# 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}
}
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 approximation… CONTINUE READING
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