Abductive Reasoning in Bayesian Belief Networks Using a Genetic Algorithm

Abstract

Bayesian belief networks (causal networks) have been extensively studied in the past ten years. It has been shown that they provide a sound formalism for probabilistic reasoning, especially if uncertainty is to be represented. A probability space can be modelled as a Bayesian belief network of propositional variables (nodes) which may be pairwise connected by directed arcs. The interpretation is that if an arc exists from node A to node $B$, the probability of node $B$ assuming a given state $b_{i}$ depends on the actual state of node $A$ ( $A$ is a direct cause of $B$ ). The absence of an arc between two nodes implies that there is no such direct dependence. Thus, in a Bayesian belief network, probabilistic dependencies are modelled as arcs between nodes, independencies are implied by the absence of arcs. If for a given probability space, for all states of the root nodes the prior probabilities are known, and in addition, for all non-root nodes the conditional probabilities, given the parent states, the joint probability distribution is completely known. Textbooks on Bayesian belief networks are [1] and [2].