We establish a new oracle inequality for kernelbased, regularized least squares regression methods, which uses the eigenvalues of the associated integral operator as a complexity measure. We then use this oracle inequality to derive learning rates for these methods. Here, it turns out that these rates are independent of the exponent of the regularization term. Finally, we show that our learning rates are asymptotically optimal whenever, e.g., the kernel is continuous and the input space is a compact metric space.
I. Steinwart, D. Hush, and C. Scovel, Optimal Rates for Regularized Least Squares Regression. In Proceedings of the 22nd Conference on Learning Theory, 2009. Los Alamos National Laboratory Technical Report LA-UR-09-00901, 2009. [ Abstract | PDF (238 KB) ]
