Abstract
Non-impeding noisy-And Trees (NATs) provide a general, expressive, and efficient causal model for conditional probability tables (CPTs) in discrete Bayesian networks (BNs). A CPT may be directly expressed as a NAT model or compressed into a NAT model. Once CPTs are NAT-modeled, efficiency of BN inference (both space and time) can be significantly improved. The most important operation in NAT modeling CPTs is extracting NAT structures from interaction patterns between causes. Early method does so through a search tree coupled with a NAT database. A recent advance allows extraction of NAT structures from full, valid causal interaction patterns based on bipartition of causes, without requiring the search tree and the NAT database. In this work, we extend the method to direct NAT structure extraction from partial and invalid causal interaction patterns. This contribution enables direct NAT extraction from all conceivable application scenarios.
Keywords
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Boutilier, C., Friedman, N., Goldszmidt, M., Koller, D.: Context-specific independence in Bayesian networks. In: Proceeding of 12th Conference on Uncertainty in Artificial Intelligence, pp. 115–123 (1996)
Darwiche, A.: A differential approach to inference in Bayesian networks. J. ACM 50(3), 280–305 (2003)
Diez, F.J.: Parameter adjustment in Bayes networks: the generalized noisy OR-gate. In: Heckerman, D., Mamdani, A. (eds.) Proceeding of 9th Conference on Uncertainty in Artificial Intelligence, pp. 99–105. Morgan Kaufmann (1993)
Henrion, M.: Some practical issues in constructing belief networks. In: Kanal, L.N., Levitt, T.S., Lemmer, J.F. (eds.) Uncertainty in Artificial Intelligence 3, pp. 161–173. Elsevier Science Publishers (1989)
Lemmer, J.F., Gossink, D.E.: Recursive noisy OR - a rule for estimating complex probabilistic interactions. IEEE Trans. Syst. Man Cybern. Part B 34(6), 2252–2261 (2004)
Maaskant, P.P., Druzdzel, M.J.: An independence of causal interactions model for opposing influences. In: Jaeger, M., Nielsen, T.D. (eds.) Proceeding 4th European Workshop on Probabilistic Graphical Models, pp. 185–192. Hirtshals, Denmark (2008)
Poon, H., Domingos, P.: Sum-product networks: a new deep architecture. In: Proceeding of 12th Conference on Uncertainty in Artificial Intelligence, pp. 2551–2558 (2011)
Pearl, J.: Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann, San Francisco (1988)
Vomlel, J., Tichavský, P.: An approximate tensor-based inference method applied to the game of minesweeper. In: van der Gaag, L.C., Feelders, A.J. (eds.) PGM 2014. LNCS, vol. 8754, pp. 535–550. Springer, Cham (2014). doi:10.1007/978-3-319-11433-0_35
Woudenberg, S., van der Gaag, L.C., Rademaker, C.: An intercausal cancellation model for Bayesian-network engineering. Inter. J. Approximate Reasoning 63, 3247 (2015)
Xiang, Y.: Acquisition and computation issues with NIN-AND tree models. In: Myllymaki, P., Roos, T., Jaakkola, T. (eds.) Proceeding of 5th European Workshop on Probabilistic Graphical Models, Finland, pp. 281–289 (2010)
Xiang, Y.: Non-impeding noisy-AND tree causal models over multi-valued variables. Int. J. Approximate Reasoning 53(7), 988–1002 (2012). Oct
Xiang, Y.: Extraction of NAT causal structures based on bipartition. In: Proceeding of 30th International Florida Artificial Intelligence Research Society Conference (2017, in press)
Xiang, Y., Jia, N.: Modeling causal reinforcement and undermining with Noisy-AND trees. In: Lamontagne, L., Marchand, M. (eds.) AI 2006. LNCS, vol. 4013, pp. 171–182. Springer, Heidelberg (2006). doi:10.1007/11766247_15
Xiang, Y., Jiang, Q.: Compression of general Bayesian Net CPTs. In: Khoury, R., Drummond, C. (eds.) AI 2016. LNCS, vol. 9673, pp. 285–297. Springer, Cham (2016). doi:10.1007/978-3-319-34111-8_35
Xiang, Y., Jin, Y.: Multiplicative factorization of multi-valued NIN-AND tree models. In: Markov, Z., Russell, I. (eds.) Proceeding of 29th International Florida Artificial Intelligence Research Society Conference, pp. 680–685. AAAI Press (2016)
Xiang, Y., Liu, Q.: Compression of Bayesian networks with NIN-AND tree modeling. In: van der Gaag, L.C., Feelders, A.J. (eds.) PGM 2014. LNCS, vol. 8754, pp. 551–566. Springer, Cham (2014). doi:10.1007/978-3-319-11433-0_36
Xiang, Y., Li, Y., Zhu, Z.J.: Towards effective elicitation of NIN-AND tree causal models. In: Godo, L., Pugliese, A. (eds.) SUM 2009. LNCS, vol. 5785, pp. 282–296. Springer, Heidelberg (2009). doi:10.1007/978-3-642-04388-8_22
Xiang, Y., Truong, M.: Acquisition of causal models for local distributions in Bayesian networks. IEEE Trans. Cybern. 44(9), 1591–1604 (2014)
Xiang, Y., Zhu, Z.J., Li, Y.: Enumerating unlabeled and root labeled trees for causal model acquisition. In: Gao, Y., Japkowicz, N. (eds.) AI 2009. LNCS, vol. 5549, pp. 158–170. Springer, Heidelberg (2009). doi:10.1007/978-3-642-01818-3_17
Zhao, H., Melibari, M., Poupart, P.: On the relationship between sum-product networks and Bayesian networks. In: Proceeding of 32nd International Conference Machine Learning (2015)
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Financial support from the NSERC Discovery Grant is acknowledged.
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Xiang, Y. (2017). Fault Tolerant Direct NAT Structure Extraction from Pairwise Causal Interaction Patterns. In: Moral, S., Pivert, O., Sánchez, D., Marín, N. (eds) Scalable Uncertainty Management. SUM 2017. Lecture Notes in Computer Science(), vol 10564. Springer, Cham. https://doi.org/10.1007/978-3-319-67582-4_10
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DOI: https://doi.org/10.1007/978-3-319-67582-4_10
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