Bayesian Belief Networks for Data Mining

In this paper we present a novel constraint based structural learning algorithm for causal networks. A set of conditional independence and dependence statements (CIDS) is derived from the data which describes the relationships among the variables. Although we implicitly assume that there exists a perfect map for the true, yet unknown, distribution , there does not need to be a perfect map for the CIDSs derived from the limited data. The reason is that the distribution of limited data might diier from the true probability distribution due to sampling noise. We derive a necessary condition for the existence of a perfect map given a set of CIDSs and utilize it to check for inconsistencies. If an inconsistency is detected, the algorithm nds all Bayesian networks with a minimum number of edges such that a maximum number of CIDSs is represented in each of the multiple solutions. The advantages of our approach are illustrated using the alarm network data set.