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Journal Article

Information-geometric approach to inferring causal directions

MPS-Authors
http://pubman.mpdl.mpg.de/cone/persons/resource/persons75626

Janzing,  D
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons84090

Mooij,  J
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons84328

Zhang,  K
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons84333

Lemeire J, Zscheischler,  J
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons83875

Daniušis,  P
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons84375

Steudel,  B
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;
Dept. Empirical Inference, Max Planck Institute for Intelligent System, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons84193

Schölkopf,  B
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Citation

Janzing, D., Mooij, J., Zhang, K., Lemeire J, Zscheischler, J., Daniušis, P., Steudel, B., et al. (2012). Information-geometric approach to inferring causal directions. Artificial Intelligence, 182-183, 1-31. doi:10.1016/j.artint.2012.01.002.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-B762-1
Abstract
While conventional approaches to causal inference are mainly based on conditional (in)dependences, recent methods also account for the shape of (conditional) distributions. The idea is that the causal hypothesis “X causes Y” imposes that the marginal distribution PX and the conditional distribution PY|X represent independent mechanisms of nature. Recently it has been postulated that the shortest description of the joint distribution PX,Y should therefore be given by separate descriptions of PX and PY|X. Since description length in the sense of Kolmogorov complexity is uncomputable, practical implementations rely on other notions of independence. Here we define independence via orthogonality in information space. This way, we can explicitly describe the kind of dependence that occurs between PY and PX|Y making the causal hypothesis “Y causes X” implausible. Remarkably, this asymmetry between cause and effect becomes particularly simple if X and Y are deterministically related. We present an inference method that works in this case. We also discuss some theoretical results for the non-deterministic case although it is not clear how to employ them for a more general inference method.