Learning Parameters of Hybrid Time Bayesian Networks

Manxia Liu, Arjen Hommersom, Maarten van der Heijden, Peter J.F. Lucas
; Proceedings of the Eighth International Conference on Probabilistic Graphical Models, PMLR 52:287-298, 2016.

Abstract

Time granularity is an important factor in characterizing dynamical systems. Hybrid time Bayesian networks model the dynamics of systems that contain both irregularly-timed variables and variables whose evolution is naturally described by discrete time. The former observations are modeled as variables in continuous-time manner and the latter are modeled by discrete-time random variables. We address the problem of learning parameters of hybrid time models from complete data where all the states are known at any time point, and from incomplete trajectories, where continuous-time variables are observed only at some time points. We show that for the complete case, the parameters can be estimated straightforwardly. When some continuous-time variables are (partially) unobserved, it becomes infeasible to learn the parameters in closed form. In that case, we propose to use Markov chain Monte Carlo sampling to estimate the posterior distribution over the parameters. We tested the approach on a number of hybrid time models where continuous-time variables are completely or partially observed, showing that close estimation of the original parameters can be recovered. A medical example is used to illustrate the learning parameters of hybrid time Bayesian networks.

Cite this Paper


BibTeX
@InProceedings{pmlr-v52-liu16, title = {Learning Parameters of Hybrid Time {B}ayesian Networks}, author = {Manxia Liu and Arjen Hommersom and Maarten van der Heijden and Peter J.F. Lucas}, booktitle = {Proceedings of the Eighth International Conference on Probabilistic Graphical Models}, pages = {287--298}, year = {2016}, editor = {Alessandro Antonucci and Giorgio Corani and Cassio Polpo Campos}}, volume = {52}, series = {Proceedings of Machine Learning Research}, address = {Lugano, Switzerland}, month = {06--09 Sep}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v52/liu16.pdf}, url = {http://proceedings.mlr.press/v52/liu16.html}, abstract = {Time granularity is an important factor in characterizing dynamical systems. Hybrid time Bayesian networks model the dynamics of systems that contain both irregularly-timed variables and variables whose evolution is naturally described by discrete time. The former observations are modeled as variables in continuous-time manner and the latter are modeled by discrete-time random variables. We address the problem of learning parameters of hybrid time models from complete data where all the states are known at any time point, and from incomplete trajectories, where continuous-time variables are observed only at some time points. We show that for the complete case, the parameters can be estimated straightforwardly. When some continuous-time variables are (partially) unobserved, it becomes infeasible to learn the parameters in closed form. In that case, we propose to use Markov chain Monte Carlo sampling to estimate the posterior distribution over the parameters. We tested the approach on a number of hybrid time models where continuous-time variables are completely or partially observed, showing that close estimation of the original parameters can be recovered. A medical example is used to illustrate the learning parameters of hybrid time Bayesian networks.} }
Endnote
%0 Conference Paper %T Learning Parameters of Hybrid Time Bayesian Networks %A Manxia Liu %A Arjen Hommersom %A Maarten van der Heijden %A Peter J.F. Lucas %B Proceedings of the Eighth International Conference on Probabilistic Graphical Models %C Proceedings of Machine Learning Research %D 2016 %E Alessandro Antonucci %E Giorgio Corani %E Cassio Polpo Campos} %F pmlr-v52-liu16 %I PMLR %J Proceedings of Machine Learning Research %P 287--298 %U http://proceedings.mlr.press %V 52 %W PMLR %X Time granularity is an important factor in characterizing dynamical systems. Hybrid time Bayesian networks model the dynamics of systems that contain both irregularly-timed variables and variables whose evolution is naturally described by discrete time. The former observations are modeled as variables in continuous-time manner and the latter are modeled by discrete-time random variables. We address the problem of learning parameters of hybrid time models from complete data where all the states are known at any time point, and from incomplete trajectories, where continuous-time variables are observed only at some time points. We show that for the complete case, the parameters can be estimated straightforwardly. When some continuous-time variables are (partially) unobserved, it becomes infeasible to learn the parameters in closed form. In that case, we propose to use Markov chain Monte Carlo sampling to estimate the posterior distribution over the parameters. We tested the approach on a number of hybrid time models where continuous-time variables are completely or partially observed, showing that close estimation of the original parameters can be recovered. A medical example is used to illustrate the learning parameters of hybrid time Bayesian networks.
RIS
TY - CPAPER TI - Learning Parameters of Hybrid Time Bayesian Networks AU - Manxia Liu AU - Arjen Hommersom AU - Maarten van der Heijden AU - Peter J.F. Lucas BT - Proceedings of the Eighth International Conference on Probabilistic Graphical Models PY - 2016/08/15 DA - 2016/08/15 ED - Alessandro Antonucci ED - Giorgio Corani ED - Cassio Polpo Campos} ID - pmlr-v52-liu16 PB - PMLR SP - 287 DP - PMLR EP - 298 L1 - http://proceedings.mlr.press/v52/liu16.pdf UR - http://proceedings.mlr.press/v52/liu16.html AB - Time granularity is an important factor in characterizing dynamical systems. Hybrid time Bayesian networks model the dynamics of systems that contain both irregularly-timed variables and variables whose evolution is naturally described by discrete time. The former observations are modeled as variables in continuous-time manner and the latter are modeled by discrete-time random variables. We address the problem of learning parameters of hybrid time models from complete data where all the states are known at any time point, and from incomplete trajectories, where continuous-time variables are observed only at some time points. We show that for the complete case, the parameters can be estimated straightforwardly. When some continuous-time variables are (partially) unobserved, it becomes infeasible to learn the parameters in closed form. In that case, we propose to use Markov chain Monte Carlo sampling to estimate the posterior distribution over the parameters. We tested the approach on a number of hybrid time models where continuous-time variables are completely or partially observed, showing that close estimation of the original parameters can be recovered. A medical example is used to illustrate the learning parameters of hybrid time Bayesian networks. ER -
APA
Liu, M., Hommersom, A., van der Heijden, M. & Lucas, P.J.. (2016). Learning Parameters of Hybrid Time Bayesian Networks. Proceedings of the Eighth International Conference on Probabilistic Graphical Models, in PMLR 52:287-298

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