Separable and transitive graphoids
This work addresses foundational issues in probabilistic reasoning for AI and expert systems, but it appears incremental as it builds on existing graphoid theory.
The paper tackles the problem of defining and relating three probabilistic formulations of 'total unrelatedness' between variables, showing their relevance to acquiring probabilistic knowledge from human experts.
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.