Improved Mean and Variance Approximations for Belief Net Response via Network Doubling

Peter Hooper, Yasin Abbasi-Yadkori, Bret Hoehn, Russell Greiner
Proceedings of the 25th Conference on Uncertainty in Artificial Intelligence, PMLR R7:232-239, 2009.

Abstract

A Bayesian belief network models a joint distribution with an directed acyclic graph representing dependencies among variables and network parameters characterizing con- ditional distributions. The parameters are viewed as random variables to quantify un- certainty about their values. Belief nets are used to compute responses to queries; i.e., conditional probabilities of interest. A query is a function of the parameters, hence a ran- dom variable. Van Allen et al. (2001, 2008) showed how to quantify uncertainty about a query via a delta method approximation of its variance. We develop more accurate ap- proximations for both query mean and vari- ance. The key idea is to extend the query mean approximation to a “doubled network” involving two independent replicates. Our method assumes complete data and can be applied to discrete, continuous, and hybrid networks (provided discrete variables have only discrete parents). We analyze several improvements, and provide empirical studies to demonstrate their effectiveness.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR7-hooper09a, title = {Improved Mean and Variance Approximations for Belief Net Response via Network Doubling}, author = {Hooper, Peter and Abbasi-Yadkori, Yasin and Hoehn, Bret and Greiner, Russell}, booktitle = {Proceedings of the 25th Conference on Uncertainty in Artificial Intelligence}, pages = {232--239}, 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/hooper09a/hooper09a.pdf}, url = {https://proceedings.mlr.press/r7/hooper09a.html}, abstract = {A Bayesian belief network models a joint distribution with an directed acyclic graph representing dependencies among variables and network parameters characterizing con- ditional distributions. The parameters are viewed as random variables to quantify un- certainty about their values. Belief nets are used to compute responses to queries; i.e., conditional probabilities of interest. A query is a function of the parameters, hence a ran- dom variable. Van Allen et al. (2001, 2008) showed how to quantify uncertainty about a query via a delta method approximation of its variance. We develop more accurate ap- proximations for both query mean and vari- ance. The key idea is to extend the query mean approximation to a “doubled network” involving two independent replicates. Our method assumes complete data and can be applied to discrete, continuous, and hybrid networks (provided discrete variables have only discrete parents). We analyze several improvements, and provide empirical studies to demonstrate their effectiveness.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Improved Mean and Variance Approximations for Belief Net Response via Network Doubling %A Peter Hooper %A Yasin Abbasi-Yadkori %A Bret Hoehn %A Russell Greiner %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-hooper09a %I PMLR %P 232--239 %U https://proceedings.mlr.press/r7/hooper09a.html %V R7 %X A Bayesian belief network models a joint distribution with an directed acyclic graph representing dependencies among variables and network parameters characterizing con- ditional distributions. The parameters are viewed as random variables to quantify un- certainty about their values. Belief nets are used to compute responses to queries; i.e., conditional probabilities of interest. A query is a function of the parameters, hence a ran- dom variable. Van Allen et al. (2001, 2008) showed how to quantify uncertainty about a query via a delta method approximation of its variance. We develop more accurate ap- proximations for both query mean and vari- ance. The key idea is to extend the query mean approximation to a “doubled network” involving two independent replicates. Our method assumes complete data and can be applied to discrete, continuous, and hybrid networks (provided discrete variables have only discrete parents). We analyze several improvements, and provide empirical studies to demonstrate their effectiveness. %Z Reissued by PMLR on 04 October 2026.
APA
Hooper, P., Abbasi-Yadkori, Y., Hoehn, B. & Greiner, R.. (2009). Improved Mean and Variance Approximations for Belief Net Response via Network Doubling. Proceedings of the 25th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R7:232-239 Available from https://proceedings.mlr.press/r7/hooper09a.html. Reissued by PMLR on 04 October 2026.

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