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 depend on the choice of kernel in the limit of infinite data, for a wide class of kernels. 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.

• Type: Conference
• Year: 2007
• Where: NIPS
• Authors: Kenji Fukumizu, Arthur Gretton, Xiaohai Sun, Bernhard Schölkopf
• Keywords: Conditional Dependence, Information Technology, NIPS 2007, Normalized Cross-covariance Operators, Reproducing Kernel Hilbert Spaces