How PC-based Methods Err: Towards Better Reporting of Assumption Violations and Small Sample Errors

Sofia Faltenbacher, Jonas Wahl, Rebecca Jean Herman, Jakob Runge
Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, PMLR 337:1498-1519, 2026.

Abstract

Causal discovery methods based on the {PC} algorithm are proven to be sound if all structural assumptions are fulfilled and all conditional independence tests are correct. This idealized setting is rarely given in real data. In this work, we first showcase how local errors can lead to untrustworthy edge orientations far away from the error source, highlighting how consequential seemingly innocuous errors can become. Next, we introduce coherency scores to find assumption violations and small sample errors in the absence of a ground truth. These scores do not require statistical tests beyond those already executed by the causal discovery algorithm. Errors detected by our approach extend the set of errors that present themselves as orientation conflicts or ambiguities. We place our computationally cheap global error detection and quantification scores as a bridge between computationally expensive global answer-set-programming-based methods and less expensive local error detection methods. The scores are analyzed on simulated and real-world datasets.

Cite this Paper

BibTeX
@InProceedings{pmlr-v337-faltenbacher26a, title = {How {PC}-based Methods Err: Towards Better Reporting of Assumption Violations and Small Sample Errors}, author = {Faltenbacher, Sofia and Wahl, Jonas and Herman, Rebecca Jean and Runge, Jakob}, booktitle = {Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence}, pages = {1498--1519}, year = {2026}, editor = {Perković, Emilija and Malinsky, Daniel}, volume = {337}, series = {Proceedings of Machine Learning Research}, month = {17--21 Aug}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v337/main/assets/faltenbacher26a/faltenbacher26a.pdf}, url = {https://proceedings.mlr.press/v337/faltenbacher26a.html}, abstract = {Causal discovery methods based on the {PC} algorithm are proven to be sound if all structural assumptions are fulfilled and all conditional independence tests are correct. This idealized setting is rarely given in real data. In this work, we first showcase how local errors can lead to untrustworthy edge orientations far away from the error source, highlighting how consequential seemingly innocuous errors can become. Next, we introduce coherency scores to find assumption violations and small sample errors in the absence of a ground truth. These scores do not require statistical tests beyond those already executed by the causal discovery algorithm. Errors detected by our approach extend the set of errors that present themselves as orientation conflicts or ambiguities. We place our computationally cheap global error detection and quantification scores as a bridge between computationally expensive global answer-set-programming-based methods and less expensive local error detection methods. The scores are analyzed on simulated and real-world datasets.} }
Endnote
%0 Conference Paper %T How PC-based Methods Err: Towards Better Reporting of Assumption Violations and Small Sample Errors %A Sofia Faltenbacher %A Jonas Wahl %A Rebecca Jean Herman %A Jakob Runge %B Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2026 %E Emilija Perković %E Daniel Malinsky %F pmlr-v337-faltenbacher26a %I PMLR %P 1498--1519 %U https://proceedings.mlr.press/v337/faltenbacher26a.html %V 337 %X Causal discovery methods based on the {PC} algorithm are proven to be sound if all structural assumptions are fulfilled and all conditional independence tests are correct. This idealized setting is rarely given in real data. In this work, we first showcase how local errors can lead to untrustworthy edge orientations far away from the error source, highlighting how consequential seemingly innocuous errors can become. Next, we introduce coherency scores to find assumption violations and small sample errors in the absence of a ground truth. These scores do not require statistical tests beyond those already executed by the causal discovery algorithm. Errors detected by our approach extend the set of errors that present themselves as orientation conflicts or ambiguities. We place our computationally cheap global error detection and quantification scores as a bridge between computationally expensive global answer-set-programming-based methods and less expensive local error detection methods. The scores are analyzed on simulated and real-world datasets.
APA
Faltenbacher, S., Wahl, J., Herman, R.J. & Runge, J.. (2026). How PC-based Methods Err: Towards Better Reporting of Assumption Violations and Small Sample Errors. Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 337:1498-1519 Available from https://proceedings.mlr.press/v337/faltenbacher26a.html.

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