Abstract
The notion of relevance that is very important in knowledge based systems can be efficiently encoded by conditional independence. Although directed acyclic graphs (DAG) are powerful means for representing conditional independencies in probability distributions it is not always possible to find a DAG that represents all conditional independencies and dependencies of a distribution. We present a new formalism that is able to do this for positive probability distributions. The main issue is to augment a DAG with a special kind of arcs that induce independencies. Furthermore, an efficient algorithm is presented for building these extended DAGs.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
R.R. Bouckaert. Optimizing causal orderings for generating dags from data. In Proceedings Uncertainty in Artificial Intelligence, pages 9–16, 1992.
R.R. Bouckaert. Conditional dependencies in probabilistic networks. In Proceedings 4th International Workshop on AI and Statistics, 1993.
A.P. Dawid. Conditional independence in statistical theory. Journal of the Royal Statistical Society B, 41(1):1–31, 1979.
J. Doyle. A truth maintenance system. Artificial Intelligence, 12:231–272, 1979.
D. Geiger. Graphoids: a qualitative framework for probabilistic inference. PhD thesis, UCLA, Cognitive Systems Laboratory, Computer Science Department, 1990.
M. Henrion. An introduction to algorithms for inference in belief nets. In Proceedings Uncertainty in Artificial Intelligence 5, pages 129–138, 1990.
S.L. Lauritzen, A.P. Dawid, A.P. Larsen, and H.G. Leimer. Independence properties of directed markov fields. Networks, Vol 20, pages 491–505, 1990.
S.L. Lauritzen and D.J. Spiegelhalter. Local computations with probabilities on graphical structures and their applications to expert systems (with discussion). J.R. Stat. Soc. (Series B),Vol. 50, pages 157–224, 1988.
J. Pearl. Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufman, inc., San Mateo, CA, 1988.
J. Pearl, D. Geiger, and T. Verma. The logic of influence diagrams. In R.M. Oliver and J.Q. Smith, editors, Influence Diagrams, Belief Nets and Decision Analysis, pages 67–87. John Wiley & Sons Ltd., 1990.
T. Verma and J. Pearl. Causal networks: Semantics and expressiveness. In Proceedings Uncertainty in Artificial Intelligence, pages 352–359, 1988.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1993 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bouckaert, R.R. (1993). IDAGs: A perfect map for any distribution. In: Clarke, M., Kruse, R., Moral, S. (eds) Symbolic and Quantitative Approaches to Reasoning and Uncertainty. ECSQARU 1993. Lecture Notes in Computer Science, vol 747. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0028181
Download citation
DOI: https://doi.org/10.1007/BFb0028181
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-57395-1
Online ISBN: 978-3-540-48130-0
eBook Packages: Springer Book Archive