Approximate Minimization of the Regularized Expected Error Over Kernel Models

Learning from data under constraints on model complexity is studied in terms of rates of approximate minimization of the regularized expected error functional. For kernel models with an increasing number n of kernel functions, upper bounds on such rates are derived. The bounds are of the form a/n+b/ √ n, where a and b depend on the regularization parameter and on properties of the kernel, and of the probability measure defining the expected error. As a special case, estimates of rates of approximate minimization of the regularized empirical error are derived.