Abstract
Graphical models have been extensively used in probabilistic reasoning for representing conditional independency (CI) information. Among them two of the well known models are undirected graphs (UGs), and directed acyclic graphs (DAGs). Given a set of CIs, it would be desirable to know whether this set can be perfectly represented by a UG or DAG. A necessary and sufficient condition using axioms has been found for a set of CIs that can be perfectly represented by a UG; while negative result has been shown for DAGs, i.e., there does not exist a finite set of axioms which can characterize a set of CIs having a perfect DAG. However, this does not exclude other possible ways for such a characterization. In this paper, by studying the relationship between CIs and factorizations of a joint probability distribution, we show that there does exist such a characterization for DAGs in terms of the structure of the given set of CIs. More precisely, we demonstrate that if the given set of CIs satisfies certain constraints, then it has a perfect DAG representation.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
C. Berge. Graphs and Hypergraphs. North-Holland, Amsterdam, 1976.
E. Castillo, J. Manual Gutierrez, and A. Hadi. Expert Systems and Probabilistic Network Models. Springer, 1997.
D. M. Chickering. A transformational characterization of equivalent bayesian network structures. In Eleventh Conference on Uncertainty in Artificial Intelligence, pages 87–98. Morgan Kaufmann Publishers, 1995.
D Geiger. The non-axiomatizability of dependencies in directed acyclic graphs. Technical Report R-83, UCLA Cognitive Systems Laboratory, 1987.
F. V. Jensen. Junction tree and decomposable hypergraphs. Technical report, JUDEX, Aalborg, Denmark, 1988.
J. Pearl. Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann Publishers, San Francisco, California, 1988.
J. Pearl and A. Paz. Graphoids: Graph-based logic for reasoning about relevance relations. Technical Report R-53-L, University of California, 1985.
G. Shafer. An axiomatic study of computation in hypertrees. School of Business Working Papers 232, University of Kansas, 1991.
T. Verma and J. Pearl. Equivalence and synthesis of causal models. In Sixth Conference on Uncertainty in Artificial Intelligence, pages 220–227. GE Corporate Research and Development, 1990.
T. Verma and J. Pearl. An algorithm for deciding if a set of observed independencies has a causal explanation. In Eighth Conference on Uncertainty in Artificial Intelligence, pages 323–330, 1992.
S. K. M. Wong and C. J. Butz. Constructing the dependency structure of a multi-agent probabilistic network. IEEE Transactions on Knowledge and Data Engineering, 30(6):395–415, 2000.
S. K. M. Wong, Tao Lin, and Dan Wu. Construction of a non-redundant cover for conditional independencies. In The Fifteenth Canadian Conference on Artificial Intelligence, 2002.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Wong, S.K.M., Wu, D., Lin, T. (2002). A Structural Characterization of DAG-Isomorphic Dependency Models. In: Cohen, R., Spencer, B. (eds) Advances in Artificial Intelligence. Canadian AI 2002. Lecture Notes in Computer Science(), vol 2338. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-47922-8_17
Download citation
DOI: https://doi.org/10.1007/3-540-47922-8_17
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-43724-6
Online ISBN: 978-3-540-47922-2
eBook Packages: Springer Book Archive