  Spirtes, Glymour and Scheines [Causation, Prediction, and Search (1993)
Springer] described a pointwise consistent estimator of the Markov equivalence
class of any causal structure that can be represented by a directed acyclic
graph for any parametric family with a uniformly consistent test of conditional
independence, under the Causal Markov and Causal Faithfulness assumptions.
Robins et al. [Biometrika 90 (2003) 491-515], however, proved that there are no
uniformly consistent estimators of Markov equivalence classes of causal
structures under those assumptions. Subsequently, Kalisch and B\"{u}hlmann [J.
Mach. Learn. Res. 8 (2007) 613-636] described a uniformly consistent estimator
of the Markov equivalence class of a linear Gaussian causal structure under the
Causal Markov and Strong Causal Faithfulness assumptions. However, the Strong
Faithfulness assumption may be false with high probability in many domains. We
describe a uniformly consistent estimator of both the Markov equivalence class
of a linear Gaussian causal structure and the identifiable structural
coefficients in the Markov equivalence class under the Causal Markov assumption
and the considerably weaker k-Triangle-Faithfulness assumption.
