Optimal learning rates for Kernel Conjugate Gradient regression

Abstract

We prove rates of convergence in the statistical sense for kernel-based least squares regression using a conjugate gradient algorithm, where regularization against overfitting is obtained by early stopping. This method is directly related to Kernel Partial Least Squares, a regression method that combines supervised dimensionality reduction with least squares projection. The rates depend on two key quantities: first, on the regularity of the target regression function and second, on the intrinsic dimensionality of the data mapped into the kernel space. Lower bounds on attainable rates depending on these two quantities were established in earlier literature, and we obtain upper bounds for the considered method that match these lower bounds (up to a log factor) if the true regression function belongs to the reproducing kernel Hilbert space. If this assumption is not fulfilled, we obtain similar convergence rates provided additional unlabeled data are available. The order of the learning rates match state-of-the-art results that were recently obtained for least squares support vector machines and for linear regularization operators.

to appear in Neural Information Processing Systems 2010

References in corpus (2)

• Discussion of ``2004 IMS Medallion Lecture: Local Rademacher complexities and oracle inequalities in risk minimization'' by V. Koltchinskii
• Kernel Partial Least Squares is Universally Consistent

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