Representing Hypoexponential Distributions in Continuous Time Bayesian Networks

Manxia Liu, Fabio Stella, Arjen Hommersom, Peter J. F. Lucas

Research output: Chapter in Book/Report/Conference proceedingConference article in proceedingAcademicpeer-review

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.
Original languageEnglish
Title of host publicationInformation Processing and Management of Uncertainty in Knowledge-Based Systems. Applications
EditorsJesús Medina, Manuel Ojeda-Aciego, José Luis Verdegay, Irina Perfilieva, Bernadette Bouchon-Meunier, Ronald R. Yager
Place of PublicationCham
PublisherSpringer International Publishing AG
Pages565-577
Number of pages13
Volume855
ISBN (Print)978-3-319-91479-4
DOIs
Publication statusPublished - 2018
EventInternational Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems: Information Processing and Management of Uncertainty in Knowledge-Based Systems. Applications - Cádiz, Spain
Duration: 11 Jun 201815 Jun 2018
https://link.springer.com/book/10.1007/978-3-319-91473-2

Publication series

NameCommunications in Computer and Information Science
PublisherSpringer
Volume855

Conference

ConferenceInternational Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems
Abbreviated titleIPMU 2018
CountrySpain
CityCádiz
Period11/06/1815/06/18
Internet address

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Bayesian networks
Random processes
Parameter estimation
Data storage equipment

Cite this

Liu, M., Stella, F., Hommersom, A., & Lucas, P. J. F. (2018). Representing Hypoexponential Distributions in Continuous Time Bayesian Networks. In J. Medina, M. Ojeda-Aciego, J. L. Verdegay, I. Perfilieva, B. Bouchon-Meunier, & R. R. Yager (Eds.), Information Processing and Management of Uncertainty in Knowledge-Based Systems. Applications (Vol. 855, pp. 565-577). (Communications in Computer and Information Science; Vol. 855). Cham: Springer International Publishing AG. https://doi.org/10.1007/978-3-319-91479-4_47
Liu, Manxia ; Stella, Fabio ; Hommersom, Arjen ; Lucas, Peter J. F. / Representing Hypoexponential Distributions in Continuous Time Bayesian Networks. Information Processing and Management of Uncertainty in Knowledge-Based Systems. Applications. editor / Jesús Medina ; Manuel Ojeda-Aciego ; José Luis Verdegay ; Irina Perfilieva ; Bernadette Bouchon-Meunier ; Ronald R. Yager. Vol. 855 Cham : Springer International Publishing AG, 2018. pp. 565-577 (Communications in Computer and Information Science).
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title = "Representing Hypoexponential Distributions in Continuous Time Bayesian Networks",
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Liu, M, Stella, F, Hommersom, A & Lucas, PJF 2018, Representing Hypoexponential Distributions in Continuous Time Bayesian Networks. in J Medina, M Ojeda-Aciego, JL Verdegay, I Perfilieva, B Bouchon-Meunier & RR Yager (eds), Information Processing and Management of Uncertainty in Knowledge-Based Systems. Applications. vol. 855, Communications in Computer and Information Science, vol. 855, Springer International Publishing AG, Cham, pp. 565-577, International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, Cádiz, Spain, 11/06/18. https://doi.org/10.1007/978-3-319-91479-4_47

Representing Hypoexponential Distributions in Continuous Time Bayesian Networks. / Liu, Manxia; Stella, Fabio; Hommersom, Arjen; Lucas, Peter J. F.

Information Processing and Management of Uncertainty in Knowledge-Based Systems. Applications. ed. / Jesús Medina; Manuel Ojeda-Aciego; José Luis Verdegay; Irina Perfilieva; Bernadette Bouchon-Meunier; Ronald R. Yager. Vol. 855 Cham : Springer International Publishing AG, 2018. p. 565-577 (Communications in Computer and Information Science; Vol. 855).

Research output: Chapter in Book/Report/Conference proceedingConference article in proceedingAcademicpeer-review

TY - GEN

T1 - Representing Hypoexponential Distributions in Continuous Time Bayesian Networks

AU - Liu, Manxia

AU - Stella, Fabio

AU - Hommersom, Arjen

AU - Lucas, Peter J. F.

PY - 2018

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N2 - 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.

AB - 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.

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Liu M, Stella F, Hommersom A, Lucas PJF. Representing Hypoexponential Distributions in Continuous Time Bayesian Networks. In Medina J, Ojeda-Aciego M, Verdegay JL, Perfilieva I, Bouchon-Meunier B, Yager RR, editors, Information Processing and Management of Uncertainty in Knowledge-Based Systems. Applications. Vol. 855. Cham: Springer International Publishing AG. 2018. p. 565-577. (Communications in Computer and Information Science). https://doi.org/10.1007/978-3-319-91479-4_47