can be
efficiently queried. Additionally, it provides a lower bound on the probability
of observations, thus making it attractive for learning tasks. We provide the
theoretical foundations for the approximation, an efficient implementation that
exploits the wide range of highly optimized ordinary differential equations
(ODE) solvers, experimentally explore characterizations of processes for which
this approximation is suitable, and show applications to a large-scale
realworld inference problem.
