A simple graphical approach for understanding probabilistic inference in Bayesian networks

We present a simple graphical method for understanding exact probabilistic inference in discrete Bayesian networks (BNs). A conditional probability table (conditional) is depicted as a directed acyclic graph involving one or more black vertices and zero or more white vertices. The probability information propagated in a network can then be graphically illustrated by introducing the black variable elimination (BVE) algorithm. We prove the correctness of BVE and establish its polynomial time complexity. Our method possesses two salient characteristics. This purely graphical approach can be used as a pedagogical tool to introduce BN inference to beginners. This is important as it is commonly stated that newcomers have difficulty learning BN inference due to intricate mathematical equations and notation. Secondly, BVE provides a more precise description of BN inference than the state-of-the-art discrete BN inference technique, called LAZY-AR. LAZY-AR propagates potentials, which are not well-defined probability distributions. Our approach only involves conditionals, a special case of potential.