An Algorithm for Finding Minimum dSeparating Sets in Belief Networks
Silvia Acid, Luis de Campos
Abstract:
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 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 dseparating set for two nodes in a dag. 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 twostep 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.
Keywords: Belief networks, dseparation criterion.
Pages: 310
PS Link: ftp://decsai.ugr.es/pub/utai/other/acid/minim_cut.ps.Z
PDF Link: /papers/96/p3acid.pdf
BibTex:
@INPROCEEDINGS{Acid96,
AUTHOR = "Silvia Acid
and Luis de Campos",
TITLE = "An Algorithm for Finding Minimum dSeparating Sets in Belief Networks",
BOOKTITLE = "Proceedings of the Twelfth Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI96)",
PUBLISHER = "Morgan Kaufmann",
ADDRESS = "San Francisco, CA",
YEAR = "1996",
PAGES = "310"
}

