Document Type

Journal article

Source Publication

Statistical Science

Publication Date

2014

Volume

29

Issue

4

First Page

662

Last Page

678

Publisher

The Institute of Mathematical Statistics

Keywords

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

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 B¨uhlmann [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.

DOI

10.1214/13-STS429

Print ISSN

08834237

E-ISSN

21688745

Publisher Statement

Copyright © Institute of Mathematical Statistics, 2014

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Full-text Version

Accepted Author Manuscript

Recommended Citation

Spirtes, P. and Zhang J. (2014). A Uniformly Consistent Estimator of Causal Effects under the k-Triangle-Faithfulness Assumption. Statistical Science, 29(4), 662-678. DOI: 10.1214/13-STS429