Equivalent characterization of a class of conditional probabilistic independencies

Abstract

Markov networks utilize nonembedded probabilistic conditional independencies in order to provide an economical representation of a joint distribution in uncertainty management. In this paper we study several properties of nonembedded conditional independencies and show that they are in fact equivalent. The results presented here not only show the useful characteristics of an important subclass of probabilistic conditional independencies, but further demonstrate the relationship between relational theory and probabilistic reasoning.