Skip to main content
SpringerLink
Log in

Representing Hypoexponential Distributions in Continuous Time Bayesian Networks

  • Conference paper
  • First Online:
Information Processing and Management of Uncertainty in Knowledge-Based Systems. Applications (IPMU 2018)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 855))

  • 1272 Accesses

Abstract

Continuous time Bayesian networks offer a compact representation for modeling structured stochastic processes that evolve over continuous time. In these models, the time duration that a variable stays in a state until a transition occurs is assumed to be exponentially distributed. In real-world scenarios, however, this assumption is rarely satisfied, in particular when describing more complex temporal processes. To relax this assumption, we propose an extension to support the modeling of the transitioning time as a hypoexponential distribution by introducing an additional hidden variable. Using such an approach, we also allow CTBNs to obtain memory, which is lacking in standard CTBNs. The parameter estimation in the proposed models is transformed into a learning task in their equivalent Markovian models.

ML is supported by China Scholarship Council, by a grant from project NanoSTIMA [NORTE-01-0145-FEDER-000016], which was financed by the North Portugal Regional Operational Programme [NORTE 2020], under the PORTUGAL 2020 Partnership Agreement, and through the European Regional Development Fund [ERDF], and by Italian Association for Artificial Intelligence (AI*IA).

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    http://rlair.cs.ucr.edu/ctbnrle/.

  2. 2.

    http://home.math.au.dk/asmus/pspapers.html.

References

  1. Nodelman, U.D.: Continuous time Bayesian Networks. Ph.D. thesis, Stanford University (2007)

    Google Scholar 

  2. Boudali, H., Dugan, J.B.: A continuous-time Bayesian network reliability modeling, and analysis framework. IEEE Trans. Reliab. 55(1), 86–97 (2006)

    Article  Google Scholar 

  3. Xu, J., Shelton, C.R.: Continuous time Bayesian networks for host level network intrusion detection. In: Daelemans, W., Goethals, B., Morik, K. (eds.) ECML PKDD 2008. LNCS (LNAI), vol. 5212, pp. 613–627. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-87481-2_40

    Chapter  Google Scholar 

  4. Xu, J., Shelton, C.R.: Intrusion detection using continuous time Bayesian networks. J. Artif. Intell. Res. 39, 745–774 (2010)

    MathSciNet  MATH  Google Scholar 

  5. Gatti, E., Luciani, D., Stella, F.: A continuous time Bayesian network model for cardiogenic heart failure. Flex. Serv, Manuf. J. 24(4), 496–515 (2012)

    Article  Google Scholar 

  6. Liu, M., Hommersom, A., van der Heijden, M., Lucas, P.J.F.: Hybrid time Bayesian networks. Int. J. Approximate Reasoning 80, 460–474 (2017)

    Article  MathSciNet  Google Scholar 

  7. Acerbi, E., Viganò, E., Poidinger, M., Mortellaro, A., Zelante, T., Stella, F.: Continuous time Bayesian networks identify Prdm1 as a negative regulator of TH17 cell differentiation in humans. Scientific reports 6 (2016)

    Google Scholar 

  8. Angus, I.: An introduction to Erlang B and Erlang C. Telemanagement 187, 6–8 (2001)

    Google Scholar 

  9. Nodelman, U., Horvitz, E.: Continuous time Bayesian networks for inferring users’ presence and activities with extensions for modeling and evaluation. Microsoft Research, July–August 2003

    Google Scholar 

  10. Gopalratnam, K., Kautz, H., Weld, D.S.: Extending continuous time Bayesian networks. In: Proceedings of the National Conference on Artificial Intelligence, vol. 20, p. 981. AAAI Press, MIT Press; 1999, Menlo Park, Cambridge, London (2005)

    Google Scholar 

  11. Nodelman, U., Shelton, C.R., Kollerthu, D.: Expectation maximization and complex duration distributions for continuous time Bayesian networks. In: Proceedings of the Twenty-First International Conference on Uncertainty in Artificial Intelligence, pp. 421–430 (2005)

    Google Scholar 

  12. Nodelman, U., Shelton, C.R., Koller, D.: Continuous time Bayesian networks. In: Proceedings of the Eighteenth Conference on Uncertainty in Artificial Intelligence, pp. 378–387 (2002)

    Google Scholar 

  13. Verbelen, R.: Phase-type distributions & mixtures of Erlangs (2013)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Radboud University, ICIS, Nijmegen, The Netherlands

    Manxia Liu, Arjen Hommersom & Peter J. F. Lucas

  2. Open University of the Netherlands, Heerlen, The Netherlands

    Arjen Hommersom

  3. Leiden University, LIACS, Leiden, The Netherlands

    Peter J. F. Lucas

  4. University of Porto, CINTESIS, Porto, Portugal

    Manxia Liu

  5. University of Milano-Bicocca, Milan, Italy

    Fabio Stella

Authors
  1. Manxia Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Fabio Stella
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Arjen Hommersom
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Peter J. F. Lucas
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Manxia Liu .

Editor information

Editors and Affiliations

  1. Universidad de Cádiz, Cádiz, Cadiz, Spain

    Jesús Medina

  2. Universidad de Málaga, Málaga, Málaga, Spain

    Manuel Ojeda-Aciego

  3. Universidad de Granada, Granada, Spain

    José Luis Verdegay

  4. Institute for Research and Applications, University of Ostrava, Ostrava, Czech Republic

    Irina Perfilieva

  5. LIP6, Université Pierre et Marie Curie, CNRS, Paris, France

    Bernadette Bouchon-Meunier

  6. Iona College, New Rochelle, New York, USA

    Ronald R. Yager

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG, part of Springer Nature

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Liu, M., Stella, F., Hommersom, A., Lucas, P.J.F. (2018). Representing Hypoexponential Distributions in Continuous Time Bayesian Networks. In: Medina, J., Ojeda-Aciego, M., Verdegay, J., Perfilieva, I., Bouchon-Meunier, B., Yager, R. (eds) Information Processing and Management of Uncertainty in Knowledge-Based Systems. Applications. IPMU 2018. Communications in Computer and Information Science, vol 855. Springer, Cham. https://doi.org/10.1007/978-3-319-91479-4_47

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-91479-4_47

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-91478-7

  • Online ISBN: 978-3-319-91479-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation