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A Note on Equivalence Classes of Directed Acyclic Independence Graphs

Madigan, David B.

Directed acyclic independence graphs (DAIGs) play an important role in recent developments in probabilistic expert systems and influence diagrams (Chyu [1]). The purpose of this note is to show that DAIGs can usefully be grouped into equivalence classes where the members of a single class share identical Markov properties. These equivalence classes can be identified via a simple graphical criterion. This result is particularly relevant to model selection procedures for DAIGs (see, e.g., Cooper and Herskovits [2] and Madigan and Raftery [4]) because it reduces the problem of searching among possible orientations of a given graph to that of searching among the equivalence classes.

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Title
Probability in the Engineering and Informational Sciences
DOI
https://doi.org/10.1017/S0269964800003004

More About This Work

Academic Units
Statistics
Publisher
Cambridge University Press
Published Here
May 13, 2014
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