Safe Inverse Marginalization in Bayesian Networks

Cory Butz, Alejandro Santoscoy-Rivero, Silja Renooij, Johan Kwisthout
Proceedings of the 13th International Conference on Probabilistic Graphical Models, PMLR 343:127-139, 2026.

Abstract

Safe inverse marginalization (SIM) was recently proposed for augmenting a Bayesian network with new discrete variables such that their marginalization exactly recovers the original network, allowing re-certification to focus exclusively on the new variables. Graph-safe marginalization (GSM) was introduced to describe when marginalizing the new variable yields a distribution that factorizes according to the original DAG, with constraint-optimization methods proposed for constructing new conditional probability tables (CPTs). In this paper, we first show that arc-reversal without fill-in (AR-NFI) strictly subsumes GSM as a sufficient graphical condition for SIM. We then propose constructing new CPTs via unity-potential expansion (UPE) rather than optimization. AR-NFI combined with UPE provides a concrete structural route to SIM. More fundamentally, UPE recovers the original Bayesian network exactly by reconstructing its factorization, from which the original DAG is uniquely identified. Hence, UPE alone guarantees SIM, establishing that neither AR-NFI nor GSM is necessary. Taken together, these results show that SIM is fundamentally a parametric property, with structural conditions characterizing only when recovery can be realized via structure-preserving transformations.

Cite this Paper

BibTeX
@InProceedings{pmlr-v343-butz26a, title = {Safe Inverse Marginalization in {Bayesian} Networks}, author = {Butz, Cory and Santoscoy-Rivero, Alejandro and Renooij, Silja and Kwisthout, Johan}, booktitle = {Proceedings of the 13th International Conference on Probabilistic Graphical Models}, pages = {127--139}, year = {2026}, editor = {Camps-Valls, Gustau and Leonelli, Manuele and Varando, Gherardo}, volume = {343}, series = {Proceedings of Machine Learning Research}, month = {09--11 Sep}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v343/main/assets/butz26a/butz26a.pdf}, url = {https://proceedings.mlr.press/v343/butz26a.html}, abstract = {Safe inverse marginalization (SIM) was recently proposed for augmenting a Bayesian network with new discrete variables such that their marginalization exactly recovers the original network, allowing re-certification to focus exclusively on the new variables. Graph-safe marginalization (GSM) was introduced to describe when marginalizing the new variable yields a distribution that factorizes according to the original DAG, with constraint-optimization methods proposed for constructing new conditional probability tables (CPTs). In this paper, we first show that arc-reversal without fill-in (AR-NFI) strictly subsumes GSM as a sufficient graphical condition for SIM. We then propose constructing new CPTs via unity-potential expansion (UPE) rather than optimization. AR-NFI combined with UPE provides a concrete structural route to SIM. More fundamentally, UPE recovers the original Bayesian network exactly by reconstructing its factorization, from which the original DAG is uniquely identified. Hence, UPE alone guarantees SIM, establishing that neither AR-NFI nor GSM is necessary. Taken together, these results show that SIM is fundamentally a parametric property, with structural conditions characterizing only when recovery can be realized via structure-preserving transformations.} }
Endnote
%0 Conference Paper %T Safe Inverse Marginalization in Bayesian Networks %A Cory Butz %A Alejandro Santoscoy-Rivero %A Silja Renooij %A Johan Kwisthout %B Proceedings of the 13th International Conference on Probabilistic Graphical Models %C Proceedings of Machine Learning Research %D 2026 %E Gustau Camps-Valls %E Manuele Leonelli %E Gherardo Varando %F pmlr-v343-butz26a %I PMLR %P 127--139 %U https://proceedings.mlr.press/v343/butz26a.html %V 343 %X Safe inverse marginalization (SIM) was recently proposed for augmenting a Bayesian network with new discrete variables such that their marginalization exactly recovers the original network, allowing re-certification to focus exclusively on the new variables. Graph-safe marginalization (GSM) was introduced to describe when marginalizing the new variable yields a distribution that factorizes according to the original DAG, with constraint-optimization methods proposed for constructing new conditional probability tables (CPTs). In this paper, we first show that arc-reversal without fill-in (AR-NFI) strictly subsumes GSM as a sufficient graphical condition for SIM. We then propose constructing new CPTs via unity-potential expansion (UPE) rather than optimization. AR-NFI combined with UPE provides a concrete structural route to SIM. More fundamentally, UPE recovers the original Bayesian network exactly by reconstructing its factorization, from which the original DAG is uniquely identified. Hence, UPE alone guarantees SIM, establishing that neither AR-NFI nor GSM is necessary. Taken together, these results show that SIM is fundamentally a parametric property, with structural conditions characterizing only when recovery can be realized via structure-preserving transformations.
APA
Butz, C., Santoscoy-Rivero, A., Renooij, S. & Kwisthout, J.. (2026). Safe Inverse Marginalization in Bayesian Networks. Proceedings of the 13th International Conference on Probabilistic Graphical Models, in Proceedings of Machine Learning Research 343:127-139 Available from https://proceedings.mlr.press/v343/butz26a.html.

Related Material