The Maximum Minimum Parents and Children Algorithm

Abstract: Given a random sample from a multivariate probability distribution p, the maximum minimum parents and children algorithm locates the skeleton of the directed acyclic graph of a Bayesian network for p provided that there exists a faithful Bayesian network and that the dependence structure derived from data is the same as that of the underlying probability distribution. The aim of this thesis is to examine the consequences when one of these conditions is not fulfilled. There are some circumstances where the algorithm works well even if there does not exist a faithful Bayesian network, but there are others where the algorithm fails. The MMPC tests for conditional independence between the variables and assumes that if conditional independence is not rejected, then the conditional independence statement holds. There are situations where this procedure leads to conditional independence being accepted that contradict conditional dependence relations in the data. This leads to edges being removed from the skeleton that are necessary for representing the dependence structure of the data.