Regularized greedy algorithms for network training with data noise

摘要

The aim of this paper is to construct a modified greedy algorithm applicable for an ill-posed function approximation problem in presence of data noise. We provide a detailed convergence analysis of the algorithm in presence of noise, and discuss the choice of the iteration parameters. This yields a stopping rule for which the corresponding algorithm is a regularization method with convergence rates in L-2 and under weak additional assumptions also in Sobolev-spaces of positive order.Finally, we discuss the application of the modified greedy algorithm to sigmoidal neural networks and radial basis functions, and supplement the theoretical results by numerical experiments.