Learning Rates for Least Square Regressions with Coefficient Regularization

We analyze the learning rates for the least square regression with data dependent hy- pothesis spaces and coefficient regularization algorithms based on general kernels. Under a very mild regularity condition on the regression function, we obtain a bound for the approximation error by esti- mating the corresponding K：-functional. Combining this estimate with the previous result of the sample error, we derive a dimensional free learning rate by the proper choice of the regularization parameter.

The Learning Rate of l_2-Coefcient Regularized Classifcation with Strong Loss

In the present paper, we give an investigation on the learning rate of l2-coefficient regularized classification with strong loss and the data dependent kernel functional spaces. The results show that the learning rate is influenced by the strong convexity.