Mean Field Variational Approximation for Continuous-Time Bayesian Networks

Ido Cohn, Tal El-hay, Nir Friedman, Raz Kupferman
Proceedings of the 25th Conference on Uncertainty in Artificial Intelligence, PMLR R7:91-100, 2009.

Abstract

Continuous-time Bayesian networks is a natural structured representation language for multicomponent stochastic processes that evolve continuously over time. Despite the compact representation, inference in such models is intractable even in relatively simple structured networks. Here we introduce a mean field variational approximation in which we use a product of inhomogeneous Markov processes to approximate a distribution over trajectories. This variational approach leads to a globally consistent distribution, which can be efficiently queried. Additionally, it provides a lower bound on the probability of observations, thus making it attractive for learning tasks. We provide the theoretical foundations for the approximation, an efficient implementation that exploits the wide range of highly optimized ordinary differential equations (ODE) solvers, experimentally explore characterizations of processes for which this approximation is suitable, and show applications to a large-scale realworld inference problem.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR7-cohn09a, title = {Mean Field Variational Approximation for Continuous-Time {B}ayesian Networks}, author = {Cohn, Ido and El-hay, Tal and Friedman, Nir and Kupferman, Raz}, booktitle = {Proceedings of the 25th Conference on Uncertainty in Artificial Intelligence}, pages = {91--100}, year = {2009}, editor = {Bilmes, Jeff and Ng, Andrew Y.}, volume = {R7}, series = {Proceedings of Machine Learning Research}, month = {18--21 Jun}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r7/main/assets/cohn09a/cohn09a.pdf}, url = {https://proceedings.mlr.press/r7/cohn09a.html}, abstract = {Continuous-time Bayesian networks is a natural structured representation language for multicomponent stochastic processes that evolve continuously over time. Despite the compact representation, inference in such models is intractable even in relatively simple structured networks. Here we introduce a mean field variational approximation in which we use a product of inhomogeneous Markov processes to approximate a distribution over trajectories. This variational approach leads to a globally consistent distribution, which can be efficiently queried. Additionally, it provides a lower bound on the probability of observations, thus making it attractive for learning tasks. We provide the theoretical foundations for the approximation, an efficient implementation that exploits the wide range of highly optimized ordinary differential equations (ODE) solvers, experimentally explore characterizations of processes for which this approximation is suitable, and show applications to a large-scale realworld inference problem.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Mean Field Variational Approximation for Continuous-Time Bayesian Networks %A Ido Cohn %A Tal El-hay %A Nir Friedman %A Raz Kupferman %B Proceedings of the 25th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2009 %E Jeff Bilmes %E Andrew Y. Ng %F pmlr-vR7-cohn09a %I PMLR %P 91--100 %U https://proceedings.mlr.press/r7/cohn09a.html %V R7 %X Continuous-time Bayesian networks is a natural structured representation language for multicomponent stochastic processes that evolve continuously over time. Despite the compact representation, inference in such models is intractable even in relatively simple structured networks. Here we introduce a mean field variational approximation in which we use a product of inhomogeneous Markov processes to approximate a distribution over trajectories. This variational approach leads to a globally consistent distribution, which can be efficiently queried. Additionally, it provides a lower bound on the probability of observations, thus making it attractive for learning tasks. We provide the theoretical foundations for the approximation, an efficient implementation that exploits the wide range of highly optimized ordinary differential equations (ODE) solvers, experimentally explore characterizations of processes for which this approximation is suitable, and show applications to a large-scale realworld inference problem. %Z Reissued by PMLR on 04 October 2026.
APA
Cohn, I., El-hay, T., Friedman, N. & Kupferman, R.. (2009). Mean Field Variational Approximation for Continuous-Time Bayesian Networks. Proceedings of the 25th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R7:91-100 Available from https://proceedings.mlr.press/r7/cohn09a.html. Reissued by PMLR on 04 October 2026.

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