Kernel Measures of Conditional Dependence

Part of Advances in Neural Information Processing Systems 20 (NIPS 2007)

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Kenji Fukumizu, Arthur Gretton, Xiaohai Sun, Bernhard Schölkopf


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.