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Approximate inference for dynamic Bayesian networks: sliding window approach

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Abstract

Dynamic Bayesian networks (DBNs) are probabilistic graphical models that have become a ubiquitous tool for compactly describing statistical relationships among a group of stochastic processes. A suite of elaborately designed inference algorithms makes it possible for intelligent systems to use a DBN to make inferences in uncertain conditions. Unfortunately, exact inference or even approximation in a DBN has been proved to be NP-hard and is generally computationally prohibitive. In this paper, we investigate a sliding window framework for approximate inference in DBNs to reduce the computational burden. By introducing a sliding window that moves forward as time progresses, inference at any time is restricted to a quite narrow region of the network. The main contributions to the sliding window framework include an exploration of its foundations, explication of how it operates, and the proposal of two strategies for adaptive window size selection. To make this framework available as an inference engine, the interface algorithm widely used in exact inference is then integrated with the framework for approximate inference in DBNs. After analyzing its computational complexity, further empirical work is presented to demonstrate the validity of the proposed algorithms.

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References

  1. Murphy KP (2002) Dynamic Bayesian networks: representation, inference and learning. PhD Dissertation, University of California, Berkeley

  2. Wang JS, Byrnes J, Valtorta M, Huhns M (2012) On the combination of logical and probabilistic models for information analysis. Appl Intell 36(2):472–497

    Article  Google Scholar 

  3. Benferhat S, Boudjelida A, Tabia K, Drias H (2012) An intrusion detection and alert correlation approach based on revising probabilistic classifiers using expert knowledge. Appl Intell 36(4):520–540

    Google Scholar 

  4. Simona C, Koller P, Evsukoffb A (2012) DBN-based combinatorial resampling for articulated object tracking. In: Proceedings of UAI’12. Kaufmann, Los Altos, pp 237–246

    Google Scholar 

  5. Donat R, Leray P, Bouillaut L, Aknin P (2010) A dynamic Bayesian network to represent discrete duration models. Neurocomputing 73(4):570–577

    Article  Google Scholar 

  6. Friedman N (2004) Inferring cellular networks using probabilistic graphical models. Science 303(5659):799–805

    Article  Google Scholar 

  7. Zhang CL, Frias MA, Mele A, Ruggiu M, Eom T, Marney CB, Wang HD, Licatalosi DD, Fak JJ, Darnell RB (2011) Integrative modeling defines the nova splicing-regulatory network and its combinatorial controls. Science 329(5990):439–443

    Article  Google Scholar 

  8. Bartels CD, Bilmes JA (2011) Creating non-minimal triangulations for use in inference in mixed stochastic/deterministic graphical models. Mach Learn 84(3):249–289

    Article  MATH  MathSciNet  Google Scholar 

  9. Yap GE, Tan AH, Pang HH (2008) Explaining inferences in Bayesian networks. Appl Intell 29(3):263–278

    Article  Google Scholar 

  10. Koller D, Friedman N (2009) Probabilistic graphical models: principles and techniques. MIT Press, Cambridge

    Google Scholar 

  11. Smyth P, Heckerman D, Jordan MI (1997) Probabilistic independence networks for hidden Markov probability models. Neural Comput 9(2):227–269

    Article  MATH  Google Scholar 

  12. Murphy K, Weiss Y (2001) The factored frontier algorithm for approximate inference in DBNs. In: Proceedings of UAI’01. Kaufmann, Los Altos, pp 378–385

    Google Scholar 

  13. Cano A, Gémez-Olmedo M, Moral S (2011) Approximate inference in Bayesian networks using binary probability trees. Int J Approx Reason 52(1):49–62

    Article  MATH  Google Scholar 

  14. Palaniappan SK, Akshay S, Liu B, Genest B, Thiagarajan PS (2012) Hybrid factored frontier algorithm for dynamic Bayesian networks with a biopathways application. IEEE/ACM Trans Comput Biol Bioinform 9(5):1352–1365

    Google Scholar 

  15. Cooper GF (1990) The computational complexity of probabilistic inference using Bayesian belief networks. Artif Intell 42(2):393–405

    Article  MATH  Google Scholar 

  16. Dagum P, Luby M (1993) Approximating probabilistic inference in Bayesian belief networks is NP-hard. Artif Intell 60(1):141–153

    Article  MATH  MathSciNet  Google Scholar 

  17. Boyen X, Koller D (1998) Tractable inference for complex stochastic processes. In: Proceedings of UAI’98, Madison, Wisconsin. Kaufmann, Los Altos, pp 33–42

    Google Scholar 

  18. Kjærulff U (1992) A computational scheme for reasoning in dynamic probabilistic networks. In: Proceedings of UAI’92, Stanford, CA. Kaufmann, Los Altos, pp 121–129

    Google Scholar 

  19. Kjærulff U (1995) dHugin: a computational system for dynamic time-sliced Bayesian networks. Int J Forecast 11(1):89–111

    Article  Google Scholar 

  20. Cho HC (2006) Dynamic Bayesian networks for online stochastic modeling. PhD thesis, University of Nevada, Reno, NV

  21. Qi Y (2004) Extending expectation propagation for graphical models. PhD thesis, Massachusetts Institute of Technology, MA

  22. Wei T (2007) Expectation propagation algorithm for Bayesian inference in dynamic systems. MS thesis, University of Texas, San Antonio, TX

  23. Cho HC, Lee KS, Fadali MS (2009) Online learning algorithm for dynamic Bayesian networks for nonstationary signal processing. Int J Innov Comput Inf Control 5(4):1037–1041

    Google Scholar 

  24. Knox WB, Mengshoel OJ (2009) Diagnosis and reconfiguration using Bayesian networks: an electrical power system case study. In: Proceedings of IJCAI’09 workshop self-* and autonomous systems: reasoning and integration challenges (SAS-09), pp 67–74

    Google Scholar 

  25. Chen HY (2011) Study on inference of structure-variable dynamic Bayesian networks. PhD thesis, Northwestern Polytechnical University, Xi’an, China

  26. Russell SJ, Norvig P, Canny JF, Malik JM, Edwards DD (1995) Artificial intelligence: a modern approach. Pearson Education, Upper Saddle River

    MATH  Google Scholar 

  27. Pavlovic VI (1999) Dynamic Bayesian networks for information fusion with applications to human-computer interfaces. PhD thesis, University of Illinois, Urbana-Champaign, IL

  28. Meyn SSP, Richard LT (2009) Markov chains and stochastic stability. Cambridge University Press, New York

    Book  MATH  Google Scholar 

  29. Chatterjee S, Russell S (2010) Why are DBNs sparse? In: Proceedings of AISTATS’10, pp 81–88

    Google Scholar 

  30. Lauritzen SL, Spiegelhalter D (1988) Local computations with probabilities on graphical structures and their application to expert systems (with discussion). J R Stat Soc B 50:157–224

    MATH  MathSciNet  Google Scholar 

  31. Jensen FV, Nielsen TD (2007) Bayesian networks and decision graphs, 2nd edn. Springer, New York

    Book  MATH  Google Scholar 

  32. Barber D (2012) Bayesian reasoning and machine learning. Cambridge University Press, New York

    MATH  Google Scholar 

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Acknowledgements

This work was supported by the National Nature Science Foundation of China (NSFC) under Grant 60774064 and the doctoral Fund of Ministry of Education of China under Grant 20116102110026. The authors thank the anonymous reviews for their insightful comments and constructive suggestions to improve this paper. We would also like to thank Wen Zengkui for his valuable advice on the structure of the paper and his remarkable work of spelling checking.

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Authors and Affiliations

  1. School of Electronic and Information, Northwestern Polytechnical University, Xi’an, China

    Xiao-Guang Gao & Jun-Feng Mei

  2. School of Electronic Information, Xi’an Polytechnic University, Xi’an, China

    Hai-Yang Chen

  3. Dept. of Informatics, London South Bank University, London, UK

    Da-Qing Chen

Authors
  1. Xiao-Guang Gao
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  2. Jun-Feng Mei
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  3. Hai-Yang Chen
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  4. Da-Qing Chen
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Correspondence to Xiao-Guang Gao.

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Gao, XG., Mei, JF., Chen, HY. et al. Approximate inference for dynamic Bayesian networks: sliding window approach. Appl Intell 40, 575–591 (2014). https://doi.org/10.1007/s10489-013-0486-9

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  • DOI: https://doi.org/10.1007/s10489-013-0486-9

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