Kernel Measures of Conditional Dependence.pdfVIP

Kernel Measures of Conditional Dependence Kenji Fukumizu Arthur Gretton Institute of Statistical Mathematics Max-Planck Institute for Biological Cybernetics ¨ 4-6-7 Minami-Azabu, Minato-ku Spemannstraße 38, 72076 Tubingen, Germany Tokyo 106-8569 Japan arthur.gretton@tuebingen.mpg.de fukumizu@ism.ac.jp Xiaohai Sun Max-Planck Institute for Biological Cybernetics ¨ Spemannstraße 38, 72076 Tubingen, Germany xiaohi@tuebingen.mpg.de ¨ Bernhard Scholkopf Max-Planck Institute for Biological Cybernetics ¨ Spemannstraße 38, 72076 Tubingen, Germany bernhard.schoelkopf@tuebingen.mpg.de Abstract 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. 1 Introduction Measuring dependence of rando