Interpreting and using CPDAGs with background knowledge

Emilija Perkovic, Markus Kalisch, Marloes H. Maathuis
Proceedings of the 33rd Conference on Uncertainty in Artificial Intelligence, PMLR R15:461-470, 2017.

Abstract

We develop terminology and methods for working with maximally oriented partially directed acyclic graphs (maximal PDAGs). Maximal PDAGs arise from imposing restrictions on a Markov equivalence class of directed acyclic graphs, or equivalently on its graphical representation as a completed partially directed acyclic graph (CPDAG), for example when adding background knowledge about certain edge orientations. Although maximal PDAGs often arise in practice, causal methods have been mostly developed for CPDAGs. In this paper, we extend such methodology to maximal PDAGs. In particular, we develop methodology to read off possible ancestral relationships, we introduce a graphical criterion for covariate adjustment to estimate total causal effects, and we adapt the IDA and joint- IDA frameworks to estimate multi-sets of possible causal effects. We also present a simulation study that illustrates the gain in identifiability of total causal effects as the background knowledge increases. All methods are implemented in the R package pcalg.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR15-perkovic17a, title = {Interpreting and using CPDAGs with background knowledge}, author = {Perkovic, Emilija and Kalisch, Markus and Maathuis, Marloes H.}, booktitle = {Proceedings of the 33rd Conference on Uncertainty in Artificial Intelligence}, pages = {461--470}, year = {2017}, editor = {Elidan, Gal and Kersting, Kristian}, volume = {R15}, series = {Proceedings of Machine Learning Research}, month = {11--15 Aug}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r15/main/assets/perkovic17a/perkovic17a.pdf}, url = {https://proceedings.mlr.press/r15/perkovic17a.html}, abstract = {We develop terminology and methods for working with maximally oriented partially directed acyclic graphs (maximal PDAGs). Maximal PDAGs arise from imposing restrictions on a Markov equivalence class of directed acyclic graphs, or equivalently on its graphical representation as a completed partially directed acyclic graph (CPDAG), for example when adding background knowledge about certain edge orientations. Although maximal PDAGs often arise in practice, causal methods have been mostly developed for CPDAGs. In this paper, we extend such methodology to maximal PDAGs. In particular, we develop methodology to read off possible ancestral relationships, we introduce a graphical criterion for covariate adjustment to estimate total causal effects, and we adapt the IDA and joint- IDA frameworks to estimate multi-sets of possible causal effects. We also present a simulation study that illustrates the gain in identifiability of total causal effects as the background knowledge increases. All methods are implemented in the R package pcalg.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Interpreting and using CPDAGs with background knowledge %A Emilija Perkovic %A Markus Kalisch %A Marloes H. Maathuis %B Proceedings of the 33rd Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2017 %E Gal Elidan %E Kristian Kersting %F pmlr-vR15-perkovic17a %I PMLR %P 461--470 %U https://proceedings.mlr.press/r15/perkovic17a.html %V R15 %X We develop terminology and methods for working with maximally oriented partially directed acyclic graphs (maximal PDAGs). Maximal PDAGs arise from imposing restrictions on a Markov equivalence class of directed acyclic graphs, or equivalently on its graphical representation as a completed partially directed acyclic graph (CPDAG), for example when adding background knowledge about certain edge orientations. Although maximal PDAGs often arise in practice, causal methods have been mostly developed for CPDAGs. In this paper, we extend such methodology to maximal PDAGs. In particular, we develop methodology to read off possible ancestral relationships, we introduce a graphical criterion for covariate adjustment to estimate total causal effects, and we adapt the IDA and joint- IDA frameworks to estimate multi-sets of possible causal effects. We also present a simulation study that illustrates the gain in identifiability of total causal effects as the background knowledge increases. All methods are implemented in the R package pcalg. %Z Reissued by PMLR on 04 October 2026.
APA
Perkovic, E., Kalisch, M. & Maathuis, M.H.. (2017). Interpreting and using CPDAGs with background knowledge. Proceedings of the 33rd Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R15:461-470 Available from https://proceedings.mlr.press/r15/perkovic17a.html. Reissued by PMLR on 04 October 2026.

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