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 in- ferred from data. Here, we present an algo- rithmic framework for efficiently testing, con- structing, and enumerating m-separators in AGs. Moreover, we present a new constructive crite- rion 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 iden- tify a desired causal effect with multivariate ex- posures 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 in- ferred from data. Here, we present an algo- rithmic framework for efficiently testing, con- structing, and enumerating m-separators in AGs. Moreover, we present a new constructive crite- rion 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 iden- tify a desired causal effect with multivariate ex- posures 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 in- ferred from data. Here, we present an algo- rithmic framework for efficiently testing, con- structing, and enumerating m-separators in AGs. Moreover, we present a new constructive crite- rion 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 iden- tify a desired causal effect with multivariate ex- posures 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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