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De-Causalizing NAT-Modeled Bayesian Networks for Inference Efficiency

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10832))

Abstract

Conditional independence encoded in Bayesian networks (BNs) avoids combinatorial explosion on the number of variables. However, BNs are still subject to exponential growth of space and inference time on the number of causes per effect variable in each conditional probability table (CPT). A number of space-efficient local models exist that allow efficient encoding of dependency between an effect and its causes, and can also be exploited for improved inference efficiency. We focus on the Non-Impeding Noisy-AND Tree (NIN-AND Tree or NAT) models due to its multiple merits. In this work, we develop a novel framework, de-causalization of NAT-modeled BNs, by which causal independence in NAT models can be exploited for more efficient inference. We demonstrate its exactness and efficiency impact on inference based on lazy propagation (LP).

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References

  1. Boutilier, C., Friedman, N., Goldszmidt, M., Koller, D.: Context-specific independence in Bayesian networks. In: Horvitz, E., Jensen, F. (eds.) Proceedings of the 12th Conference on Uncertainty in Artificial Intelligence, pp. 115–123 (1996)

    Google Scholar 

  2. Diez, F.J.: Parameter adjustment in Bayes networks: the generalized noisy OR-gate. In: Heckerman, D., Mamdani, A. (eds.) Proceedings of the 9th Conference on Uncertainty in Artificial Intelligence, pp. 99–105. Morgan Kaufmann (1993)

    Google Scholar 

  3. Diez, F.J., Druzdzel, M.J.: Canonical probabilistic models for knowledge engineering. Technical report cisiad-06-01, UNED (2007)

    Google Scholar 

  4. 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)

    Google Scholar 

  5. 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)

    Article  Google Scholar 

  6. Maaskant, P.P., Druzdzel, M.J.: An independence of causal interactions model for opposing influences. In: Jaeger, M., Nielsen, T.D. (eds.) Proceedings of the 4th European Workshop on Probabilistic Graphical Models, Hirtshals, Denmark, pp. 185–192 (2008)

    Google Scholar 

  7. Madsen, A.L., Jensen, F.V.: Lazy propagation: a junction tree inference algorithm based on lazy evaluation. Artif. Intell. 113(1–2), 203–245 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  8. Olesen, K.G., Kjrulff, U., Jensen, F., Jensen, F.V., Falck, B., Andreassen, S., Andersen, S.K.: A munin network for the median nerve-a case study on loops. Appl. Artif. Intell. 3(2–3), 385–403 (1989)

    Article  Google Scholar 

  9. Pearl, J.: Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann, San Francisco (1988)

    MATH  Google Scholar 

  10. 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 (LNAI), vol. 8754, pp. 535–550. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-11433-0_35

    Google Scholar 

  11. Woudenberg, S., van der Gaag, L.C., Rademaker, C.: An intercausal cancellation model for Bayesian-network engineering. Int. J. Approximate Reason. 63, 32–47 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  12. Xiang, Y.: Acquisition and computation issues with NIN-AND tree models. In: Myllymaki, P., Roos, T., Jaakkola, T. (eds.) Proceedings of the 5th European Workshop on Probabilistic Graphical Models, Finland, pp. 281–289 (2010)

    Google Scholar 

  13. Xiang, Y.: Non-impeding noisy-AND tree causal models over multi-valued variables. Int. J. Approximate Reason. 53(7), 988–1002 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  14. Xiang, Y., Jiang, Q.: NAT model based compression of Bayesian network CPTs over multi-valued variables. Comput. Intell. (2017). https://doi.org/10.1111/coin.12126. (Paper version in press)

  15. Xiang, Y., Jin, Y.: Efficient probabilistic inference in Bayesian networks with multi-valued NIN-AND tree local models. Int. J. Approximate Reason. 87, 67–89 (2017)

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgement

Financial support from NSERC Discovery Grant to first author is acknowledged.

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Correspondence to Yang Xiang .

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Xiang, Y., Loker, D. (2018). De-Causalizing NAT-Modeled Bayesian Networks for Inference Efficiency. In: Bagheri, E., Cheung, J. (eds) Advances in Artificial Intelligence. Canadian AI 2018. Lecture Notes in Computer Science(), vol 10832. Springer, Cham. https://doi.org/10.1007/978-3-319-89656-4_2

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  • DOI: https://doi.org/10.1007/978-3-319-89656-4_2

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-89655-7

  • Online ISBN: 978-3-319-89656-4

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