Nonparametric regression with modified ReLU networks

Abstract

We consider regression estimation with modified ReLU neural networks in which network weight matrices are first modified by a function before being multiplied by input vectors. We give an example of continuous, piecewise linear function for which the empirical risk minimizers over the classes of modified ReLU networks with l_1 and squared l_2 penalties attain, up to a logarithmic factor, the minimax rate of prediction of unknown -smooth function.

Tasks

Reproductions