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

Peter SPIRTES, Jiji ZHANG

Research output: Journal PublicationsJournal Article (refereed)

11 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

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

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