Visualizing the Elimination of Arbitrary Variables in Bayesian Networks as Compound Bayesian Networks

Cory Butz, Brandon Sasyniuk
Proceedings of the The 39th Canadian Conference on Artificial Intelligence, PMLR 318:1116-1121, 2026.

Abstract

Research on Bayesian network (BN) inference continues to this day along two main fronts: scalable inference and deepening our understanding of the semantics of intermediate inference steps. In this theoretical paper, falling in the latter direction, we give a novel graphical representation of eliminating arbitrary variables from discrete BNs. This includes methods that represent both multiplication and marginalization operations and involves extending classical BNs to compound BNs. Our main result formally establishes a one-to-one correspondence between intermediate numeric factorizations and graphical representations.

Cite this Paper

BibTeX
@InProceedings{pmlr-v318-butz26a, title = {Visualizing the Elimination of Arbitrary Variables in Bayesian Networks as Compound Bayesian Networks}, author = {Butz, Cory and Sasyniuk, Brandon}, booktitle = {Proceedings of the The 39th Canadian Conference on Artificial Intelligence}, pages = {1116--1121}, year = {2026}, editor = {Bouzar-Benlabiod, Lydia and Leung, Carson}, volume = {318}, series = {Proceedings of Machine Learning Research}, month = {25--29 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v318/main/assets/butz26a/butz26a.pdf}, url = {https://proceedings.mlr.press/v318/butz26a.html}, abstract = {Research on Bayesian network (BN) inference continues to this day along two main fronts: scalable inference and deepening our understanding of the semantics of intermediate inference steps. In this theoretical paper, falling in the latter direction, we give a novel graphical representation of eliminating arbitrary variables from discrete BNs. This includes methods that represent both multiplication and marginalization operations and involves extending classical BNs to compound BNs. Our main result formally establishes a one-to-one correspondence between intermediate numeric factorizations and graphical representations.} }
Endnote
%0 Conference Paper %T Visualizing the Elimination of Arbitrary Variables in Bayesian Networks as Compound Bayesian Networks %A Cory Butz %A Brandon Sasyniuk %B Proceedings of the The 39th Canadian Conference on Artificial Intelligence %C Proceedings of Machine Learning Research %D 2026 %E Lydia Bouzar-Benlabiod %E Carson Leung %F pmlr-v318-butz26a %I PMLR %P 1116--1121 %U https://proceedings.mlr.press/v318/butz26a.html %V 318 %X Research on Bayesian network (BN) inference continues to this day along two main fronts: scalable inference and deepening our understanding of the semantics of intermediate inference steps. In this theoretical paper, falling in the latter direction, we give a novel graphical representation of eliminating arbitrary variables from discrete BNs. This includes methods that represent both multiplication and marginalization operations and involves extending classical BNs to compound BNs. Our main result formally establishes a one-to-one correspondence between intermediate numeric factorizations and graphical representations.
APA
Butz, C. & Sasyniuk, B.. (2026). Visualizing the Elimination of Arbitrary Variables in Bayesian Networks as Compound Bayesian Networks. Proceedings of the The 39th Canadian Conference on Artificial Intelligence, in Proceedings of Machine Learning Research 318:1116-1121 Available from https://proceedings.mlr.press/v318/butz26a.html.

Related Material