Characterizations of Decomposable Dependency Models

Decomposable dependency models possess a number of interesting and useful properties. This paper presents new characterizations of decomposable models in terms of independence relationships, which are obtained by adding a single axiom to the well-known set characterizing dependency models that are isomorphic to undirected graphs. We also briefly discuss a potential application of our results to the problem of learning graphical models from data. 1. Introduction Graphical models are knowledge representation tools commonly used by an increasing number of researchers, particularly from the Artificial Intelligence and Statistics communities. The reason for the success of graphical models is their capacity to represent and handle independence relationships, which have proved crucial for the efficient management and storage of information (Pearl, 1988). There are different kinds of graphical models, although we are particularly interested in undirected and directed graphs (which, in a proba..