A Junction Tree Propagation Algorithm for Bayesian Networks with Second-Order Uncertainties

Bayesian networks (BNs) have been widely used as a model for knowledge representation and probabilistic inferences. However, the single probability representation of conditional dependencies has been proven to be over-constrained in realistic applications. Many efforts have proposed to represent the dependencies using probability intervals instead of single probabilities. In this paper, we move one step further and adopt a probability distribution schema. This results in a higher order representation of uncertainties in a BN. We formulate probabilistic inferences in this context and then propose a mean/covariance propagation algorithm based on the well-known junction tree propagation for standard BNs. For algorithm validation, we develop a two-layered Markov likelihood weighting approach that handles high-order uncertainties and provides "ground-truth" solutions to inferences, albeit very slowly. Our experiments show that the mean/covariance propagation algorithm can efficiently produce high-quality solutions that compare favorably to results obtained through painstaking sampling