Comparison of worst case errors in linear and neural network approximation

Sets of multivariable functions are described for which worst case errors in linear approximation are larger than those in approximation by neural networks. A theoretical framework for such a description is developed in the context of nonlinear approximation by fixed versus variable basis functions. Comparisons of approximation rates are formulated in terms of certain norms tailored to sets of basis functions. The results are applied to perceptron networks.

• Type: Journal
• Year: 2002
• Where: TIT
• Authors: Vera Kurková, Marcello Sanguineti
• Keywords: Approximation, Linear Approximation, TIT 2002, Worst Case Errors