The Long-Run Behavior of Continuous Time Bayesian Networks

Liessman Sturlaugson Montana State University, John Sheppard Montana State University
Proceedings of the 31st Conference on Uncertainty in Artificial Intelligence, PMLR R13:29-38, 2015.

Abstract

The continuous time Bayesian network (CTBN) is a temporal model consisting of interdependent continuous time Markov chains (Markov processes). One common analysis performed on Markov processes is determining their long-run behavior, such as their stationary distributions. While the CTBN can be transformed into a single Markov process of all nodes’ state combinations, the size is exponential in the number of nodes, making traditional long-run analysis intractable. To address this, we show how to perform "long-run" node marginalization that removes a node’s conditional dependence while preserving its long-run behavior. This allows long-run analysis of CTBNs to be performed in a top-down process without dealing with the entire network all at once.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR13-university15a, title = {The Long-Run Behavior of Continuous Time {B}ayesian Networks}, author = {University, Liessman Sturlaugson Montana State and University, John Sheppard Montana State}, booktitle = {Proceedings of the 31st Conference on Uncertainty in Artificial Intelligence}, pages = {29--38}, year = {2015}, editor = {Meila, Marina and Heskes, Tom}, volume = {R13}, series = {Proceedings of Machine Learning Research}, month = {12--16 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r13/main/assets/university15a/university15a.pdf}, url = {https://proceedings.mlr.press/r13/university15a.html}, abstract = {The continuous time Bayesian network (CTBN) is a temporal model consisting of interdependent continuous time Markov chains (Markov processes). One common analysis performed on Markov processes is determining their long-run behavior, such as their stationary distributions. While the CTBN can be transformed into a single Markov process of all nodes’ state combinations, the size is exponential in the number of nodes, making traditional long-run analysis intractable. To address this, we show how to perform "long-run" node marginalization that removes a node’s conditional dependence while preserving its long-run behavior. This allows long-run analysis of CTBNs to be performed in a top-down process without dealing with the entire network all at once.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T The Long-Run Behavior of Continuous Time Bayesian Networks %A Liessman Sturlaugson Montana State University %A John Sheppard Montana State University %B Proceedings of the 31st Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2015 %E Marina Meila %E Tom Heskes %F pmlr-vR13-university15a %I PMLR %P 29--38 %U https://proceedings.mlr.press/r13/university15a.html %V R13 %X The continuous time Bayesian network (CTBN) is a temporal model consisting of interdependent continuous time Markov chains (Markov processes). One common analysis performed on Markov processes is determining their long-run behavior, such as their stationary distributions. While the CTBN can be transformed into a single Markov process of all nodes’ state combinations, the size is exponential in the number of nodes, making traditional long-run analysis intractable. To address this, we show how to perform "long-run" node marginalization that removes a node’s conditional dependence while preserving its long-run behavior. This allows long-run analysis of CTBNs to be performed in a top-down process without dealing with the entire network all at once. %Z Reissued by PMLR on 04 October 2026.
APA
University, L.S.M.S. & University, J.S.M.S.. (2015). The Long-Run Behavior of Continuous Time Bayesian Networks. Proceedings of the 31st Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R13:29-38 Available from https://proceedings.mlr.press/r13/university15a.html. Reissued by PMLR on 04 October 2026.

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