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

<p>Spirtes, Glymour and Scheines [<em>Causation</em>, <em>Prediction</em>, <em>and Search</em> (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. [<em>Biometrika</em> <strong>90</strong> (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 Bühlmann [<em>J. Mach. Learn. Res.</em> <strong>8</strong> (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 <em>k</em>-Triangle-Faithfulness assumption.</p>