Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Algorithmic graph theory
Causal networks: semantics and expressiveness
UAI '88 Proceedings of the Fourth Annual Conference on Uncertainty in Artificial Intelligence
Learning Bayesian networks from data: an information-theory based approach
Artificial Intelligence
Learning Right Sized Belief Networks by Means of a Hybrid Methodology
PKDD '00 Proceedings of the 4th European Conference on Principles of Data Mining and Knowledge Discovery
Using Bayesian Networks to Model Emergency Medical Services
ISMDA '01 Proceedings of the Second International Symposium on Medical Data Analysis
The Search of Causal Orderings: A Short Cut for Learning Belief Networks
ECSQARU '01 Proceedings of the 6th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
Decomposition of search for v-structures in DAGs
Journal of Multivariate Analysis
Construction of minimal d-separators in a dependency system
Cybernetics and Systems Analysis
An improved bayesian network learning algorithm based on dependency analysis
CIS'05 Proceedings of the 2005 international conference on Computational Intelligence and Security - Volume Part I
Review: learning bayesian networks: Approaches and issues
The Knowledge Engineering Review
Artificial Intelligence in Medicine
International Journal of Approximate Reasoning
Hypergraph learning with hyperedge expansion
ECML PKDD'12 Proceedings of the 2012 European conference on Machine Learning and Knowledge Discovery in Databases - Volume Part I
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The criterion commonly used in directed acyclic graphs (dags) for testing graphical independence is the well-known d-separation criterion. It allows us to build graphical representations of dependency models (usually probabilistic dependency models) in the form of belief networks, which make easy interpretation and management of independence relationships possible, without reference to numerical parameters (conditional probabilities). In this paper, we study the following combinatorial problem: finding the minimum d-separating set for two nodes in a dug. This set would represent the minimum information (in the sense of minimum number of variables) necessary to prevent these two nodes from influencing each other. The solution to this basic problem and some of its extensions can be useful in several ways, as we shall see later. Our solution is based on a two-step process: first, we reduce the original problem to the simpler one of finding a minimum separating set in an undirected graph, and second, we develop an algorithm for solving it.