Behaviour and Convergence of the Constrained Covariance

  title={Behaviour and Convergence of the Constrained Covariance},
  author={Arthur Gretton and Alexander J. Smola and Olivier Bousquet and Ralf Herbrich and Bernhard Sch{\"o}lkopf and Nikos K. Logothetis},
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, 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… CONTINUE READING