PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Behaviour and Convergence of the Constrained Covariance
Arthur Gretton, Alex Smola, Olivier Bousquet, Ralf Herbrich, Bernhard Schoelkopf and Nikos Logothetis
(2004) Technical Report. MPI for Biological Cybernetics, Tuebingen, Germany.


We discuss reproducing kernel Hilbert space (RKHS)-based measures of statistical dependence, with emphasis on constrained covariance (COCO), a novel criterion to test dependence of random variables. We show that COCO is a test for independence if and only if the associated RKHSs are universal. That said, \emph{no} independence test exists that can distinguish dependent and independent random variables in all circumstances. Dependent random variables can result in a COCO which is arbitrarily close to zero when the source densities are highly non-smooth. All current kernel-based independence tests share this behaviour. We demonstrate exponential convergence between the population and empirical COCO.

EPrint Type:Monograph (Technical Report)
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Computational, Information-Theoretic Learning with Statistics
Learning/Statistics & Optimisation
Theory & Algorithms
ID Code:590
Deposited By:Arthur Gretton
Deposited On:26 December 2004