Using Score-based Structure Learning to Computationally Learn Direct Influence between Hierarchical Dynamic Bayesian Networks

Numerous fields of science have investigated stochastic processes which are partially observable. However, the discovery and analysis of the interaction between, and the influence upon each other, of several of these processes, have not been probed extensively. This paper uses probabilistic structure learning in an attempt to learn influence relationships between stochastic processes that are partially observed. These processes are represented by hierarchical dynamic Bayesian networks (HDBNs). To track the direct influence between the these processes, we provide an algorithm that extends the BIC structure score as well as the cumbersome (greedy hill-climbing) local search procedure. Our method leverages the temporal nature of the HDBN through the use of assembles thereby surpassing the standard approach that treats each process as a single variable. The derived BIC-score for HDBN families is clearly shown to be theoretically decomposable and empirically consistent.