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Spirtes, Glymour and Scheines [Causation, Prediction, and Search (1993)Springer] described a pointwise consistent estimator of the Markov equivalenceclass of any causal structure that can be represented by a directed acyclicgraph for any parametric family with a uniformly consistent test of conditionalindependence, under the Causal Markov and Causal Faithfulness assumptions.Robins et al. [Biometrika 90 (2003) 491-515], however, proved that there are nouniformly consistent estimators of Markov equivalence classes of causalstructures under those assumptions. Subsequently, Kalisch and B\"{u}hlmann [J.Mach. Learn. Res. 8 (2007) 613-636] described a uniformly consistent estimatorof the Markov equivalence class of a linear Gaussian causal structure under theCausal Markov and Strong Causal Faithfulness assumptions. However, the StrongFaithfulness assumption may be false with high probability in many domains. Wedescribe a uniformly consistent estimator of both the Markov equivalence classof a linear Gaussian causal structure and the identifiable structuralcoefficients in the Markov equivalence class under the Causal Markov assumptionand the considerably weaker k-Triangle-Faithfulness assumption.

A Uniformly Consistent Estimator of Causal Effects under the $k$-Triangle-Faithfulness Assumption