A uniformly consistent estimator of causal effects under the k-Triangle-Faithfulness assumption

Peter SPIRTES, Jiji ZHANG

Research output: Journal PublicationsJournal Article (refereed)Researchpeer-review

7 Citations (Scopus)

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.
Original languageEnglish
Pages (from-to)662-678
Number of pages17
JournalStatistical Science
Volume29
Issue number4
DOIs
Publication statusPublished - Nov 2014

Fingerprint

Causal Effect
Consistent Estimator
Triangle
Equivalence class
Consistent Test
Causation
Conditional Independence
Estimator
Causal effect
Directed Acyclic Graph
Equivalence
Prediction
Coefficient

Bibliographical note

Zhang’s research was supported in part by the Research grants Council of Hong Kong under the General Research Fund LU341910.

Keywords

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

Cite this

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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.",
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A uniformly consistent estimator of causal effects under the k-Triangle-Faithfulness assumption. / SPIRTES, Peter; ZHANG, Jiji.

In: Statistical Science, Vol. 29, No. 4, 11.2014, p. 662-678.

Research output: Journal PublicationsJournal Article (refereed)Researchpeer-review

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