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