Kernel Measures of Conditional Dependence

We propose a new measure of conditional dependence of random variables, based on normalized cross-covariance operators on reproducing kernel Hilbert spaces. Unlike previous kernel dependence measures, the proposed criterion does not de- pend on the choice of kernel in the limit of infinite data, for a wide class of ker- nels. At the same time, it has a straightforward empirical estimate with good convergence behaviour. We discuss the theoretical properties of the measure, and demonstrate its application in experiments.

Authors

• Kenji Fukumizu
• Arthur Gretton University College London
• Xiaohai Sun
• Bernhard Schölkopf

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