On Convergence of Kernel Learning Estimators

The paper studies kernel regression learning from stochastic optimization and ill-posedness point of view. Namely, the convergence properties of kernel learning estimators are investigated under a gradual elimination of the regularization parameter with rising number of observations. We derive computable non-asymptotic bounds on the deviation of the expected risk from its best possible value and obtain an optimal value for the regularization parameter that minimizes these bounds. We establish conditions for almost sure convergence of function estimates, jointly with a rule for downward adjustment of the regularization factor with increasing sample size.