Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Management Science
Probabilistic reasoning in expert systems: theory and algorithms
Probabilistic reasoning in expert systems: theory and algorithms
Introduction to algorithms
An algorithm for deciding if a set of observed independencies has a causal explanation
UAI '92 Proceedings of the eighth conference on Uncertainty in Artificial Intelligence
Generating all the acyclic orientations of an undirected graph
Information Processing Letters
Introduction to Bayesian Networks
Introduction to Bayesian Networks
Equivalence and synthesis of causal models
UAI '90 Proceedings of the Sixth Annual Conference on Uncertainty in Artificial Intelligence
Operations for learning with graphical models
Journal of Artificial Intelligence Research
A graphical characterization of the largest chain graphs
International Journal of Approximate Reasoning
A transformational characterization of equivalent Bayesian network structures
UAI'95 Proceedings of the Eleventh conference on Uncertainty in artificial intelligence
Causal inference and causal explanation with background knowledge
UAI'95 Proceedings of the Eleventh conference on Uncertainty in artificial intelligence
Learning equivalence classes of Bayesian network structures
UAI'96 Proceedings of the Twelfth international conference on Uncertainty in artificial intelligence
Review: learning bayesian networks: Approaches and issues
The Knowledge Engineering Review
Maximum Likelihood Estimation Over Directed Acyclic Gaussian Graphs
Statistical Analysis and Data Mining
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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.