Indirect Causes in Dynamic Bayesian Networks Revisited

Modeling causal dependencies often demands cycles at a coarse-grained temporal scale. If Bayesian networks are to be used for modeling uncertainties, cycles are eliminated with dynamic Bayesian networks, spreading indirect dependencies over time and enforcing an infinitesimal resolution of time. Without a ``causal design,'' i.e., without anticipating indirect influences appropriately in time, we argue that such networks return spurious results. By identifying activator random variables, we propose activator dynamic Bayesian networks (ADBNs) which are able to rapidly adapt to contexts under a causal use of time, anticipating indirect influences on a solid mathematical basis using familiar Bayesian network semantics. ADBNs are well-defined dynamic probabilistic graphical models allowing one to model cyclic dependencies from local and causal perspectives while preserving a classical, familiar calculus and classically known algorithms, without introducing any overhead in modeling or inference.