Open Access
November 2014 A Uniformly Consistent Estimator of Causal Effects under the $k$-Triangle-Faithfulness Assumption
Peter Spirtes, Jiji Zhang
Statist. Sci. 29(4): 662-678 (November 2014). DOI: 10.1214/13-STS429

Abstract

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.

Citation

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Peter Spirtes. Jiji Zhang. "A Uniformly Consistent Estimator of Causal Effects under the $k$-Triangle-Faithfulness Assumption." Statist. Sci. 29 (4) 662 - 678, November 2014. https://doi.org/10.1214/13-STS429

Information

Published: November 2014
First available in Project Euclid: 15 January 2015

zbMATH: 1331.62277
MathSciNet: MR3300364
Digital Object Identifier: 10.1214/13-STS429

Keywords: Bayesian networks , Causal inference , estimation , model search , Model selection , structural equation models , uniform consistency

Rights: Copyright © 2014 Institute of Mathematical Statistics

Vol.29 • No. 4 • November 2014
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