Enumerating Markov Equivalence Classes of Acyclic Digraph Models

Enumerating Markov Equivalence Classes of Acyclic Digraph Models (2001)

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by Steven B. Gillispie , Michael D. Perlman

Venue:	PROC. OF THE CONF. ON UNCERTAINTY IN ARTIFICIAL INTELLIGENCE
Citations:	14 - 0 self

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Datum	Value	Source
TITLE	Enumerating Markov Equivalence Classes of Acyclic Digraph Models	user correction - Legacy Corrections
AUTHOR NAME	Steven B. Gillispie	user correction
AUTHOR AFFIL	Department of Radiology; University of Washington	user correction
AUTHOR ADDR	Box 356004; Seattle, WA 98195-6004	user correction
AUTHOR NAME	Michael D. Perlman	user correction
ABSTRACT	Graphical Markov models determined by acyclic digraphs (ADGs), also called directed acyclic graphs (DAGs), are widely studied in statistics, computer science (as Bayesian networks), operations research (as influence diagrams), and many related fields. Because different ADGs may determine the same Markov equivalence class, it long has been of interest to determine the efficiency gained in model specification and search by working directly with Markov equivalence classes of ADGs rather than with ADGs themselves. A computer program was written to enumerate the equivalence classes of ADG models as specified by Pearl & Verma's equivalence criterion. The program counted equivalence classes for models up to and including 10 vertices. The ratio of numbers of classes to ADGs appears to approach an asymptote of about 0.267. Classes were analyzed according to number of edges and class size. By edges, the distribution of number of classes approaches a Gaussian shape. By class size, classes of size 1 are most common, with the proportions for larger sizes initially decreasing but then following a more irregular pattern. The maximum number of classes generated by any undirected graph was found to increase approximately factorially. The program also includes a new variation of orderly algorithm for generating undirected graphs.	user correction - Legacy Corrections
YEAR	2001	INFERENCE
VENUE	PROC. OF THE CONF. ON UNCERTAINTY IN ARTIFICIAL INTELLIGENCE	user correction
VENUE TYPE	CONFERENCE	INFERENCE
PAGES	171--177	INFERENCE
CITATIONS	31 found	ParsCit 1.0