Kernel Measures of Conditional Dependence
K. Fukumizu, A. Gretton, X. Sun and B. Schölkopf
Advances in Neural Information Processing Systems 20: Proceedings of the 2007 Conference
, Cambridge, MA, USA
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.