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Conditional independence and chain event graphs

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Smith, J. Q. and Anderson, Paul E.. (2008) Conditional independence and chain event graphs. Artificial Intelligence, Vol.172 (No.1). pp. 42-68. ISSN 0004-3702

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Official URL: http://dx.doi.org/10.1016/j.artint.2007.05.004

Abstract

Graphs provide an excellent framework for interrogating symmetric models of measurement random. variables and discovering their implied conditional independence structure. However, it is not unusual for a model to be specified from a description of how a process unfolds (i.e. via its event tree), rather than through relationships between a given set of measurements. Here we introduce a new mixed graphical structure called the chain event graph that is a function of this event tree and a set of elicited equivalence relationships. This graph is more expressive and flexible than either the Bayesian network-equivalent in the symmetric case-or the probability decision graph. Various separation theorems are proved for the chain event graph. These enable implied conditional independencies to be read from the graph's topology. We also show how the topology can be exploited to tease out the interesting conditional independence structure of functions of random variables associated with the underlying event tree. (c) 2007 Elsevier B.V. All rights reserved.

Item Type:

Journal Article

Subjects:

Q Science > QA Mathematics

Divisions:

Faculty of Science > Statistics

Library of Congress Subject Headings (LCSH):

Graph theory, Random variables, Probabilites, Bayesian statistical decision theory

Journal or Publication Title:

Artificial Intelligence

Publisher:

Elsevier BV

ISSN:

0004-3702

Official Date:

January 2008

Dates:

Date	Event
January 2008	Published

Volume:

Vol.172

Number:

No.1

Number of Pages:

Page Range:

pp. 42-68

Identification Number:

10.1016/j.artint.2007.05.004

Status:

Peer Reviewed

Publication Status:

Published

Access rights to Published version:

Open Access

References:

[1] P.E. Anderson, J.Q. Smith, A graphical framework for representing the semantics of asymmetric models, Technical Report 05-12, CRiSM
paper, Department of Statistics, University of Warwick, 2005.
[2] T. Bedford, R. Cooke, Probabilistic Risk Analysis—Foundations and Methods, Cambridge University Press, 2001, pp. 99–151.
[3] C. Boutilier, N. Friedman,M. Goldszmidt, D. Koller, Context-specific independence in Bayesian networks, in: Proceedings of the 12th Annual
Conference on Uncertainty in Artificial Intelligence, San Francisco, CA, Morgan Kaufmann, 1996, pp. 115–123.
[4] R.E. Bryant, Graphical algorithms for Boolean function manipulation, IEEE Trans. Comput. C-35 (1986) 677–691.
[5] G.A. Churchill, Accurate restoration of DNA sequences, in: C. Gatsaris, J.S. Hodges, R.E. Kass, N.D. Singpurwalls (Eds.), Case Studies in
Bayesian Statistics, vol. 2, Springer-Verlag, 1995, pp. 90–148.
[6] J. Corander, Labelled graphical models, Scand. J. Stat. 30 (3) (2003) 493–508.
[7] S. French (Ed.), Readings in Decision Analysis, Chapman Hall, 1989.
[8] D. Geiger, D. Heckerman, C. Meek, Asymptotic model selection for directed networks with hidden variables, in: Proceedings of the 12th
Annual Conference on Uncertainty in Artificial Intelligence (UAI-96), Portland, OR, Morgan Kaufmann, 1996, pp. 283–290.
[9] S. Hojsgaard, Statistical inference in context specific interaction models for contingency tables, Scand. J. Stat. 31 (1) (2004) 143–158.
[10] M. Jaeger, Probabilistic decision graphs—combining verification and AI techniques for probabilistic inference, Int. J. Uncertainty, Fuzziness
Knowledge-Based Syst. 12 (2004) 19–42.
[11] F.V. Jensen, Bayesian Networks and Decision Graphs, Springer-Verlag, 2001.
[12] H. Kiiveri, T.P. Speed, J.B. Carlin, Recursive causal models, J. Austral. Math. Soc. A 36 (1984) 30–52.
[13] S.L. Lauritzen, Graphical Models, first ed., Oxford Science Press, 1996.
[14] R. Lyons, Random walks and percolation on trees, Ann. Probab. 20 (1992) 2043–2088.
[15] D. McAllester, M. Collins, F. Pereira, Case-factor diagrams for structured probability modelling, in: Proceedings of the 20th Annual Conference
on Uncertainty in Artificial Intelligence (UAI-04), 2004, pp. 382–391.
[16] S.M. Olmsted, On representing and solving decision problems, PhD thesis, Engineering-Economic Systems, Stanford University, 1983.
[17] J. Pearl, Probabilistic Reasoning in Intelligent Systems, Morgan Kauffman, 1988.
[18] J. Pearl, Causality, Models, Reasoning and Inference, Cambridge University Press, 2000.
[19] J. Pearl, Statistics and causal inference: A review (with discussion), Sociedad de Estadistica e Investigacion Operativa Test 12 (2) (2003)
281–345.
[20] D. Poole, N.L. Zhang, Exploiting contextual independence in probabilistic inference, J. Artificial Intelligence Res. 18 (2003) 263–313.
[21] E. Riccomagno, J.Q. Smith, Identifying a cause in models which are not simple Bayesian networks, in: Proceedings of the 10th Conference
on Information Processing and Management of Uncertainty in Knowledge-Based Systems, Perugia, 2004, pp. 1315–1322.
[22] E. Riccomagno, J.Q. Smith, The causal manipulation and Bayesian estimation of chain event graphs, Technical report, University ofWarwick,
2005.
[23] R.D. Shachter, Evaluating influence diagrams, in: E.P. Basu (Ed.), Reliability and Control, Elsevier, Amsterdam, 1986, pp. 321–344.
[24] R.D. Shachter, Intelligent probabilistic inference, in: L.N. Kanal, J. Lemmer (Eds.), Uncertainty in Artificial Intelligence, North-Holland,
Amsterdam, 1986, pp. 371–382.
[25] G. Shafer, The Art of Causal Conjecture, MIT Press, Cambridge, MA, 1996.
[26] G. Shafer, P.R. Gillett, R.B. Scherl, A new understanding of subjective probability and its generalization to lower and upper prevision, Int. J.
Approx. Reason. 33 (1) (2003) 1–49.
[27] J.Q. Smith, Influence diagrams for statistical modelling, Ann. Stat. 17 (1989) 654–672.
[28] P. Spirtes, C. Glymour, R. Scheines, Causation, Prediction, and Search, Springer-Verlag, 1993.
[29] M. Studeny, Probabilistic Conditional Independence Structures, Springer-Verlag, 2005.