Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-27T20:29:34.545Z Has data issue: false hasContentIssue false
  • English
  • Français

A Note on Equivalence Classes of Directed Acyclic Independence Graphs

Published online by Cambridge University Press:  27 July 2009

David Madigan
David Madigan
Affiliation:
Department of Statistics, GN-22, University of Washington, Seattle, Washington 98195
Get access Rights & Permissions [Opens in a new window]

Extract

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.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 7 , Issue 3 , July 1993 , pp. 409 - 412
Copyright
Copyright © Cambridge University Press 1993

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Chyu, C.C. (1991). Decomposable probabilistic influence diagrams. Probability in the Engineering and Informational Sciences 5: 229–243.CrossRefGoogle Scholar
2.Cooper, G.F. & Herskovits, E. (1991). A Bayesian method for constructing Bayesian belief networks from databases. In D'Ambrosio, B.D., Smets, P., & Bonissone, P.P. (eds.), Proceedings of the Seventh Conference on Uncertainty in Artificial Intelligence. San Mateo, CA: Morgan Kaufman, pp. 86–94.Google Scholar
3.Lauritzen, S.L., Dawid, A.P., Larsen, B.N., & Leimer, H.-G. (1990). Independence properties of directed Markov fields. Networks 20: 491–505.CrossRefGoogle Scholar
4.Madigan, D. & Raftery, A.E. (1991). Model selection and accounting for model uncertainty in graphical models using Occam's window. Technical Report 213, Department of Statistics, University of Washington, Seattle.Google Scholar
5.Shachter, R.D. (1990). An ordered examination of influence diagrams. Networks 20: 535–563.CrossRefGoogle Scholar
6.Whittaker, J. (1990). Graphical models in applied multivariate statistics. Chichester: Wiley.Google Scholar