Abstract
The machine learning community has recently devoted much attention to the problem of inferring causal relationships from statistical data. Most of this work has focused on uncovering connections among scalar random variables. We generalize existing methods to apply to collections of multi-dimensional random vectors, focusing on techniques applicable to linear models. The performance of the resulting algorithms is evaluated and compared in simulations, which show that our methods can, in many cases, provide useful information on causal relationships even for relatively small sample sizes.
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References
Spirtes, P., Glymour, C., Scheines, R.: Causation, Prediction, and Search, 2nd edn. MIT Press (2000)
Pearl, J.: Causality: Models, Reasoning, and Inference, 2nd edn. Cambridge University Press (2009)
Chickering, D.M., Meek, C.: Finding optimal bayesian networks. In: UAI (2002)
Shimizu, S., Hoyer, P.O., Hyvärinen, A., Kerminen, A.J.: A linear non-gaussian acyclic model for causal discovery. JMLR 7, 2003–2030 (2006)
Shimizu, S., Inazumi, T., Sogawa, Y., Hyvärinen, A., Kawahara, Y., Washio, T., Hoyer, P.O., Bollen, K.: DirectLiNGAM: A direct method for learning a linear non-Gaussian structural equation model. JMLR 12, 1225–1248 (2011)
Hyvärinen, A.: Pairwise measures of causal directions in linear non-gaussian acyclic models. JMLR W.&C.P. 13, 1–16 (2010)
Kawahara, Y., Bollen, K., Shimizu, S., Washio, T.: GroupLiNGAM: Linear non-gaussian acyclic models for sets of variables. arXiv, 1006.5041v1 (June 2010)
Janzing, D., Hoyer, P.O., Schölkopf, B.: Telling cause from effect based on high-dimensional observations. In: ICML (2010)
Zscheischler, J., Janzing, D., Zhang, K.: Testing whether linear equations are causal: A free probability theory approach. In: UAI (2011)
Scheines, R., Spirtes, P.: Causal structure search: Philosophical foundations and problems, 2008. In: NIPS 2008 Workshop: Causality: Objectives and Assessment (2008)
Fisher, R.A.: Statistical Methods for Research Workers, 11th edn. Oliver and Boyd, London (1950)
Gretton, A., Fukumizu, K., Teo, C.H., Song, L., Schölkopf, B., Smola, A.J.: A kernel statistical test of independence. In: NIPS (2008)
Hastie, T., Tibshirani, R., Friedman, J.: The Elements of Statistical Learning: Data Mining, Inference and Prediction, 2nd edn. Springer (2008)
Shimizu, S.: Joint estimation of linear non-gaussian acyclic models. Neurocomputing 81, 104–107 (2012)
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Entner, D., Hoyer, P.O. (2012). Estimating a Causal Order among Groups of Variables in Linear Models. In: Villa, A.E.P., Duch, W., Érdi, P., Masulli, F., Palm, G. (eds) Artificial Neural Networks and Machine Learning – ICANN 2012. ICANN 2012. Lecture Notes in Computer Science, vol 7553. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33266-1_11
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DOI: https://doi.org/10.1007/978-3-642-33266-1_11
Publisher Name: Springer, Berlin, Heidelberg
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