Adjacency-faithfulness and conservative causal inference

Joseph D. Ramsey, Peter L. Spirtes, Jiji Zhang

Research output: Chapter in book/report/conference proceedingConference contributionpeer-review

128 Citations (Scopus)


Most causal inference algorithms in the literature (e.g., Pearl (2000), Spirtes et al. (2000), Heckerman et al. (1999)) exploit an assumption usually referred to as the causal Faithfulness or Stability condition. In this paper, we highlight two components of the condition used in constraint-based algorithms, which we call "Adjacency-Faithfulness" and "Orientation-Faithfulness". We point out that assuming Adjacency-Faithfulness is true, it is in principle possible to test the validity of Orientation-Faithfulness. Based on this observation, we explore the consequence of making only the Adjacency-Faithfulness assumption. We show that the familiar PC algorithm has to be modified to be (asymptotically) correct under the weaker, Adjacency-Faithfulness assumption. Roughly the modified algorithm, called Conservative PC (CPC), checks whether Orientation-Faithfulness holds in the orientation phase, and if not, avoids drawing certain causal conclusions the PC algorithm would draw. However, if the stronger, standard causal Faithfulness condition actually obtains, the CPC algorithm is shown to output the same pattern as the PC algorithm does in the large sample limit. We also present a simulation study showing that the CPC algorithm runs almost as fast as the PC algorithm, and outputs significantly fewer false causal arrowheads than the PC algorithm does on realistic sample sizes. We end our paper by discussing how score-based algorithms such as GES perform when the Adjacency-Faithfulness but not the standard causal Faithfulness condition holds, and how to extend our work to the FCI algorithm, which allows for the possibility of latent variables.
Original languageEnglish
Title of host publicationProceedings of the 22nd Conference on Uncertainty in Artificial Intelligence (UAI)
EditorsRina Dechter, Thomas Richardson
PublisherAUAI Press
Number of pages8
ISBN (Print)9780974903927
Publication statusPublished - Jul 2006
Event22nd Conference on Uncertainty in Artificial Intelligence, UAI 2006 - Cambridge, MA, United States
Duration: 13 Jul 200616 Jul 2006 (Conference website) (Conference proceedings)


Conference22nd Conference on Uncertainty in Artificial Intelligence, UAI 2006
Country/TerritoryUnited States
CityCambridge, MA
Internet address

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