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 overconstrained 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 [1]. 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.