Minimal enumeration of all possible total effects in a Markov equivalence class

Richard Guo, Emilija Perkovic
Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, PMLR 130:2395-2403, 2021.

Abstract

In observational studies, when a total causal effect of interest is not identified, the set of all possible effects can be reported instead. This typically occurs when the underlying causal DAG is only known up to a Markov equivalence class, or a refinement thereof due to background knowledge. As such, the class of possible causal DAGs is represented by a maximally oriented partially directed acyclic graph (MPDAG), which contains both directed and undirected edges. We characterize the minimal additional edge orientations required to identify a given total effect. A recursive algorithm is then developed to enumerate subclasses of DAGs, such that the total effect in each subclass is identified as a distinct functional of the observed distribution. This resolves an issue with existing methods, which often report possible total effects with duplicates, namely those that are numerically distinct due to sampling variability but are in fact causally identical.

Cite this Paper


BibTeX
@InProceedings{pmlr-v130-guo21c, title = { Minimal enumeration of all possible total effects in a Markov equivalence class }, author = {Guo, Richard and Perkovic, Emilija}, booktitle = {Proceedings of The 24th International Conference on Artificial Intelligence and Statistics}, pages = {2395--2403}, year = {2021}, editor = {Banerjee, Arindam and Fukumizu, Kenji}, volume = {130}, series = {Proceedings of Machine Learning Research}, month = {13--15 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v130/guo21c/guo21c.pdf}, url = {http://proceedings.mlr.press/v130/guo21c.html}, abstract = { In observational studies, when a total causal effect of interest is not identified, the set of all possible effects can be reported instead. This typically occurs when the underlying causal DAG is only known up to a Markov equivalence class, or a refinement thereof due to background knowledge. As such, the class of possible causal DAGs is represented by a maximally oriented partially directed acyclic graph (MPDAG), which contains both directed and undirected edges. We characterize the minimal additional edge orientations required to identify a given total effect. A recursive algorithm is then developed to enumerate subclasses of DAGs, such that the total effect in each subclass is identified as a distinct functional of the observed distribution. This resolves an issue with existing methods, which often report possible total effects with duplicates, namely those that are numerically distinct due to sampling variability but are in fact causally identical. } }
Endnote
%0 Conference Paper %T Minimal enumeration of all possible total effects in a Markov equivalence class %A Richard Guo %A Emilija Perkovic %B Proceedings of The 24th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2021 %E Arindam Banerjee %E Kenji Fukumizu %F pmlr-v130-guo21c %I PMLR %P 2395--2403 %U http://proceedings.mlr.press/v130/guo21c.html %V 130 %X In observational studies, when a total causal effect of interest is not identified, the set of all possible effects can be reported instead. This typically occurs when the underlying causal DAG is only known up to a Markov equivalence class, or a refinement thereof due to background knowledge. As such, the class of possible causal DAGs is represented by a maximally oriented partially directed acyclic graph (MPDAG), which contains both directed and undirected edges. We characterize the minimal additional edge orientations required to identify a given total effect. A recursive algorithm is then developed to enumerate subclasses of DAGs, such that the total effect in each subclass is identified as a distinct functional of the observed distribution. This resolves an issue with existing methods, which often report possible total effects with duplicates, namely those that are numerically distinct due to sampling variability but are in fact causally identical.
APA
Guo, R. & Perkovic, E.. (2021). Minimal enumeration of all possible total effects in a Markov equivalence class . Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 130:2395-2403 Available from http://proceedings.mlr.press/v130/guo21c.html.

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