Lower Bound Bayesian Networks - Efficient Inference of Lower Bounds on Probability Distributions

Daniel Andrade, Bernhard Sick
Proceedings of the 25th Conference on Uncertainty in Artificial Intelligence, PMLR R7:10-18, 2009.

Abstract

We present a new method to propagate lower bounds on conditional probability distribu- tions in conventional Bayesian networks. Our method guarantees to provide outer approx- imations of the exact lower bounds. A key advantage is that we can use any available algorithms and tools for Bayesian networks in order to represent and infer lower bounds. This new method yields results that are prov- able exact for trees with binary variables, and results which are competitive to existing ap- proximations in credal networks for all other network structures. Our method is not lim- ited to a specific kind of network structure. Basically, it is also not restricted to a specific kind of inference, but we restrict our analysis to prognostic inference in this article. The computational complexity is superior to that of other existing approaches.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR7-andrade09a, title = {Lower Bound {B}ayesian Networks - Efficient Inference of Lower Bounds on Probability Distributions}, author = {Andrade, Daniel and Sick, Bernhard}, booktitle = {Proceedings of the 25th Conference on Uncertainty in Artificial Intelligence}, pages = {10--18}, 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/andrade09a/andrade09a.pdf}, url = {https://proceedings.mlr.press/r7/andrade09a.html}, abstract = {We present a new method to propagate lower bounds on conditional probability distribu- tions in conventional Bayesian networks. Our method guarantees to provide outer approx- imations of the exact lower bounds. A key advantage is that we can use any available algorithms and tools for Bayesian networks in order to represent and infer lower bounds. This new method yields results that are prov- able exact for trees with binary variables, and results which are competitive to existing ap- proximations in credal networks for all other network structures. Our method is not lim- ited to a specific kind of network structure. Basically, it is also not restricted to a specific kind of inference, but we restrict our analysis to prognostic inference in this article. The computational complexity is superior to that of other existing approaches.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Lower Bound Bayesian Networks - Efficient Inference of Lower Bounds on Probability Distributions %A Daniel Andrade %A Bernhard Sick %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-andrade09a %I PMLR %P 10--18 %U https://proceedings.mlr.press/r7/andrade09a.html %V R7 %X We present a new method to propagate lower bounds on conditional probability distribu- tions in conventional Bayesian networks. Our method guarantees to provide outer approx- imations of the exact lower bounds. A key advantage is that we can use any available algorithms and tools for Bayesian networks in order to represent and infer lower bounds. This new method yields results that are prov- able exact for trees with binary variables, and results which are competitive to existing ap- proximations in credal networks for all other network structures. Our method is not lim- ited to a specific kind of network structure. Basically, it is also not restricted to a specific kind of inference, but we restrict our analysis to prognostic inference in this article. The computational complexity is superior to that of other existing approaches. %Z Reissued by PMLR on 04 October 2026.
APA
Andrade, D. & Sick, B.. (2009). Lower Bound Bayesian Networks - Efficient Inference of Lower Bounds on Probability Distributions. Proceedings of the 25th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R7:10-18 Available from https://proceedings.mlr.press/r7/andrade09a.html. Reissued by PMLR on 04 October 2026.

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