Inferring interventions in product-based possibilistic causal networks. (English) Zbl 1214.68395

Summary: Many algorithms deal with non-experimental data in possibilistic networks. Most of them are direct adaptations of the probabilistic approaches. In this paper, we propose to represent another kind of data which is experimental data caused by external interventions in possibilistic networks. In particular, we present different and equivalent graphical interpretations of such manipulations using an adaptation of the ‘do’ operator to a possibilistic framework. We then propose an efficient algorithm to evaluate effects of non-simultaneous sequences of both experimental and non-experimental data. The main advantage of our algorithm is that it unifies treatments of the two kinds of data through the conditioning process with only a small extra-cost.


68T37 Reasoning under uncertainty in the context of artificial intelligence
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[1] Pearl, J., Causality: models, reasoning, and inference, (2000), Cambridge University Press New York, NY, USA · Zbl 0959.68116
[2] Halpern, J.; Pearl, J., Causes and explanations: a structural-model approach—part i: causes, (), 194-220
[3] Lauritzen, S.L., Causal inference from graphical models, (), 63-107 · Zbl 1010.62004
[4] M. Valtorta, Y. Huang, Identifiability in causal Bayesian networks: a sound and complete algorithm, in: Twenty-First National Conference on Artificial Intelligence, Manabu Kuroki and Masami, 2006, pp. 1149-1154.
[5] Shpitser, I.; Pearl, J., Complete identification methods for the causal hierarchy, Journal of machine learning research, 9, 1941-1979, (2008) · Zbl 1225.68216
[6] S. Li, Causal models have no complete axiomatic characterization, CoRR abs/0804.2401.
[7] C. Borgelt, J. Gebhardt, R. Kruse, Possibilistic graphical models, in: Proceedings of International School for the Synthesis of Expert Knowledge (ISSEK’98), Udine, Italy, 1998, pp. 51-68. · Zbl 0979.68106
[8] Benferhat, S.; Dubois, D.; Garcia, L.; Prade, H., On the transformation between possibilistic logic bases and possibilistic causal networks, International journal of approximate reasoning, 29, 2, 135-173, (2002) · Zbl 1015.68204
[9] Fonck, P., A comparative study of possibilistic conditional independence and lack of interaction, International journal of approximate reasoning, 16, 2, 149-171, (1997) · Zbl 0939.68115
[10] J. Gebhardt, R. Kruse, Background and perspectives of possibilistic graphical models, in: Proceedings of European Conference of Symbolic and Quantitative Approaches to Reasoning and Uncertainty (ECSQARU’1997), Bad Honnef, Germany, 1997, pp. 108-121.
[11] Darwiche, A., Modeling and reasoning with Bayesian networks, (2009), Cambridge University Press · Zbl 1231.68003
[12] Jensen, F.V., Introduction to Bayesian networks, (1996), UCL Press University College, London
[13] Jensen, F.V.; Nielsen, T.D., Bayesian networks and decision graphs, (2007), Springer · Zbl 1277.62007
[14] D.E. Holmes, L.C. Jain, Introduction to Bayesian networks, in: Innovations in Bayesian Networks, 2008, pp. 1-5. · Zbl 1188.68226
[15] Lauritzen, S.L.; Spiegelhalter, D.J., Local computations with probabilities on graphical structures and their application to expert systems, Journal of the royal statistical society, 50, 157-224, (1988) · Zbl 0684.68106
[16] D. Dubois, H. Prade, Possibility theory, in: Encyclopedia of Complexity and Systems Science, 2009, pp. 6927-6939.
[17] Zadeh, L.A., Fuzzy sets as a basis for a theory of possibility, Fuzzy sets and systems, 1, 3-28, (1978) · Zbl 0377.04002
[18] M. Goldszmidt, J. Pearl, Rank-based systems: a simple approach to belief revision, belief update, and reasoning about evidence and actions, in: Proceeding of the Third International Conference (KR’92), Kaufmann, 1992, pp. 661-672.
[19] W. Spohn, Ordinal conditional functions: a dynamic theory of epistemic states causation in decision, in: W. Harper, B. Skyrms (Eds.), Belief Changes and Statistics, 1988, pp. 105-134.
[20] W. Spohn, A general non-probabilistic theory of inductive reasoning, in: Proceedings of the Fourth Conference on Uncertainty in Artificial Intelligence (UAI’88), 1988, pp. 149-158.
[21] D. Dubois, H. Prade, Possibilistic logic, preferential models, non-monotonicity and related issues, in: International Joint Conferences on Artificial Intelligence (IJCAI’91), 1991, pp. 419-425. · Zbl 0744.68116
[22] S. Benferhat, S. Smaoui, Possibilistic causal networks for handling interventions: a new propagation algorithm, in: Twenty-Second Conference on Artificial Intelligence (AAAI’07), 2007, pp. 373-378.
[23] D. Dubois, J. Lang, H. Prade, Possibilistic logic, in: Handbook on Logic in Artificial Intelligence and Logic Programming, vol. 3, OUP, 1994, pp. 439-513.
[24] Hisdal, E., Conditional possibilities independence and non interaction, Fuzzy sets and systems, 1, 283-297, (1978) · Zbl 0393.94050
[25] Shafer, G., A mathematical theory of evidence, (1976), Princeton University Press NJ, USA · Zbl 0359.62002
[26] Dubois, D.; Prade, H., Possibility theory: an approach to computerized, processing of uncertainty, (1988), Plenium Press New York
[27] P. Leray, S. Meganck, S. Maes, B. Manderick, Causal graphical models with latent variables: Learning and inference, in: Innovations in Bayesian Networks, 2008, pp. 219-249. · Zbl 1187.68610
[28] Meganck, S.; Leray, P.; Manderick, B., Causal discovery in non-ideal frameworks, Information interaction intelligence (I3), 9, 1, 11-45, (2009)
[29] Neapolitan, R.E., Learning Bayesian networks, (2003), Prentice Hall
[30] T. Verma, J. Pearl, Equivalence and synthesis of causal models, in: UAI, 1990, pp. 255-270.
[31] Jeffrey, R., The logic of decision, (1965), Mc. Graw Hill New York
[32] J. Pearl, Comment: graphical models, causality and intervention, Statistical Sciences 8 (1993) 266- 269.
[33] Bonnefon, J.-F.; Neves, R.D.S.; Dubois, D.; Prade, H., Background default knowledge and causality ascriptions, (), 11-15
[34] Benferhat, S.; Bonnefon, J.-F.; Chassy, P.; Da Silva Neves, R.; Dubois, D.; Dupin de Saint Cyr Bannay, F.; Kayser, D.; Nouioua, F.; Nouioua-Boutouhami, S.; Prade, H.; Smaoui, S., A comparative study of six formal models of causal ascription, (), 47-62
[35] F.D. de Saint-Cyr, Scenario update applied to causal reasoning, in: Proceedings of the Eleventh International Conference on Knowledge Representation and Reasoning, KR 2008, 2008, pp. 188-197.
[36] J.Y. Halpern, Defaults and normality in causal structures, in: Proceedings of the Eleventh International Conference of Knowledge Representation and Reasoning, KR 2008, 2008, pp. 198-208.
[37] Amor, N.B.; Benferhat, S., Graphoid properties of qualitative possibilistic independence, International journal of uncertainty, fuzziness and knowledge-based, 13, 59-96, (2005) · Zbl 1096.68147
[38] Benferhat, S.; Smaoui, S., Hybrid possibilistic networks, (), 584-589
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