Adjustment Criteria in Causal Diagrams: An Algorithmic Perspective

Johannes Textor, Maciej Liskiewicz
Proceedings of the 27th Conference on Uncertainty in Artificial Intelligence, PMLR R9:754-761, 2011.

Abstract

Identifying and controlling bias is a key problem in empirical sciences. Causal diagram theory provides graphical criteria for deciding whether and how causal effects can be identified from observed (nonexperimental) data by covariate adjustment. Here we prove equivalences between existing as well as new criteria for adjustment and we provide a new simplified but still equivalent notion of d-separation. These lead to efficient algorithms for two important tasks in causal diagram analysis: (1) listing minimal covariate adjustments (with polynomial delay); and (2) identifying the subdiagram involved in biasing paths (in linear time). Our results improve upon existing exponential-time solutions for these problems, enabling users to assess the effects of covariate adjustment on diagrams with tens to hundreds of variables interactively in real time.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR9-textor11a, title = {Adjustment Criteria in Causal Diagrams: An Algorithmic Perspective}, author = {Textor, Johannes and Liskiewicz, Maciej}, booktitle = {Proceedings of the 27th Conference on Uncertainty in Artificial Intelligence}, pages = {754--761}, year = {2011}, editor = {Cozman, Fabio and Pfeffer, Avi}, volume = {R9}, series = {Proceedings of Machine Learning Research}, month = {14--17 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r9/main/assets/textor11a/textor11a.pdf}, url = {https://proceedings.mlr.press/r9/textor11a.html}, abstract = {Identifying and controlling bias is a key problem in empirical sciences. Causal diagram theory provides graphical criteria for deciding whether and how causal effects can be identified from observed (nonexperimental) data by covariate adjustment. Here we prove equivalences between existing as well as new criteria for adjustment and we provide a new simplified but still equivalent notion of d-separation. These lead to efficient algorithms for two important tasks in causal diagram analysis: (1) listing minimal covariate adjustments (with polynomial delay); and (2) identifying the subdiagram involved in biasing paths (in linear time). Our results improve upon existing exponential-time solutions for these problems, enabling users to assess the effects of covariate adjustment on diagrams with tens to hundreds of variables interactively in real time.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Adjustment Criteria in Causal Diagrams: An Algorithmic Perspective %A Johannes Textor %A Maciej Liskiewicz %B Proceedings of the 27th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2011 %E Fabio Cozman %E Avi Pfeffer %F pmlr-vR9-textor11a %I PMLR %P 754--761 %U https://proceedings.mlr.press/r9/textor11a.html %V R9 %X Identifying and controlling bias is a key problem in empirical sciences. Causal diagram theory provides graphical criteria for deciding whether and how causal effects can be identified from observed (nonexperimental) data by covariate adjustment. Here we prove equivalences between existing as well as new criteria for adjustment and we provide a new simplified but still equivalent notion of d-separation. These lead to efficient algorithms for two important tasks in causal diagram analysis: (1) listing minimal covariate adjustments (with polynomial delay); and (2) identifying the subdiagram involved in biasing paths (in linear time). Our results improve upon existing exponential-time solutions for these problems, enabling users to assess the effects of covariate adjustment on diagrams with tens to hundreds of variables interactively in real time. %Z Reissued by PMLR on 04 October 2026.
APA
Textor, J. & Liskiewicz, M.. (2011). Adjustment Criteria in Causal Diagrams: An Algorithmic Perspective. Proceedings of the 27th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R9:754-761 Available from https://proceedings.mlr.press/r9/textor11a.html. Reissued by PMLR on 04 October 2026.

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