Alternative Markov and Causal Properties for Acyclic Directed Mixed Graphs

Jose M. Peña
Proceedings of the 32nd Conference on Uncertainty in Artificial Intelligence, PMLR R14:58-67, 2016.

Abstract

We extend Andersson-Madigan-Perlman chain graphs by (i) relaxing the semidirected acyclity constraint so that only directed cycles are forbidden, and (ii) allowing up to two edges between any pair of nodes. We introduce global, and ordered local and pairwise Markov properties for the new models. We show the equivalence of these properties for strictly positive probability distributions. We also show that when the random variables are continuous, the new models can be interpreted as systems of structural equations with correlated errors. This enables us to adapt Pearl’s do-calculus to them. Finally, we describe an exact algorithm for learning the new models from observational and interventional data via answer set programming.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR14-pena16a, title = {Alternative {M}arkov and Causal Properties for Acyclic Directed Mixed Graphs}, author = {Pe{\~n}a, Jose M.}, booktitle = {Proceedings of the 32nd Conference on Uncertainty in Artificial Intelligence}, pages = {58--67}, year = {2016}, editor = {Ihler, Alexander and Janzing, Dominik}, volume = {R14}, series = {Proceedings of Machine Learning Research}, month = {25--29 Jun}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r14/main/assets/pena16a/pena16a.pdf}, url = {https://proceedings.mlr.press/r14/pena16a.html}, abstract = {We extend Andersson-Madigan-Perlman chain graphs by (i) relaxing the semidirected acyclity constraint so that only directed cycles are forbidden, and (ii) allowing up to two edges between any pair of nodes. We introduce global, and ordered local and pairwise Markov properties for the new models. We show the equivalence of these properties for strictly positive probability distributions. We also show that when the random variables are continuous, the new models can be interpreted as systems of structural equations with correlated errors. This enables us to adapt Pearl’s do-calculus to them. Finally, we describe an exact algorithm for learning the new models from observational and interventional data via answer set programming.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Alternative Markov and Causal Properties for Acyclic Directed Mixed Graphs %A Jose M. Peña %B Proceedings of the 32nd Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2016 %E Alexander Ihler %E Dominik Janzing %F pmlr-vR14-pena16a %I PMLR %P 58--67 %U https://proceedings.mlr.press/r14/pena16a.html %V R14 %X We extend Andersson-Madigan-Perlman chain graphs by (i) relaxing the semidirected acyclity constraint so that only directed cycles are forbidden, and (ii) allowing up to two edges between any pair of nodes. We introduce global, and ordered local and pairwise Markov properties for the new models. We show the equivalence of these properties for strictly positive probability distributions. We also show that when the random variables are continuous, the new models can be interpreted as systems of structural equations with correlated errors. This enables us to adapt Pearl’s do-calculus to them. Finally, we describe an exact algorithm for learning the new models from observational and interventional data via answer set programming. %Z Reissued by PMLR on 04 October 2026.
APA
Peña, J.M.. (2016). Alternative Markov and Causal Properties for Acyclic Directed Mixed Graphs. Proceedings of the 32nd Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R14:58-67 Available from https://proceedings.mlr.press/r14/pena16a.html. Reissued by PMLR on 04 October 2026.

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