Markov equivalence of max-linear Bayesian networks

Carlos Améndola, Benjamin Hollering, Seth Sullivant, Ngoc Tran
Proceedings of the Thirty-Seventh Conference on Uncertainty in Artificial Intelligence, PMLR 161:1746-1755, 2021.

Abstract

Max-linear Bayesian networks have emerged as highly applicable models for causal inference from extreme value data. However, conditional independence (CI) for max-linear Bayesian networks behaves differently than for classical Gaussian Bayesian networks. We establish the parallel between the two theories via tropicalization, and establish the surprising result that the Markov equivalence classes for max-linear Bayesian networks coincide with the ones obtained by regular CI. Our paper opens up many open problems at the intersection of extreme value statistics, causal inference and tropical geometry.

Cite this Paper

BibTeX
@InProceedings{pmlr-v161-amendola21a, title = {Markov equivalence of max-linear {B}ayesian networks}, author = {Am\'endola, Carlos and Hollering, Benjamin and Sullivant, Seth and Tran, Ngoc}, booktitle = {Proceedings of the Thirty-Seventh Conference on Uncertainty in Artificial Intelligence}, pages = {1746--1755}, year = {2021}, editor = {de Campos, Cassio and Maathuis, Marloes H.}, volume = {161}, series = {Proceedings of Machine Learning Research}, month = {27--30 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v161/amendola21a/amendola21a.pdf}, url = {https://proceedings.mlr.press/v161/amendola21a.html}, abstract = {Max-linear Bayesian networks have emerged as highly applicable models for causal inference from extreme value data. However, conditional independence (CI) for max-linear Bayesian networks behaves differently than for classical Gaussian Bayesian networks. We establish the parallel between the two theories via tropicalization, and establish the surprising result that the Markov equivalence classes for max-linear Bayesian networks coincide with the ones obtained by regular CI. Our paper opens up many open problems at the intersection of extreme value statistics, causal inference and tropical geometry.} }
Endnote
%0 Conference Paper %T Markov equivalence of max-linear Bayesian networks %A Carlos Améndola %A Benjamin Hollering %A Seth Sullivant %A Ngoc Tran %B Proceedings of the Thirty-Seventh Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2021 %E Cassio de Campos %E Marloes H. Maathuis %F pmlr-v161-amendola21a %I PMLR %P 1746--1755 %U https://proceedings.mlr.press/v161/amendola21a.html %V 161 %X Max-linear Bayesian networks have emerged as highly applicable models for causal inference from extreme value data. However, conditional independence (CI) for max-linear Bayesian networks behaves differently than for classical Gaussian Bayesian networks. We establish the parallel between the two theories via tropicalization, and establish the surprising result that the Markov equivalence classes for max-linear Bayesian networks coincide with the ones obtained by regular CI. Our paper opens up many open problems at the intersection of extreme value statistics, causal inference and tropical geometry.
APA
Améndola, C., Hollering, B., Sullivant, S. & Tran, N.. (2021). Markov equivalence of max-linear Bayesian networks. Proceedings of the Thirty-Seventh Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 161:1746-1755 Available from https://proceedings.mlr.press/v161/amendola21a.html.

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