Mean Field Variational Approximation for Continuous-Time Bayesian Networks
This addresses inference challenges for researchers and practitioners working with multicomponent stochastic processes in fields like systems biology or finance, though it is an incremental improvement based on existing variational methods.
The paper tackles the intractability of inference in continuous-time Bayesian networks by introducing a mean field variational approximation using a product of inhomogeneous Markov processes, which leads to a globally consistent distribution that can be efficiently queried and provides a lower bound for learning tasks.
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.