Risk Bounds and Model Selection for Regularized Least Squares
Motivation: A central problem in learning theory is a quantitative assessment of the inference property of a learning algorithm ensuring consistency. A number of seminal works show that the essential feature of an algorithm should be its capacity of controlling the complexity of the solution, this is usually realized introducing a parametric family of learning algorithms in which the parameters control the generalization properties. We focus on a particularly simple algorithm, the regularized least squares. In this context the central problem is in fact the optimal choice of the regularization parameter as a function of the number of available examples, the used kernel and the a priori knowledge about the searched regression function.