Constructing Separators and Adjustment Sets in Ancestral Graphs

Benito van der Zander, Maciej Liskiewicz, Johannes Textor
Proceedings of the 30th Conference on Uncertainty in Artificial Intelligence, PMLR R12:136-145, 2014.

Abstract

Ancestral graphs (AGs) are graphical causal models that can represent uncertainty about the presence of latent confounders, and can be inferred from data. Here, we present an algorithmic framework for efficiently testing, constructing, and enumerating m-separators in AGs. Moreover, we present a new constructive criterion for covariate adjustment in directed acyclic graphs (DAGs) and maximal ancestral graphs (MAGs) that characterizes adjustment sets as m-separators in a subgraph. Jointly, these results allow to find all adjustment sets that can identify a desired causal effect with multivariate exposures and outcomes in the presence of latent confounding. Our results generalize and improve upon several existing solutions for special cases of these problems.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR12-zander14a, title = {Constructing Separators and Adjustment Sets in Ancestral Graphs}, author = {der Zander, Benito van and Liskiewicz, Maciej and Textor, Johannes}, booktitle = {Proceedings of the 30th Conference on Uncertainty in Artificial Intelligence}, pages = {136--145}, year = {2014}, editor = {Zhang, Nevin L. and Tian, Jin}, volume = {R12}, series = {Proceedings of Machine Learning Research}, month = {23--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r12/main/assets/zander14a/zander14a.pdf}, url = {https://proceedings.mlr.press/r12/zander14a.html}, abstract = {Ancestral graphs (AGs) are graphical causal models that can represent uncertainty about the presence of latent confounders, and can be inferred from data. Here, we present an algorithmic framework for efficiently testing, constructing, and enumerating m-separators in AGs. Moreover, we present a new constructive criterion for covariate adjustment in directed acyclic graphs (DAGs) and maximal ancestral graphs (MAGs) that characterizes adjustment sets as m-separators in a subgraph. Jointly, these results allow to find all adjustment sets that can identify a desired causal effect with multivariate exposures and outcomes in the presence of latent confounding. Our results generalize and improve upon several existing solutions for special cases of these problems.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Constructing Separators and Adjustment Sets in Ancestral Graphs %A Benito van der Zander %A Maciej Liskiewicz %A Johannes Textor %B Proceedings of the 30th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2014 %E Nevin L. Zhang %E Jin Tian %F pmlr-vR12-zander14a %I PMLR %P 136--145 %U https://proceedings.mlr.press/r12/zander14a.html %V R12 %X Ancestral graphs (AGs) are graphical causal models that can represent uncertainty about the presence of latent confounders, and can be inferred from data. Here, we present an algorithmic framework for efficiently testing, constructing, and enumerating m-separators in AGs. Moreover, we present a new constructive criterion for covariate adjustment in directed acyclic graphs (DAGs) and maximal ancestral graphs (MAGs) that characterizes adjustment sets as m-separators in a subgraph. Jointly, these results allow to find all adjustment sets that can identify a desired causal effect with multivariate exposures and outcomes in the presence of latent confounding. Our results generalize and improve upon several existing solutions for special cases of these problems. %Z Reissued by PMLR on 04 October 2026.
APA
der Zander, B.v., Liskiewicz, M. & Textor, J.. (2014). Constructing Separators and Adjustment Sets in Ancestral Graphs. Proceedings of the 30th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R12:136-145 Available from https://proceedings.mlr.press/r12/zander14a.html. Reissued by PMLR on 04 October 2026.

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