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
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
Dispositional versus epistemic causality
Minds and Machines
Spatiotemporal Models for Data-Anomaly Detection in Dynamic Environmental Monitoring Campaigns
ACM Transactions on Sensor Networks (TOSN)
Review: learning bayesian networks: Approaches and issues
The Knowledge Engineering Review
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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 about 3.7. Distributions of the classes according to number of edges and class size were produced which also appear to be approaching asymptotic limits. Imposing a bound on the maximum number of parents to any vertex causes little change if the bound is sufficiently large, with four being a possible minimum. The program also includes a new variation of orderly algorithm for generating undirected graphs.