*Continuous-time Bayesian networks* is a natural structured
representation language for multi-component 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 real-world inference problem.

nir@cs.huji.ac.il