Almost instant time inference for hybrid partially dynamic Bayesian networks

A Bayesian network (BN) is a compact representation for probabilistic models and inference. They have been used successfully for many military and civilian applications. It is well known that, in general, the inference algorithms to compute the exact a posterior probability of a target node given observed evidence are either computationally infeasible for dense networks or impossible for general hybrid networks. In those cases, one either computes the approximate results using stochastic simulation methods or approximates the model using discretization or a Gaussian mixture model before applying an exact inference algorithm. This paper combines the concept of simulation and model approximation to propose an efficient algorithm for those cases. The main contribution here is a unified treatment of arbitrary (nonlinear non-Gaussian) hybrid (discrete and continuous) BN inference having both computation and accuracy scalability. The key idea is to precompile the high-dimensional hybrid distribution using a hypercube representation and apply it for both static and dynamic BN inference. Since the inference process essentially becomes a combination of table look-up and some simple operations, the method is shown to be extremely efficient. It can also he scaled to achieve any desirable accuracy given sufficient preprocessing time and memory for the cases where exact inference is not possible