Regularized greedy algorithms for network training with data noise

Authors:
Martin Burger;Andreas Hofinger
Affiliations:
Industrial Mathematics Institute, Johannes-Kepler-University Linz, Altenbergerstr., Linz, Austria;SFB Numerical and Symbolic Scientific Computing, Johannes-Kepler-University Linz, Altenbergerstr., Linz, Austria
Venue:
Computing
Year:
2005

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Abstract

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 L2 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.