Statistical Consistency of Kernel Canonical Correlation Analysis

Fukumizu, K; Bach, FR; Gretton, A

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Statistical Consistency of Kernel Canonical Correlation Analysis

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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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http://jmlr.csail.mit.edu/papers/volume8/fukumizu07a/fukumizu07a.pdf
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Fukumizu, K., Bach, F., & Gretton, A. (2007). Statistical Consistency of Kernel Canonical Correlation Analysis. The Journal of Machine Learning Research, 8, 361-383.

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

Abstract

While kernel canonical correlation analysis (CCA) has been applied in many contexts, the convergence of finite sample estimates of the associated functions to their population counterparts has not yet been established. This paper gives a mathematical proof of the statistical convergence of kernel CCA, providing a theoretical justification for the method. The proof uses covariance operators defined on reproducing kernel Hilbert spaces, and analyzes the convergence of their empirical estimates of finite rank to their population counterparts, which can have infinite rank. The result also gives a sufficient condition for convergence on the regularization coefficient involved in kernel CCA: this should decrease as n^-1/3, where n is the number of data.