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Distinguishing Between Cause and Effect via Kernel-Based Complexity Measures for Conditional Distributions

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http://pubman.mpdl.mpg.de/cone/persons/resource/persons84243

Sun,  X
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

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/persons84193

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

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Citation

Sun, X., Janzing, D., & Schölkopf, B. (2007). Distinguishing Between Cause and Effect via Kernel-Based Complexity Measures for Conditional Distributions. Proceedings of the 15th European Symposium on Artificial Neural Networks (ESANN 2007), 441-446.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-CE19-C
Abstract
We propose a method to evaluate the complexity of probability measures from data that is based on a reproducing kernel Hilbert space seminorm of the logarithm of conditional probability densities. The motivation is to provide a tool for a causal inference method which assumes that conditional probabilities for effects given their causes are typically simpler and smoother than vice-versa. We present experiments with toy data where the quantitative results are consistent with our intuitive understanding of complexity and smoothness. Also in some examples with real-world data the probability measure corresponding to the true causal direction turned out to be less complex than those of the reversed order.