A Stronger Calculus of Intervention for Max-Linear Bayesian Networks

Leon Sierau, Francesco Nowell, Nihat Ay
Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, PMLR 337:6342-6365, 2026.

Abstract

Max-linear {Bayesian} networks (MLBNs) are a novel class of directed acyclic graphical models which are of interest to statistics and data science due to their relevance to causality and probabilistic inference, particularly of extreme events. Interestingly, MLBNs encode strictly more conditional independence than general structural causal models. Because of this, MLBNs are {Markov} to a strengthening of the $d$-separation criterion called $\ast$-separation. As many tools for causal inference (most notably, Judea {Pearl}’s $do$-calculus) are based on $d$-separation, we address the natural question of whether assuming Markovianity to $\ast$-separation can lead to additional causal effect identifiability under intervention. We answer this question in the affirmative and develop a stronger version of the $do$-calculus rules for models which are {Markov} to $\ast$-separation. However, we note that restrictions inherent to the max-linear setting (in particular, that they give rise to non strictly positive joint probability distributions) mean that our calculus is only applicable to specific kinds of policy intervention.

Cite this Paper

BibTeX
@InProceedings{pmlr-v337-sierau26a, title = {A Stronger Calculus of Intervention for Max-Linear {Bayesian} Networks}, author = {Sierau, Leon and Nowell, Francesco and Ay, Nihat}, booktitle = {Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence}, pages = {6342--6365}, year = {2026}, editor = {Perković, Emilija and Malinsky, Daniel}, volume = {337}, series = {Proceedings of Machine Learning Research}, month = {17--21 Aug}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v337/main/assets/sierau26a/sierau26a.pdf}, url = {https://proceedings.mlr.press/v337/sierau26a.html}, abstract = {Max-linear {Bayesian} networks (MLBNs) are a novel class of directed acyclic graphical models which are of interest to statistics and data science due to their relevance to causality and probabilistic inference, particularly of extreme events. Interestingly, MLBNs encode strictly more conditional independence than general structural causal models. Because of this, MLBNs are {Markov} to a strengthening of the $d$-separation criterion called $\ast$-separation. As many tools for causal inference (most notably, Judea {Pearl}’s $do$-calculus) are based on $d$-separation, we address the natural question of whether assuming Markovianity to $\ast$-separation can lead to additional causal effect identifiability under intervention. We answer this question in the affirmative and develop a stronger version of the $do$-calculus rules for models which are {Markov} to $\ast$-separation. However, we note that restrictions inherent to the max-linear setting (in particular, that they give rise to non strictly positive joint probability distributions) mean that our calculus is only applicable to specific kinds of policy intervention.} }
Endnote
%0 Conference Paper %T A Stronger Calculus of Intervention for Max-Linear Bayesian Networks %A Leon Sierau %A Francesco Nowell %A Nihat Ay %B Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2026 %E Emilija Perković %E Daniel Malinsky %F pmlr-v337-sierau26a %I PMLR %P 6342--6365 %U https://proceedings.mlr.press/v337/sierau26a.html %V 337 %X Max-linear {Bayesian} networks (MLBNs) are a novel class of directed acyclic graphical models which are of interest to statistics and data science due to their relevance to causality and probabilistic inference, particularly of extreme events. Interestingly, MLBNs encode strictly more conditional independence than general structural causal models. Because of this, MLBNs are {Markov} to a strengthening of the $d$-separation criterion called $\ast$-separation. As many tools for causal inference (most notably, Judea {Pearl}’s $do$-calculus) are based on $d$-separation, we address the natural question of whether assuming Markovianity to $\ast$-separation can lead to additional causal effect identifiability under intervention. We answer this question in the affirmative and develop a stronger version of the $do$-calculus rules for models which are {Markov} to $\ast$-separation. However, we note that restrictions inherent to the max-linear setting (in particular, that they give rise to non strictly positive joint probability distributions) mean that our calculus is only applicable to specific kinds of policy intervention.
APA
Sierau, L., Nowell, F. & Ay, N.. (2026). A Stronger Calculus of Intervention for Max-Linear Bayesian Networks. Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 337:6342-6365 Available from https://proceedings.mlr.press/v337/sierau26a.html.

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