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Kernel Constrained Covariance for Dependence Measurement

2005

Conference Paper

ei


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, AJ. and Bousquet, O. and Herbrich, R. and Belitski, A. and Augath, M. and Murayama, Y. and Pauls, J. and Schölkopf, B. and Logothetis, NK.
Book Title: Proceedings of the 10th International Workshop on Artificial Intelligence and Statistics
Journal: AISTATS 2005
Pages: 112-119
Year: 2005
Month: January
Day: 0
Editors: R Cowell, R and Z Ghahramani

Department(s): Empirical Inference
Bibtex Type: Conference Paper (inproceedings)

Event Name: AISTATS 2005
Event Place: Barbados

Digital: 0
Institution: MPI for Biological Cybernetics, Spemannstr 38 72076 Tuebingen
ISBN: 0-9727358-1-X
Language: en
Organization: Max-Planck-Gesellschaft
School: Biologische Kybernetik

Links: PDF
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BibTex

@inproceedings{3174,
  title = {Kernel Constrained Covariance for Dependence Measurement},
  author = {Gretton, A. and Smola, AJ. and Bousquet, O. and Herbrich, R. and Belitski, A. and Augath, M. and Murayama, Y. and Pauls, J. and Sch{\"o}lkopf, B. and Logothetis, NK.},
  journal = {AISTATS 2005},
  booktitle = {Proceedings of the 10th International Workshop on Artificial Intelligence and Statistics},
  pages = {112-119},
  editors = {R Cowell, R and Z Ghahramani},
  organization = {Max-Planck-Gesellschaft},
  institution = {MPI for Biological Cybernetics, Spemannstr 38 72076 Tuebingen},
  school = {Biologische Kybernetik},
  month = jan,
  year = {2005},
  month_numeric = {1}
}