Electronic Journal of Statistics
- Electron. J. Statist.
- Volume 9, Number 2 (2015), 2130-2169.
The dynamic chain event graph
Lorna M. Barclay, Rodrigo A. Collazo, Jim Q. Smith, Peter A. Thwaites, and Ann E. Nicholson
Full-text: Open access
Abstract
In this paper we develop a formal dynamic version of Chain Event Graphs (CEGs), a particularly expressive family of discrete graphical models. We demonstrate how this class links to semi-Markov models and provides a convenient generalization of the Dynamic Bayesian Network (DBN). In particular we develop a repeating time-slice Dynamic CEG providing a useful and simpler model in this family. We demonstrate how the Dynamic CEG’s graphical formulation exhibits asymmetric conditional independence statements and also how each model can be estimated in a closed form enabling fast model search over the class. The expressive power of this model class together with its estimation is illustrated throughout by a variety of examples that include the risk of childhood hospitalization and the efficacy of a flu vaccine.
Article information
Source
Electron. J. Statist., Volume 9, Number 2 (2015), 2130-2169.
Dates
Received: September 2014
First available in Project Euclid: 21 September 2015
Permanent link to this document
https://projecteuclid.org/euclid.ejs/1442840119
Digital Object Identifier
doi:10.1214/15-EJS1068
Mathematical Reviews number (MathSciNet)
MR3400535
Zentralblatt MATH identifier
1336.62205
Keywords
Chain Event Graphs Markov processes probabilistic graphical models dynamic Bayesian networks
Citation
Barclay, Lorna M.; Collazo, Rodrigo A.; Smith, Jim Q.; Thwaites, Peter A.; Nicholson, Ann E. The dynamic chain event graph. Electron. J. Statist. 9 (2015), no. 2, 2130--2169. doi:10.1214/15-EJS1068. https://projecteuclid.org/euclid.ejs/1442840119
References
- Barbu, V. S. and Limnios, N., Semi-Markov chains and hidden semi-Markov models toward applications: their use in reliability and DNA analysis, volume 191. Springer, 2008.
- Barclay, L. M., Hutton, J. L., and Smith, J. Q. Refining a Bayesian Network using a Chain Event Graph., International Journal of Approximate Reasoning, 54 (9): 1300–1309, 2013.Mathematical Reviews (MathSciNet): MR3115418
Digital Object Identifier: doi:10.1016/j.ijar.2013.05.006 - Barclay, L. M., Hutton, J. L., and Smith, J. Q. Chain Event Graphs for Informed Missingness., Bayesian Analysis, 9 (1): 53–76, 2014.Mathematical Reviews (MathSciNet): MR3188299
Digital Object Identifier: doi:10.1214/13-BA843
Project Euclid: euclid.ba/1393251770 - Bilmes, J. A. Dynamic Bayesian Multinets. In, Proceedings of the Sixteenth Conference on Uncertainty in Artificial Intelligence, pages 38–45. Morgan Kaufmann Publishers Inc., 2000.
- Boutilier, C., Friedman, N., Goldszmidt, M., and Koller, D. Context-specific independence in Bayesian Networks. In, Proceedings of the 12th Conference on Uncertainty in Artificial Intelligence, 1996, pages 115–123. Morgan Kaufmann Publishers Inc., 1996.Mathematical Reviews (MathSciNet): MR1617129
- Collazo, R. A. and Smith, J. Q. A new family of non-local priors for chain event graph model selection. CRiSM Research Report 15-02, 2015.
- Cowell, R. G. and Smith, J. Q. Causal discovery through MAP selection of stratified chain event graphs., Electronic Journal of Statistics, 8 (1): 965–997, 2014.Mathematical Reviews (MathSciNet): MR3263109
Zentralblatt MATH: 06322944
Digital Object Identifier: doi:10.1214/14-EJS917
Project Euclid: euclid.ejs/1406638931 - Cowell, R. G., Dawid, A. P., Lauritzen, S. L., and Spiegelhalter, D. J., Probabilistic Networks and Expert Systems. Springer Verlag, New York, USA, 2007.Mathematical Reviews (MathSciNet): MR1697175
- Dawid, A. P. Conditional independence. In S. Kotz, C. B. Read, and D. L. Banks, editors, Encyclopedia of Statistical Science, volume 2, pages 146–153. Wiley-Interscience, update edition, 1998.Mathematical Reviews (MathSciNet): MR1605063
- Dean, T. and Kanazawa, K. A model for reasoning about persistence and causation., Computational Intelligence, 5 (3): 142–150, 1989.
- Didelez, V. Graphical models for marked point processes based on local independence., Journal of the Royal Statistical Society: Series B (Statistical Methodology), 70 (1): 245–264, 2008.Mathematical Reviews (MathSciNet): MR2412641
Zentralblatt MATH: 05563353
Digital Object Identifier: doi:10.1111/j.1467-9868.2007.00634.x - Fergusson, D. M., Horwood, L. J., and Shannon, F. T. Social and family factors in childhood hospital admission., Journal of Epidemiology and Community Health, 40 (1): 50, 1986.
- Freeman, G. and Smith, J. Q. Bayesian MAP model selection of Chain Event Graphs., Journal of Multivariate Analysis, 102 (7): 1152–1165, 2011a.Mathematical Reviews (MathSciNet): MR2805655
Zentralblatt MATH: 1216.62039
Digital Object Identifier: doi:10.1016/j.jmva.2011.03.008 - Freeman, G. and Smith, J. Q. Dynamic staged trees for discrete multivariate time series: forecasting, model selection and causal analysis., Bayesian Analysis, 6 (2): 279–305, 2011b.Mathematical Reviews (MathSciNet): MR2806245
Digital Object Identifier: doi:10.1214/11-BA610
Project Euclid: euclid.ba/1339612047 - French, S. and Insua, D. Rios., Statistical Decision Theory: Kendall’s Library of Statistics 9. Wiley, 2010.
- Friedman, N. and Goldszmidt, M.. Learning Bayesian Networks with local structure. In M. I. Jordan, editor, Learning in Graphical Models, pages 421–460. MIT Press, 1998.
- Geiger, D. and Heckerman, D. Knowledge representation and inference in similarity networks and Bayesian multinets., Artificial Intelligence, 82 (1): 45–74, 1996. Mathematical Reviews (MathSciNet): MR1391056
Digital Object Identifier: doi:10.1016/0004-3702(95)00014-3 - Gottard, A. On the inclusion of bivariate marked point processes in graphical models., Metrika, 66 (3): 269–287, 2007.Mathematical Reviews (MathSciNet): MR2336480
Digital Object Identifier: doi:10.1007/s00184-006-0110-7 - Heckerman, D. A tutorial on learning with Bayesian Networks., Innovations in Bayesian Networks, pages 33–82, 2008.
- Johnson, N. L., Kotz, S., and Balakrishnan, N., Continuous Univariate Distributions. Number v. 1 in Wiley Series in Probability and Mathematical Statistics: Applied Probability and Statistics. Wiley & Sons, 1995.
- Kjærulff, U. A computational scheme for reasoning in dynamic probabilistic networks. In, Proceedings of the Eighth International Conference on Uncertainty in Artificial Intelligence, UAI’92, pages 121–129, 1992.
- Korb, K. B. and Nicholson, A. E., Bayesian Artificial Intelligence, volume 1. CRC Press, 2004.Mathematical Reviews (MathSciNet): MR2130189
- Kulkarni, V. G., Modeling and analysis of stochastic systems, volume 36. CRC Press, 1995.Mathematical Reviews (MathSciNet): MR1357414
- Medhi, J., Stochastic Processes. New Age International, 1994.Mathematical Reviews (MathSciNet): MR1287161
- Murphy, K. P., Machine Learning: a Probabilistic Perspective. The MIT Press, 2012.Zentralblatt MATH: 1295.68003
- Neapolitan, R. E., Learning Bayesian Networks. Pearson Prentice Hall Upper Saddle River, 2004.
- Nicholson, A. E. Monitoring Discrete Environments Using Dynamic Belief Networks. PhD thesis, Department of Engineering Sciences, Oxford, 1992.
- Nodelman, U., Shelton, C. R., and Koller, D. Continuous time Bayesian networks. In, Proceedings of the Eighteenth Conference on Uncertainty in Artificial Intelligence (UAI), pages 378–387, 2002.
- Nodelman, U., Shelton, C. R., and Koller, D. Learning continuous time Bayesian networks. In, Proceedings of the Nineteenth International Conference on Uncertainty in Artificial Intelligence, pages 451–458, 2003.
- Pearl, J., Causality: Models, Reasoning, and Inference. Cambridge University Press, Cambridge, second edition, 2009.Mathematical Reviews (MathSciNet): MR2548166
- Riccomagno, E. and Smith, J. Q. The geometry of causal probability trees that are algebraically constrained., Optimal Design and Related Areas in Optimization and Statistics, pages 133–154, 2009.Mathematical Reviews (MathSciNet): MR2513349
Zentralblatt MATH: 1192.62007
Digital Object Identifier: doi:10.1007/978-0-387-79936-0_6 - Rubio, F., Flores, M. J., Gómez, J. M., and Nicholson A. Dynamic Bayesian Networks for semantic localization in robotics. In, XV Workshop of Physical Agents: Book of Proceedings, WAF 2014, June 12th and 13th, 2014 León, Spain, pages 144–155, 2014.
- Smith, J. Q., Decision Analysis – Principles and Practice. Cambridge University Press, 2010.Mathematical Reviews (MathSciNet): MR2828346
- Smith, J. Q. and Anderson, P. E. Conditional independence and Chain Event Graphs., Artificial Intelligence, 172 (1): 42–68, 2008.Mathematical Reviews (MathSciNet): MR2388535
Zentralblatt MATH: 1182.68303
Digital Object Identifier: doi:10.1016/j.artint.2007.05.004 - Thwaites, P. A. Causal identifiability via Chain Event Graphs., Artificial Intelligence, 195: 291–315, 2013.Mathematical Reviews (MathSciNet): MR3024205
Zentralblatt MATH: 1270.68300
Digital Object Identifier: doi:10.1016/j.artint.2012.09.003 - Thwaites, P. A. and Smith, J. Q. Evaluating causal effects using Chain Event Graphs. In, Proceedings of PGM, 2006, pages 293–300, 2006a.
- Thwaites, P. A. and Smith, J. Q. Non-symmetric models, Chain Event Graphs and propagation. In, Proceedings of IPMU, 2006, pages 2339–2347, 2006b.
- Thwaites, P. A. and Smith, J. Q. Separation theorems for Chain Event Graphs., CRiSM Research Report 11-09, 2011.
- Thwaites, P. A., Smith, J. Q., and Cowell, R. G. Propagation using Chain Event Graphs. In, Proceedings of the Twenty-Fourth Annual Conference on Uncertainty in Artificial Intelligence (UAI-08), pages 546–553. AUAI Press, 2008.
- Thwaites, P. A., Smith, J. Q., and Riccomagno, E. Causal analysis with Chain Event Graphs., Artificial Intelligence, 174 (12): 889–909, 2010.Mathematical Reviews (MathSciNet): MR2722255
Zentralblatt MATH: 1205.68431
Digital Object Identifier: doi:10.1016/j.artint.2010.05.004
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