Discovering Unconfounded Causal Relationships Using Linear Non-Gaussian Models

  • Doris Entner
  • Patrik O. Hoyer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6797)


Causal relationships among a set of observed variables are often modeled using directed acyclic graph (DAG) structures, and learning such structures from data is known as the causal discovery problem. We here consider the learning of linear non-Gaussian acyclic models [9] with hidden variables [5]. Estimation of such models is computationally challenging and hence only possible when the number of variables is small. We present an algorithm for obtaining partial but in the large sample limit correct information about pairwise total causal effects in such a model. In particular, we obtain consistent estimates of the total effects for all variable pairs for which there exist an unconfounded superset of observed variables. Simulations show that the estimated pairwise total effects are good approximations of the true total effects.


Causal Discovery Latent Variables Non-Gaussianity 


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  1. 1.
    Bollen, K.A.: Structural Equations with Latent Variables. John Wiley & Sons, Chichester (1989)CrossRefzbMATHGoogle Scholar
  2. 2.
    Darmois, G.: Analyse générale des liaisons stochastiques. RIIS 21 (1953)Google Scholar
  3. 3.
    Eriksson, J., Koivunen, V.: Identifiability, Separability, and Uniqueness of Linear ICA Models. IEEE Signal Processing Letters 11(7) (2004)Google Scholar
  4. 4.
    Gretton, A., Fukumizu, K., Teo, C.H., Song, L., Schölkopf, B., Smola, A.J.: A Kernel Statistical Test of Independence. In: Adv. NIPS (2008)Google Scholar
  5. 5.
    Hoyer, P.O., Shimizu, S., Kerminen, A.J., Palviainen, M.: Estimation of causal effects using linear non-Gaussian models with hidden variables. IJAR 49 (2008)Google Scholar
  6. 6.
    Hyvärinen, A., Karhunen, J., Oja, E.: Independent Component Analysis. Wiley Interscience, Hoboken (2001)CrossRefGoogle Scholar
  7. 7.
    Kawahara, Y., Bollen, K., Shimizu, S., Washio, T.: GroupLiNGAM: Linear non-Gaussian acyclic models for sets of variables. arXiv:1006.5041v1 (2010)Google Scholar
  8. 8.
    Pearl, J.: Causality: Models, Reasoning, and Inference. Cambridge University Press, Cambridge (2000)zbMATHGoogle Scholar
  9. 9.
    Shimizu, S., Hoyer, P.O., Hyvärinen, A., Kerminen, A.: A linear non-gaussian acyclic model for causal discovery. JMLR 7 (2006)Google Scholar
  10. 10.
    Skitovitch, W.P.: On a property of the normal distribution. DAN SSSR 89 (1953)Google Scholar
  11. 11.
    Spirtes, P., Glymour, C., Scheines, R.: Causation, Prediction and Search, 2nd edn. MIT Press, Cambridge (2000)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Doris Entner
    • 1
  • Patrik O. Hoyer
    • 1
  1. 1.Helsinki Institute for Information Technology, Department of Computer ScienceUniversity of HelsinkiFinland

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