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Kernel Constrained Covariance for Dependence Measurement

MPS-Authors
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Gretton,  A
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;
Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Bousquet,  O
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;
Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Belitski,  A
Max Planck Institute for Biological Cybernetics, Max Planck Society;
Department Physiology of Cognitive Processes, Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Augath,  M
Max Planck Institute for Biological Cybernetics, Max Planck Society;
Department Physiology of Cognitive Processes, Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Murayama,  Y
Max Planck Institute for Biological Cybernetics, Max Planck Society;
Department Physiology of Cognitive Processes, Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Pauls,  J
Max Planck Institute for Biological Cybernetics, Max Planck Society;
Department Physiology of Cognitive Processes, Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Schölkopf,  B
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;
Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Logothetis,  NK
Max Planck Institute for Biological Cybernetics, Max Planck Society;
Department Physiology of Cognitive Processes, Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Citation

Gretton, A., Smola, A., Bousquet, O., Herbrich, R., Belitski, A., Augath, M., et al. (2005). Kernel Constrained Covariance for Dependence Measurement. In R. Cowell, & Z. Ghahramani (Eds.), AISTATS 2005: Tenth International Workshop onArtificial Intelligence and Statistics (pp. 112-119). The Society for Artificial Intelligence and Statistics.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-D693-A
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.