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Identifying Cause and Effect on Discrete Data using Additive Noise Models

2010

Conference Paper

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Inferring the causal structure of a set of random variables from a finite sample of the joint distribution is an important problem in science. Recently, methods using additive noise models have been suggested to approach the case of continuous variables. In many situations, however, the variables of interest are discrete or even have only finitely many states. In this work we extend the notion of additive noise models to these cases. Whenever the joint distribution P(X;Y ) admits such a model in one direction, e.g. Y = f(X) + N; N ? X, it does not admit the reversed model X = g(Y ) + ~N ; ~N ? Y as long as the model is chosen in a generic way. Based on these deliberations we propose an efficient new algorithm that is able to distinguish between cause and effect for a finite sample of discrete variables. We show that this algorithm works both on synthetic and real data sets.

Author(s): Peters, J. and Janzing, D. and Schölkopf, B.
Book Title: JMLR Workshop and Conference Proceedings Volume 9: AISTATS 2010
Journal: Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics (AISTATS 2010)
Pages: 597-604
Year: 2010
Month: May
Day: 0
Editors: YW Teh and M Titterington
Publisher: JMLR

Department(s): Empirical Inference
Research Project(s): Causality (Causal Inference)
Bibtex Type: Conference Paper (inproceedings)

Address: Cambridge, MA, USA
Digital: 0
Event Name: 13th International Conference on Artificial Intelligence and Statistics
Event Place: Chia Laguna Resort, Italy
Language: en
Organization: Max-Planck-Gesellschaft
School: Biologische Kybernetik

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BibTex

@inproceedings{6387,
  title = {Identifying Cause and Effect on Discrete Data using Additive Noise Models},
  author = {Peters, J. and Janzing, D. and Sch{\"o}lkopf, B.},
  journal = {Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics (AISTATS 2010)},
  booktitle = {JMLR Workshop and Conference Proceedings Volume 9: AISTATS 2010},
  pages = {597-604},
  editors = {YW Teh and M Titterington},
  publisher = {JMLR},
  organization = {Max-Planck-Gesellschaft},
  school = {Biologische Kybernetik},
  address = {Cambridge, MA, USA},
  month = may,
  year = {2010},
  month_numeric = {5}
}