Nonparametric regression with modified ReLU networks

Aleksandr Beknazaryan, Hailin Sang
7/17/2022
stat.MLcs.LGmath.ST

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Abstract

We consider regression estimation with modified ReLU neural networks in which network weight matrices are first modified by a function $α$ before being multiplied by input vectors. We give an example of continuous, piecewise linear function $α$ 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 $β$-smooth function.

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Cite this paper

@article{beknazaryan2022nonparametric,
  title  = {Nonparametric regression with modified ReLU networks},
  author = {Aleksandr Beknazaryan and Hailin Sang},
  year   = {2022},
  eprint = {2207.08306},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2207.08306v1}
}

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