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An Algorithm for Finding Minimum dSeparating Sets in Belief Networks
 Proceedings of the twelfth Conference of Uncertainty in Artificial Intelligence
, 1996
"... The criterion commonly used in directed acyclic graphs (dags) for testing graphical independence is the wellknown dseparation criterion. It allows us to build graphical representations of dependency models (usually probabilistic dependency models) in the form of belief networks, which make possibl ..."
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Cited by 14 (4 self)
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The criterion commonly used in directed acyclic graphs (dags) for testing graphical independence is the wellknown dseparation criterion. It allows us to build graphical representations of dependency models (usually probabilistic dependency models) in the form of belief networks, which make possible an easy interpretation and management of independence relationships, without reference to numerical parameters (conditional probabilities). In this paper we study the following combinatorial problem: to find the minimum dseparating set for two nodes in a dag. This set would represent the minimum information necessary to prevent these two nodes to influence each other. The solution of this basic problem and of some of its extensions can be useful in several ways, as we will see later. Our solution is based on a twosteps 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 solvi...
Characterizations of Decomposable Dependency Models
 Journal of Artificial Intelligence Research
, 1996
"... Decomposable dependency models possess a number of interesting and useful properties. This paper presents new characterizations of decomposable models in terms of independence relationships, which are obtained by adding a single axiom to the wellknown set characterizing dependency models that are i ..."
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Cited by 4 (2 self)
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Decomposable dependency models possess a number of interesting and useful properties. This paper presents new characterizations of decomposable models in terms of independence relationships, which are obtained by adding a single axiom to the wellknown set characterizing dependency models that are isomorphic to undirected graphs. We also briefly discuss a potential application of our results to the problem of learning graphical models from data. 1. Introduction Graphical models are knowledge representation tools commonly used by an increasing number of researchers, particularly from the Artificial Intelligence and Statistics communities. The reason for the success of graphical models is their capacity to represent and handle independence relationships, which have proved crucial for the efficient management and storage of information (Pearl, 1988). There are different kinds of graphical models, although we are particularly interested in undirected and directed graphs (which, in a proba...
A Universal Algebraic Approach for Conditional Indepencence
 ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS
"... In this paper we show that elementary properties of joint probability density functions naturally induce a universal algebraic structure suitable for studying probabilistic conditional independence (PCI) relations. We call this algebraic system the cain. In the cain algebra, PCI relations are repre ..."
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In this paper we show that elementary properties of joint probability density functions naturally induce a universal algebraic structure suitable for studying probabilistic conditional independence (PCI) relations. We call this algebraic system the cain. In the cain algebra, PCI relations are represented in equational forms. In particular we show that the cain satisfies the axioms of the graphoid of Pearl and Paz