AdjacencyFaithfulness and Conservative Causal Inference
Joseph Ramsey, Jiji Zhang, Peter Spirtes
Abstract:
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 constraintbased algorithms, which we call "AdjacencyFaithfulness" and "OrientationFaithfulness". We point out that assuming AdjacencyFaithfulness is true, it is in principle possible to test the validity of OrientationFaithfulness. Based on this observation, we explore the consequence of making only the AdjacencyFaithfulness assumption. We show that the familiar PC algorithm has to be modified to be (asymptotically) correct under the weaker, AdjacencyFaithfulness assumption. Roughly the modified algorithm, called Conservative PC (CPC), checks whether OrientationFaithfulness 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 scorebased algorithms such as GES perform when the AdjacencyFaithfulness 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.
Keywords:
Pages: 401408
PS Link:
PDF Link: /papers/06/p401ramsey.pdf
BibTex:
@INPROCEEDINGS{Ramsey06,
AUTHOR = "Joseph Ramsey
and Jiji Zhang and Peter Spirtes",
TITLE = "AdjacencyFaithfulness and Conservative Causal Inference",
BOOKTITLE = "Proceedings of the TwentySecond Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI06)",
PUBLISHER = "AUAI Press",
ADDRESS = "Arlington, Virginia",
YEAR = "2006",
PAGES = "401408"
}

