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Empirische Inferenz Talk 2005

Kernel Constrained Covariance for Dependence Measurement

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Empirische Inferenz
Arthur Gretton
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Empirische Inferenz
Bernhard Schölkopf
  • Director
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Empirische Inferenz
Olivier Bousquet

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.

Author(s): Gretton, A. and Smola, A. and Bousquet, O. and Herbrich, R. and Belitski, A. and Augath, M. and Murayama, Y. and Schölkopf, B. and Logothetis, NK.
Year: 2005
Month: January
Day: 0
Bibtex Type: Talk (talk)
Digital: 0
Electronic Archiving: grant_archive
Event Name: AISTATS 2005
Language: en
Organization: Max-Planck-Gesellschaft
School: Biologische Kybernetik
Links:

BibTex 

@talk{4277,
  title = {Kernel Constrained Covariance for Dependence Measurement},
  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.},
  organization = {Max-Planck-Gesellschaft},
  school = {Biologische Kybernetik},
  month = jan,
  year = {2005},
  slug = {4277},
  author = {Gretton, A. and Smola, A. and Bousquet, O. and Herbrich, R. and Belitski, A. and Augath, M. and Murayama, Y. and Sch{\"o}lkopf, B. and Logothetis, NK.},
  month_numeric = {1}
}