Efficient iterative importance sampling inference for dynamic Bayesian networks

Probabilistic inference for Bayesian networks is in general computationally intensive using either exact algorithms or approximate methods. For general hybrid dynamic Bayesian networks, one has to rely on the approximate methods such as stochastic simulation to provide a solution. Sequential Monte Carlo methods, also known as particle filters, have been introduced to deal with these problems. They allow us to treat any type of probability distribution and nonlinearity although they often suffer major drawbacks of sample degeneracy and inefficiency in high-dimensional cases. This is particularly true when the dynamic networks have extremely unlikely evidence. In this paper, we introduce a very efficient importance sampling inference algorithm for discrete dynamic Bayesian network. This method is designed to iteratively learn the importance function adoptively and asymptotically. We used several partially dynamic Bayesian network models to test our inference method. The preliminary simulation results show that the algorithm is very promising.