Error Estimates for Multi-Penalty Regularization Under General Source Condition

摘要

In learning theory, the convergence issues of the regression problem are investigated withthe least square Tikhonov regularization schemes in both the RKHS-norm and the L2-norm.We consider the multi-penalized least square regularization scheme under the general sourcecondition with the polynomial decay of the eigenvalues of the integral operator. One of themotivation for this work is to discuss the convergence issues for widely considered manifoldregularization scheme. The optimal convergence rates of multi-penalty regularizer is achievedin the interpolation norm using the concept of e ective dimension. Further we also proposethe penalty balancing principle based on augmented Tikhonov regularization for the choice ofregularization parameters. The superiority of multi-penalty regularization over single-penaltyregularization is shown using the academic example and moon data set.