Learning Rates of Least-Square Regularized Regression

This paper considers the regularized learning algorithm associated with the leastsquare loss and reproducing kernel Hilbert spaces. The target is the error analysis for the regression problem in learning theory. A novel regularization approach is presented, which yields satisfactory learning rates. The rates depend on the approximation property and the capacity of the reproducing kernel Hilbert space measured by covering numbers. When the kernel is C∞ and the regression function lies in the corresponding reproducing kernel Hilbert space, the rate is m−ζ with ζ arbitrarily close to 1, regardless of the variance of the bounded probability distribution. Short Title: Least-square Regularized Regression