Model Selection for Regularized Least-Squares Algorithm in Learning Theory

We investigate the problem of model selection for learning algorithms depending on a continuous parameter. We propose a model selection procedure based on a worst-case analysis and on a data-independent choice of the parameter. For the regularized least-squares algorithm we bound the generalization error of the solution by a quantity depending on a few known constants and we show that the corresponding model selection procedure reduces to solving a bias-variance problem. Under suitable smoothness conditions on the regression function, we estimate the optimal parameter as a function of the number of data and we prove that this choice ensures consistency of the algorithm.