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A fundamental question in causal inference is whether it is possible toreliably infer manipulation effects from observational data. There are avariety of senses of asymptotic reliability in the statistical literature,among which the most commonly discussed frequentist notions are pointwiseconsistency and uniform consistency. Uniform consistency is in generalpreferred to pointwise consistency because the former allows us to control theworst case error bounds with a finite sample size. In the sense of pointwiseconsistency, several reliable causal inference algorithms have been establishedunder the Markov and Faithfulness assumptions [Pearl 2000, Spirtes et al.2001]. In the sense of uniform consistency, however, reliable causal inferenceis impossible under the two assumptions when time order is unknown and/orlatent confounders are present [Robins et al. 2000]. In this paper we presenttwo natural generalizations of the Faithfulness assumption in the context ofstructural equation models, under which we show that the typical algorithms inthe literature (in some cases with modifications) are uniformly consistent evenwhen the time order is unknown. We also discuss the situation where latentconfounders may be present and the sense in which the Faithfulness assumptionis a limiting case of the stronger assumptions.

Strong Faithfulness and Uniform Consistency in Causal Inference