In this paper we consider conditional independence models closed under graphoid properties. We investigate their representation by means of acyclic directed graphs (DAG). A new algorithm to build a DAG, given an ordering among random variables, is described and peculiarities and advantages of this approach are discussed. Finally, some properties ensuring the existence of perfect maps are provided. These conditions can be used to define a procedure able to find a perfect map for some classes of independence models. © 2009 Springer Berlin Heidelberg.
Acyclic directed graphs to represent conditional independence models / Marco, Baioletti; Busanello, Giuseppe; Vantaggi, Barbara. - STAMPA. - 5590 LNAI(2009), pp. 530-541. ((Intervento presentato al convegno 10th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty, ECSQARU 2009 tenutosi a Verona nel 1 July 2009 through 3 July 2009. - LECTURE NOTES IN COMPUTER SCIENCE. [10.1007/978-3-642-02906-6_46].