# Approximation and Estimation Bounds for Artificial Neural Networks

@article{Barron1991ApproximationAE, title={Approximation and Estimation Bounds for Artificial Neural Networks}, author={Andrew R. Barron}, journal={Machine Learning}, year={1991}, volume={14}, pages={115-133} }

- Published 1991 in Machine Learning
DOI:10.1023/A:1022650905902

For a common class of artificial neural networks, the mean integrated squared error between the estimated network and a target function f is shown to be bounded by $${\text{O}}\left( {\frac{{C_f^2 }}{n}} \right) + O(\frac{{ND}}{N}\log N)$$ where n is the number of nodes, d is the input dimension of the function, N is the number of training observations, and C f is the first absolute moment of the Fourier magnitude distribution of f. The two contributions to this total risk are the approximationâ€¦Â CONTINUE READING

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