Unfaithful distributions with respect to Bayesian networks
Yan Wu · Caai Transactions on Intelligent Systems · 2009
Bayesian networks are a marriage between probability theory and graph theory,and thus are probabilistic graphical models. They are mainly used for statistical inference and intelligent data analysis. It is usually supposed that the network retains the d-separation criterion that characterize graph structure from the independence constraints based on distribution,that is,the distribution is a faithful distribution with respect to a Bayesian network. In this paper,some unfaithful distributions are characterized with respect to discrete Bayesian networks in a Boolean domain. It was shown that distributions trivially expanded from faithfulness or unfaithfulness are unfaithful distributions with respect to Bayesian networks.