Independence Decomposition in Dynamic Bayesian Networks

Dynamic Bayesian networks are a special type of Bayesian network that explicitly incorporate the dimension of time. They can be distinguished into repetitive and non-repetitive networks. Repetitiveness implies that the set of random variables of the network and their independence relations are the same at each time step. Due to their structural symmetry, repetitive networks are easier to use and are, therefore, often taken as the standard. However, repetitiveness is a very strong assumption, which normally does not hold, as particular dependences and independences may only hold at certain time steps. In this paper, we propose a new framework for independence modularisation in dynamic Bayesian networks. Our theory provides a method for separating atemporal and temporal independence relations, and offers a practical approach to building dynamic Bayesian networks that are possibly non-repetitive. A composition operator for temporal and atemporal independence relations is proposed and its properties are studied. Experimental results obtained by learning dynamic Bayesian networks from real data show that this framework offers a more accurate way for knowledge representation in dynamic Bayesian networks.