Nonparametric regression with modified ReLU networks
- Institute of Environmental and Agricultural Biology (X-BIO), University of Tyumen（秋明大学生态与农业生物学研究所（X-BIO））
- University of Mississippi（密西西比大学）
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英文摘要：
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.
