# zbMATH — the first resource for mathematics

A generic framework for a compilation-based inference in probabilistic and possibilistic networks. (English) Zbl 1320.68177
Summary: Probabilistic and possibilistic networks are important tools proposed for an efficient representation and analysis of uncertain information. The inference process has been studied in depth in these graphical models. We cite in particular compilation-based inference which has recently triggered the attention of several researchers. In this paper, we are interested in comparing this inference mechanism in the probabilistic and possibilistic frameworks in order to unveil common points and differences between these two settings. In fact, we will propose a generic framework supporting both Bayesian networks and possibilistic networks (product-based and min-based ones). The proposed comparative study points out that the inference process depends on the specificity of each framework, namely in the interpretation of the handled uncertainty degrees (probability$$\backslash$$possibility) and appropriate operators ($${^\ast\backslash \min}$$ and $${+\backslash\max}$$).

##### MSC:
 68T37 Reasoning under uncertainty in the context of artificial intelligence
Full Text:
##### References:
 [1] Ayachi, R.; Ben Amor, N.; Benferhat, S., Experimental comparative study of compilation-based inference in Bayesian and possibilitic networks, (Proceedings of 9th International Workshop on Fuzzy Logic and Applications, (2011), Springer Verlag), 155-163 [2] Ayachi, R.; Ben Amor, N.; Benferhat, S.; Haenni, R., Compiling possibilistic networks: alternative approaches to possibilistic inference, (Proceedings of 26th Conference on Uncertainty on Artificial Intelligence, (2010), AUAI Press), 40-47 [3] C. Borgelt, J. Gebhardt, R. Kruse, Possibilistic graphical models, in: Proceedings of International School for the Synthesis of Expert Knowledge, 1998, Udine (Italy). · Zbl 0979.68106 [4] Boutilier, C.; Brafman, R. I.; Hoos, H. H.; Poole, D., Reasoning with conditional ceteris paribus preference statements, (Proceedings of 15th Conference on Uncertainty on Artificial Intelligence, (1999), AUAI Press) [5] Cadoli, M.; Donini, F. M., A survey on knowledge compilation, AI Communications - The European Journal for Artificial Intelligence, 137-150, (1998) [6] Chavez, R. M.; Cooper, G. F., A randomized approximation algorithm for probabilistic inference on Bayesian belief networks, Networks, 20, 661-685, (1990) · Zbl 0719.68078 [7] Chavira, M.; Darwiche, A., Compiling Bayesian networks with local structure, (Proceedings of the 19th International Joint Conference on Artificial Intelligence, (2005), Morgan Kaufman Publishers Inc.), 1306-1312 [8] Chavira, M.; Darwiche, A., Compiling Bayesian networks using variable elimination, (Proceedings of the 20th International Joint Conference on Artificial Intelligence, (2007), Morgan Kaufman Publishers Inc.), 2443-2449 [9] Darwiche, A., Decomposable negation normal form, Journal of the ACM, 48, 608-647, (2001) · Zbl 1127.03321 [10] Darwiche, A., A compiler for deterministic, decomposable negation normal form, (Proceedings of the Eighteenth National Conference on Artificial Intelligence, (2002), AAAI Press Menlo Park, California), 627-634 [11] Darwiche, A., A logical approach to factoring belief networks, (Proceedings of Knowledge Representation, (2002), ACM), 409-420 [12] Darwiche, A., New advances in compiling CNF to decomposable negation normal form, (Proceedings of European Conference on Artificial Intelligence, (2004), IOS Press), 328-332 [13] Darwiche, A., Modeling and reasoning with Bayesian networks, (2009), Cambridge Univ. Press · Zbl 1231.68003 [14] Darwiche, A., Generalized decision diagrams: the game is not over yet!, (Proceedings of the 20th European Conference on Artificial Intelligence, (2012), IOS Press), 4 [15] Darwiche, A.; Marquis, P., A knowledge compilation map, Journal of Artificial Intelligence Research, 17, 229-264, (2002) · Zbl 1045.68131 [16] Dubois, D.; Prade, H., Possibility Theory: An Approach to Computerized, Processing of Uncertainty, (1988), Plenum Press New York [17] Dubois, D.; Prade, H., Possibility theory, (Meyers, R. A., Encyclopedia of Complexity and Systems Science, (2009), Springer), 6927-6939 [18] Dubois, D.; Prade, H.; Smets, P., Representing partial ignorance, Transactions of Systems, Man and Cybernetics, Part A, 26, 361-377, (1996) [19] Fargier, H.; Marquis, P., On valued negation normal form formulas, (Proceedings of the 20th International Joint Conference on Artificial Intelligence, (2007), Morgan Kaufman Publishers Inc. San Francisco, CA, USA), 360-365 [20] P. Fonck, Réseaux d’inférence pour le raisonnement possibiliste, Ph.D. thesis, UniversitT de LiFge, FacultT des Sciences, 1994. [21] Gebhardt, J.; Kruse, R., Background and perspectives of possibilistic graphical models, (Proceedings of European Conference of Symbolic and Quantitative Approaches to Reasoning and Uncertainty, (1997), Springer Bad Honnef (Germany)), 108-121 [22] Hisdal, E., Conditional possibilities independence and non interaction, Fuzzy Sets and Systems, 1, (1978) · Zbl 0393.94050 [23] Kim, J. H.; Pearl, J., A computational model for causal and diagnostic reasoning in inference systems, (Proceedings of International Joint Conference on Artificial Intelligence, (1983), Morgan Kaufman Publishers Inc. Karlsruhe (Germany)), 190-193 [24] Marquis, P., Existential closures for knowledge compilation, (Proceedings of the 22th International Joint Conference on Artificial Intelligence, (2011), AAAI Press), 996-1001 [25] Pearl, J., Fusion propagation and structuring in belief networks, Artificial Intelligence, 29, 241-288, (1986) · Zbl 0624.68081 [26] Pearl, J., Probabilistic reasoning in intelligent systems: networks of plausible inference, (1988), Morgan Kaufman Publishers Inc. San Francisco, CA, USA [27] Pinzon, C. I.; De Paz, J. F.; Herrero, A.; Corchado, E.; Bajo, J.; Corchado, J. M., Idmas-SQL: intrusion detection based on MAS to detect and block SQL injection through data mining, Information Sciences, 231, 15-31, (2013) [28] Pipatsrisawat, K.; Darwiche, A., Top-down algorithms for constructing structured dnnf: theoretical and practical implications, (Proceeings of the 19th European Conference on Artificial Intelligence, (2010), IOS Press), 3-8 · Zbl 1211.68439 [29] Song, J.; Takakura, H.; Okabe, Y.; Nakao, K., Toward a more practical unsupervised anomaly detection system, Information Sciences, 231, 4-14, (2013) [30] Wachter, M.; Haenni, R., Logical compilation of Bayesian networks with discrete variables, (European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty, (2007), Springer-Verlag), 536-547 · Zbl 1148.68540 [31] Xu, H.; Smets, P., Reasoning in evidential networks with conditional belief functions, International Journal of Approximate Reasoning., 14, 155-185, (1996) · Zbl 0941.68764 [32] Zadeh, L. A., Fuzzy sets as a basis for a theory of possibility, Fuzzy Sets Systems, 100, 9-34, (1999)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.