A kernel-based causal learning algorithm

Authors:
Xiaohai Sun;Dominik Janzing;Bernhard Schölkopf;Kenji Fukumizu
Affiliations:
Max Planck Institute for Biological Cybernetics, Tübingen, Germany;Universität Karlsruhe (TH), Karlsruhe, Germany;Max Planck Institute for Biological Cybernetics, Tübingen, Germany;Institute of Statistical Mathematics, Tokyo, Japan
Venue:
Proceedings of the 24th international conference on Machine learning
Year:
2007

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Abstract

We describe a causal learning method, which employs measuring the strength of statistical dependences in terms of the Hilbert-Schmidt norm of kernel-based cross-covariance operators. Following the line of the common faithfulness assumption of constraint-based causal learning, our approach assumes that a variable Z is likely to be a common effect of X and Y, if conditioning on Z increases the dependence between X and Y. Based on this assumption, we collect "votes" for hypothetical causal directions and orient the edges by the majority principle. In most experiments with known causal structures, our method provided plausible results and outperformed the conventional constraint-based PC algorithm.