Table-based Probability Trees: a New Hybrid Potential Representation for Probabilistic Inference in Graphical Models

Francisco Bonillo, Andrés Cano, Manuel Gómez-Olmedo, Serafín Moral
Proceedings of the 13th International Conference on Probabilistic Graphical Models, PMLR 343:73-91, 2026.

Abstract

Probabilistic inference in graphical models, such as Bayesian and Markov networks, has traditionally relied either on tabular representations of conditional probability distributions (CPDs) or on probability trees. Tables offer straightforward marginalization and combination at the cost of exponential memory in the number of variables, while pure probability trees exploit zero entries and repeated subdistributions to achieve compact representations, but their arithmetic is subject to structural overhead when non-zero subtrees dominate. This paper introduces Table-based Probability Tree (TBPT) potentials as a hybrid potential representation that unifies both paradigms within a single, flexible data structure: a rooted ordered tree in which internal nodes are discrete random-variable selectors as usual, and terminal nodes are not only scalar values, but also table nodes storing multidimensional arrays covering the variables below a given branching point. After formalizing the operations to be applied in these potentials, empirical evaluation on standard UAI competition benchmarks is conducted by using the TBPT structure running exact inference via variable elimination (VE). This data structure is useful in cases in which potential have a high zero percentage. We propose to compute the total set of zeros in advance with a previous Boolean propagation.

Cite this Paper

BibTeX
@InProceedings{pmlr-v343-bonillo26a, title = {Table-based Probability Trees: a New Hybrid Potential Representation for Probabilistic Inference in Graphical Models}, author = {Bonillo, Francisco and Cano, Andr{\'e}s and G{\'o}mez-Olmedo, Manuel and Moral, Seraf{\'i}n}, booktitle = {Proceedings of the 13th International Conference on Probabilistic Graphical Models}, pages = {73--91}, 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/bonillo26a/bonillo26a.pdf}, url = {https://proceedings.mlr.press/v343/bonillo26a.html}, abstract = {Probabilistic inference in graphical models, such as Bayesian and Markov networks, has traditionally relied either on tabular representations of conditional probability distributions (CPDs) or on probability trees. Tables offer straightforward marginalization and combination at the cost of exponential memory in the number of variables, while pure probability trees exploit zero entries and repeated subdistributions to achieve compact representations, but their arithmetic is subject to structural overhead when non-zero subtrees dominate. This paper introduces Table-based Probability Tree (TBPT) potentials as a hybrid potential representation that unifies both paradigms within a single, flexible data structure: a rooted ordered tree in which internal nodes are discrete random-variable selectors as usual, and terminal nodes are not only scalar values, but also table nodes storing multidimensional arrays covering the variables below a given branching point. After formalizing the operations to be applied in these potentials, empirical evaluation on standard UAI competition benchmarks is conducted by using the TBPT structure running exact inference via variable elimination (VE). This data structure is useful in cases in which potential have a high zero percentage. We propose to compute the total set of zeros in advance with a previous Boolean propagation.} }
Endnote
%0 Conference Paper %T Table-based Probability Trees: a New Hybrid Potential Representation for Probabilistic Inference in Graphical Models %A Francisco Bonillo %A Andrés Cano %A Manuel Gómez-Olmedo %A Serafín Moral %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-bonillo26a %I PMLR %P 73--91 %U https://proceedings.mlr.press/v343/bonillo26a.html %V 343 %X Probabilistic inference in graphical models, such as Bayesian and Markov networks, has traditionally relied either on tabular representations of conditional probability distributions (CPDs) or on probability trees. Tables offer straightforward marginalization and combination at the cost of exponential memory in the number of variables, while pure probability trees exploit zero entries and repeated subdistributions to achieve compact representations, but their arithmetic is subject to structural overhead when non-zero subtrees dominate. This paper introduces Table-based Probability Tree (TBPT) potentials as a hybrid potential representation that unifies both paradigms within a single, flexible data structure: a rooted ordered tree in which internal nodes are discrete random-variable selectors as usual, and terminal nodes are not only scalar values, but also table nodes storing multidimensional arrays covering the variables below a given branching point. After formalizing the operations to be applied in these potentials, empirical evaluation on standard UAI competition benchmarks is conducted by using the TBPT structure running exact inference via variable elimination (VE). This data structure is useful in cases in which potential have a high zero percentage. We propose to compute the total set of zeros in advance with a previous Boolean propagation.
APA
Bonillo, F., Cano, A., Gómez-Olmedo, M. & Moral, S.. (2026). Table-based Probability Trees: a New Hybrid Potential Representation for Probabilistic Inference in Graphical Models. Proceedings of the 13th International Conference on Probabilistic Graphical Models, in Proceedings of Machine Learning Research 343:73-91 Available from https://proceedings.mlr.press/v343/bonillo26a.html.

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