Title
A uniformly consistent estimator of causal effects under the k-Triangle-Faithfulness assumption
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
Access to external full text or publisher's version may require subscription.
Full-text Version
Accepted Author Manuscript
Language
English
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
