A Kernel-based Causal Learning Algorithm

A Kernel-based Causal Learning Algorithm
Xiaohai Sun - Max Planck Institute for Biological Cybernetics, Germany Dominik Janzing - Universitaet Karlsruhe (TH), Germany Bernhard Schölkopf - Max Planck Institute for Biological Cybernetics, Germany Kenji Fukumizu - Institute of Statistical Mathematics, 4-6-7 Minami-Azabu, Minato-ku, Tokyo 106-8569, Japan
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.

Xiaohai Sun - Max Planck Institute for Biological Cybernetics, Germany
Dominik Janzing - Universitaet Karlsruhe (TH), Germany
Bernhard Schölkopf - Max Planck Institute for Biological Cybernetics, Germany
Kenji Fukumizu - Institute of Statistical Mathematics, 4-6-7 Minami-Azabu, Minato-ku, Tokyo 106-8569, Japan

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.