PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Kernel Constrained Covariance for Dependence Measurement
Arthur Gretton, Alex Smola, Olivier Bousquet, Ralf Herbrich, Andrei Belitski, Mark Augath, Yusuke Murayama, John Pauls, Bernhard Schölkopf and Nikos Logothetis
In: AISTATS 2005, January 6-8, 2005, Barbados.

Abstract

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 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. Finally, we use COCO as a measure of joint neural activity between voxels in MRI recordings of the macaque monkey, and compare the results to the mutual information and the correlation. We also show the effect of removing breathing artefacts from the MRI recording.

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EPrint Type:Conference or Workshop Item (Paper)
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Computational, Information-Theoretic Learning with Statistics
Theory & Algorithms
ID Code:1625
Deposited By:Arthur Gretton
Deposited On:28 November 2005