Separable and transitive graphoids
Dan Geiger, David Heckerman
We examine three probabilistic formulations of the sentence a and b are totally unrelated with respect to a given set of variables U. First, two variables a and b are totally independent if they are independent given any value of any subset of the variables in U. Second, two variables are totally uncoupled if U can be partitioned into two marginally independent sets containing a and b respectively. Third, two variables are totally disconnected if the corresponding nodes are disconnected in every belief network representation. We explore the relationship between these three formulations of unrelatedness and explain their relevance to the process of acquiring probabilistic knowledge from human experts.
PDF Link: /papers/90/p538-geiger.pdf
AUTHOR = "Dan Geiger
and David Heckerman",
TITLE = "Separable and transitive graphoids",
BOOKTITLE = "Proceedings of the Sixth Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI-90)",
PUBLISHER = "AUAI Press",
ADDRESS = "Corvallis, Oregon",
YEAR = "1990",
PAGES = "538--545"