# Nonparametric regression using deep neural networks with ReLU activation function

@article{SchmidtHieber2020NonparametricRU,
title={Nonparametric regression using deep neural networks with ReLU activation function},
author={Johannes Schmidt-Hieber},
journal={ArXiv},
year={2020},
volume={abs/1708.06633}
}
Consider the multivariate nonparametric regression model. It is shown that estimators based on sparsely connected deep neural networks with ReLU activation function and properly chosen network architecture achieve the minimax rates of convergence (up to $\log n$-factors) under a general composition assumption on the regression function. The framework includes many well-studied structural constraints such as (generalized) additive models. While there is a lot of flexibility in the network…
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