A uniformly consistent estimator of causal effects under the k-triangle-faithfulness assumption

• Autores: Peter Spirtes, Jiji Zhang
• Localización: Statistical science, ISSN 0883-4237, Vol. 29, Nº. 4, 2014 (Ejemplar dedicado a: Semiparametrics and Causal Inference), págs. 662-678
• Idioma: inglés
• DOI: 10.1214/13-sts429
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• Resumen

  • 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 Bühlmann [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.