The size distribution for Markov equivalence classes of acyclic digraph models

Bayesian networks, equivalently graphical Markov models determined by acyclic digraphs or ADGs (also called directed acyclic graphs or dags), have proved to be both effective and efficient for representing complex multivariate dependence structures in terms of local relations. However, model search and selection is potentially complicated by the many-to-one correspondence between ADGs and the statistical models that they represent. If the ADGs/models ratio is large, search procedures based on unique graphical representations of equivalence classes of ADGs could provide substantial computational efficiency. Hitherto, the value of the ADGs/models ratio has been calculated only for graphs with n=5 or fewer vertices. In the present study, a computer program was written to enumerate the equivalence classes of ADG models and study the distributions of class sizes and number of edges for graphs up to n=10 vertices. The ratio of ADGs to numbers of classes appears to approach an asymptote of a...

• Type: Journal
• Year: 2002
• Where: AI
• Authors: Steven B. Gillispie, Michael D. Perlman
• Keywords: AI 2002, Artificial Intelligence, Class Size, Equivalence Classes, Graphical Markov Models