Statistical Science

A Uniformly Consistent Estimator of Causal Effects under the $k$-Triangle-Faithfulness Assumption

Peter Spirtes and Jiji Zhang

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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 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.

Article information

Source
Statist. Sci., Volume 29, Number 4 (2014), 662-678.

Dates
First available in Project Euclid: 15 January 2015

Permanent link to this document
https://projecteuclid.org/euclid.ss/1421330552

Digital Object Identifier
doi:10.1214/13-STS429

Mathematical Reviews number (MathSciNet)
MR3300364

Zentralblatt MATH identifier
1331.62277

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

Citation

Spirtes, Peter; Zhang, Jiji. A Uniformly Consistent Estimator of Causal Effects under the $k$-Triangle-Faithfulness Assumption. Statist. Sci. 29 (2014), no. 4, 662--678. doi:10.1214/13-STS429. https://projecteuclid.org/euclid.ss/1421330552


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References

  • Colombo, D., Maathuis, M. H., Kalisch, M. and Richardson, T. S. (2012). Learning high-dimensional directed acyclic graphs with latent and selection variables. Ann. Statist. 40 294–321.
  • Kalisch, M. and Bühlmann, P. (2007). Estimating high-dimensional directed acyclic graphs with the PC-algorithm. J. Mach. Learn. Res. 8 613–636.
  • Lin, S., Uhler, C., Sturmfels, B. and Bühlmann, P. (2012). Hypersurfaces and their singularities in partial correlation testing. Available at arXiv:1209.0285.
  • Maathuis, M. H., Colombo, D., Kalisch, M. and Bühlmann, P. (2010). Predicting causal effects in large-scale systems from observational data. Nat. Methods 7 247–248.
  • Meek, C. (1995). Causal inference and causal explanation with background knowledge. In Proceedings of the Eleventh Conference on Uncertainty in Artificial Intelligence 403–411. Morgan Kaufmann, San Francisco, CA.
  • Pearl, J. (1988). Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann, San Mateo, CA.
  • Pearl, J. (2000). Causality: Models, Reasoning, and Inference. Cambridge Univ. Press, Cambridge.
  • Ramsey, J., Zhang, J. and Spirtes, P. (2006). Adjacency-faithfulness and conservative causal inference. In Proceedings of the 22nd Conference on Uncertainty in Artificial Intelligence 401–408. AUAI Press, Arlington, VA.
  • Robins, J. M., Scheines, R., Spirtes, P. and Wasserman, L. (2003). Uniform consistency in causal inference. Biometrika 90 491–515.
  • Spirtes, P., Glymour, C. and Scheines, R. (1993). Causation, Prediction, and Search. Lecture Notes in Statistics 81. Springer, New York.
  • Spirtes, P., Glymour, C. and Scheines, R. (2000). Causation, Prediction, and Search, 2nd ed. MIT Press, Cambridge, MA.
  • Uhler, C., Raskutti, G., Bühlmann, P. and Yu, B. (2013). Geometry of faithfulness assumption in causal inference. Ann. Statist. 41 436–463.
  • Verma, T. and Pearl, P. (1990). Equivalence and synthesis of causal models. In Proceedings of the 6th Conference on Uncertainty in Artificial Intelligence 220–227. AUAI Press, Corvallis, OR.
  • Whittaker, J. (1990). Graphical Models in Applied Multivariate Statistics. Wiley, Chichester.
  • Woodward, J. (2003). Making Things Happen: A Theory of Causal Explanation. Oxford Univ. Press, London.
  • Zhang, J. and Spirtes, P. (2008). Detection of unfaithfulness and robust causal inference. Minds and Machines 18 239–271.
  • Zhang, J. and Spirtes, P. (2011). Intervention, determinism, and the causal minimality condition. Synthese 182 335–347.