Making Continuous Time Bayesian Networks More Flexible

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

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

Abstract

The time duration in continuous time Bayesian networks, i.e., the time that a variable stays in a state until it transitions to another state, follows an exponential distribution. The exponential distribution is widely applied to describe the waiting time between events in a Poisson process, which describes the distribution of the number of events in one unit of time. This distribution is parameterized by a single rate and has mode zero, implying that the highest probability mass for events to happen is attributed to the earliest times. To describe biological processes, the exponential distribution is not always natural. For example, if the immune system has not encountered a pathogen before, it most likely responds to a viral infection after a few days, rather than immediately. In this paper, we generalize our recently proposed hypoexponential continuous time Bayesian networks, by allowing any number of hypoexponential variables, i.e., variables having a hypoexponential time duration distribution. In addition, we propose and compare two learning methods to estimate parameters for the generalized models. Finally, the practical value of the generalized models is demonstrated by means of a realistic medical problem.
Original languageEnglish
Title of host publicationProceedings of the Ninth International Conference on Probabilistic Graphical Models
EditorsVáclav Kratochvíl, Milan Studený
Place of PublicationPrague, Czech Republic
PublisherPMLR
Pages237-248
Number of pages12
Volume72
Publication statusPublished - 1 Nov 2018

Publication series

NameProceedings of Machine Learning Research
PublisherPMLR

Fingerprint

Bayesian Networks
Continuous Time
Exponential distribution
Unit of time
Immune System
Poisson process
Waiting Time
Infection
Immediately
Likely
Generalise
Zero
Model
Estimate

Cite this

Liu, M., Stella, F., Hommersom, A., & Lucas, P. J. F. (2018). Making Continuous Time Bayesian Networks More Flexible. In V. Kratochvíl, & M. Studený (Eds.), Proceedings of the Ninth International Conference on Probabilistic Graphical Models (Vol. 72, pp. 237-248). (Proceedings of Machine Learning Research). Prague, Czech Republic: PMLR.
Liu, Manxia ; Stella, Fabio ; Hommersom, Arjen ; Lucas, Peter J.F. / Making Continuous Time Bayesian Networks More Flexible. Proceedings of the Ninth International Conference on Probabilistic Graphical Models. editor / Václav Kratochvíl ; Milan Studený. Vol. 72 Prague, Czech Republic : PMLR, 2018. pp. 237-248 (Proceedings of Machine Learning Research).
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Liu, M, Stella, F, Hommersom, A & Lucas, PJF 2018, Making Continuous Time Bayesian Networks More Flexible. in V Kratochvíl & M Studený (eds), Proceedings of the Ninth International Conference on Probabilistic Graphical Models. vol. 72, Proceedings of Machine Learning Research, PMLR, Prague, Czech Republic, pp. 237-248.

Making Continuous Time Bayesian Networks More Flexible. / Liu, Manxia; Stella, Fabio; Hommersom, Arjen; Lucas, Peter J.F.

Proceedings of the Ninth International Conference on Probabilistic Graphical Models. ed. / Václav Kratochvíl; Milan Studený. Vol. 72 Prague, Czech Republic : PMLR, 2018. p. 237-248 (Proceedings of Machine Learning Research).

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

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AB - The time duration in continuous time Bayesian networks, i.e., the time that a variable stays in a state until it transitions to another state, follows an exponential distribution. The exponential distribution is widely applied to describe the waiting time between events in a Poisson process, which describes the distribution of the number of events in one unit of time. This distribution is parameterized by a single rate and has mode zero, implying that the highest probability mass for events to happen is attributed to the earliest times. To describe biological processes, the exponential distribution is not always natural. For example, if the immune system has not encountered a pathogen before, it most likely responds to a viral infection after a few days, rather than immediately. In this paper, we generalize our recently proposed hypoexponential continuous time Bayesian networks, by allowing any number of hypoexponential variables, i.e., variables having a hypoexponential time duration distribution. In addition, we propose and compare two learning methods to estimate parameters for the generalized models. Finally, the practical value of the generalized models is demonstrated by means of a realistic medical problem.

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Liu M, Stella F, Hommersom A, Lucas PJF. Making Continuous Time Bayesian Networks More Flexible. In Kratochvíl V, Studený M, editors, Proceedings of the Ninth International Conference on Probabilistic Graphical Models. Vol. 72. Prague, Czech Republic: PMLR. 2018. p. 237-248. (Proceedings of Machine Learning Research).