# Detection of Unfaithfulness and Robust Causal Inference

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## Abstract

Much of the recent work on the epistemology of causation has centered on two assumptions, known as the Causal Markov Condition and the Causal Faithfulness Condition. Philosophical discussions of the latter condition have exhibited situations in which it is likely to fail. This paper studies the Causal Faithfulness Condition as a conjunction of weaker conditions. We show that some of the weaker conjuncts can be empirically tested, and hence do not have to be *assumed* a priori. Our results lead to two methodologically significant observations: (1) some common types of counterexamples to the Faithfulness condition constitute objections only to the empirically testable part of the condition; and (2) some common defenses of the Faithfulness condition do not provide justification or evidence for the testable parts of the condition. It is thus worthwhile to study the possibility of reliable causal inference under weaker Faithfulness conditions. As it turns out, the modification needed to make standard procedures work under a weaker version of the Faithfulness condition also has the practical effect of making them more robust when the standard Faithfulness condition actually holds. This, we argue, is related to the possibility of controlling error probabilities with finite sample size (“uniform consistency”) in causal inference.

## Keywords

Bayesian network Causal inference Epistemology of causation Faithfulness condition Machine learning Uniform consistency## Notes

### Acknowledgements

We thank Clark Glymour, Kevin Kelly, Thomas Richardson, Richard Scheines, Oliver Schulte, and James Woodward for very helpful comments. An earlier draft of this paper was presented to the Confirmation, Induction and Science conference held at the London School of Economics and Political Science in March 2007, and we are grateful to the participates for their useful feedback. Special thanks are due to Joseph Ramsey for providing empirical results on the performance of causal discovery algorithms discussed in the paper.

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