Statistical Convergence of Kernel CCA

Fukumizu, K; Bach, F; Gretton, A

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Statistical Convergence of Kernel CCA

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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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https://papers.nips.cc/paper/2891-statistical-convergence-of-kernel-cca.pdf
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Citation

Fukumizu, K., Bach, F., & Gretton, A. (2006). Statistical Convergence of Kernel CCA. In Y. Weiss, B. Schölkopf, & J. Platt (Eds.), Advances in Neural Information Processing Systems 18: Proceedings of the 2005 Conference (pp. 387-394). Cambridge, MA, USA: MIT Press.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-D1EF-8

Abstract

While kernel canonical correlation analysis (kernel CCA) has been applied in many problems, the asymptotic convergence of the functions estimated from a finite sample to the true functions has not yet been established. This paper gives a rigorous proof of the statistical convergence of kernel CCA and a related method (NOCCO), which provides a theoretical justification for these methods. The result also gives a sufficient condition on the decay of the regularization coefficient in the methods to ensure convergence.