Mean field variational approximation for continuous-time Bayesian networks

Continuous-time Bayesian networks is a natural structured representation language for multicomponent stochastic processes that evolve continuously over time. Despite the compact representation provided by this language, inference in such models is intractable even in relatively simple structured networks. We introduce a mean field variational approximation in which we use a product of inhomogeneous Markov processes to approximate a joint 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. Here we describe 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.