On the Modularisation of Independence in Dynamic Bayesian Networks

Dynamic Bayesian networks are Bayesian networks which explicitly incorporating the dimension of time. They are distinguished into repetitive and non-repetitive networks. Repetitive networks have the same set of random (statistical) variables and independence relations at each time step, whereas in non-repetitive networks the set of random variables and the independence relations between these random variables may vary in time. Due to their structural symmetry, repetitive networks are easier to use and are, therefore, often considered as the standard dynamic Bayesian networks. However, repetitiveness is a very strong assumption, which usually does not hold, because dependences and independences that only hold at certain time steps may be lost. In this paper, we propose a new framework for the modularisation of non-repetitive dynamic Bayesian networks, which offers a practical approach to coping with the computational and structural difficulties associated with unrestricted dynamic Bayesian networks. This framework is based on separating temporal and atemporal independence relations in the model. We investigate properties of the modularisation and show to be compositive.