Nonasymptotic bounds on the L2 error of neural network regression estimates
نویسندگان
چکیده
The estimation of multivariate regression functions from bounded i.i.d. data is considered. TheL2 error with integration with respect to the design measure is used as an error criterion. The distribution of the design is assumed to be concentrated on a finite set. Neural network estimates are defined by minimizing the empirical L2 risk over various sets of feedforward neural networks. Nonasymptotic bounds on the L2 error of these estimates are presented. The results imply that neural networks are able to adapt to additive regression functions and to regression functions which are a sum of ridge functions, and hence are able to circumvent the curse of dimensionality in these cases.
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