Research on modeling with dynamic Bayesian networks

For simplicity of calculation, dynamic Bayesian networks (DBNs) make assumptions that their evolvement follows Markov process and the transition probabilities in the evolvement are time-invariant. While this is not the case in many real complex systems. For the purpose of modeling these complex systems with DBNs, we attempt to add hidden variables to the evolutional process so as to build Markov models and expand the EM-EA algorithm to the DBNs learning in the presence of hidden variables. Moreover, as for the time-variant transition probabilities, we estimate the suffcient statistics of posterior time slices using polynomial fitting algorithm, and then learns the time-variant transition probabilities with both current sufficient statistics and estimated sufficient statistics. The theoretical analysis demonstrates the validity of the methods. The future work is to do experimental analysis with real complex systems.