Mean Field Variational Approximation for Continuous-Time Bayesian Networks
arXiv:1205.2655
Abstract
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.
Appears in Proceedings of the Twenty-Fifth Conference on Uncertainty in Artificial Intelligence (UAI2009)
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- Particle Gibbs algorithms for Markov jump processes
- Variational inequalities and mean-field approximations for partially observed systems of queueing networks