A Graph-Based Inference Method for Conditional Independence
This provides a purely graphical proof technique for conditional independence, which is incremental as it builds on existing graphoid axioms without introducing new methods or broad applications.
The paper tackles the problem of proving conditional independence statements by introducing a graphical representation using multiple undirected graphs and transformations, showing that it is equivalent to the graphoid axioms without relying on numerical definitions.
The graphoid axioms for conditional independence, originally described by Dawid [1979], are fundamental to probabilistic reasoning [Pearl, 19881. Such axioms provide a mechanism for manipulating conditional independence assertions without resorting to their numerical definition. This paper explores a representation for independence statements using multiple undirected graphs and some simple graphical transformations. The independence statements derivable in this system are equivalent to those obtainable by the graphoid axioms. Therefore, this is a purely graphical proof technique for conditional independence.