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August 2020 Discussion of: “Nonparametric regression using deep neural networks with ReLU activation function”
Gitta Kutyniok
Ann. Statist. 48(4): 1902-1905 (August 2020). DOI: 10.1214/19-AOS1911

Abstract

I would like to congratulate Johannes Schmidt–Hieber on a very interesting paper in which he considers regression functions belonging to the class of so-called compositional functions and analyzes the ability of estimators based on the multivariate nonparametric regression model of deep neural networks to achieve minimax rates of convergence.

In my discussion, I will first regard such a type of result from the general viewpoint of the theoretical foundations of deep neural networks. This will be followed by a discussion from the viewpoint of expressivity, optimization and generalization. Finally, I will consider some specific aspects of the main result.

Citation

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Gitta Kutyniok. "Discussion of: “Nonparametric regression using deep neural networks with ReLU activation function”." Ann. Statist. 48 (4) 1902 - 1905, August 2020. https://doi.org/10.1214/19-AOS1911

Information

Received: 1 September 2019; Published: August 2020
First available in Project Euclid: 14 August 2020

MathSciNet: MR4134776
Digital Object Identifier: 10.1214/19-AOS1911

Subjects:
Primary: 62G08

Rights: Copyright © 2020 Institute of Mathematical Statistics

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Vol.48 • No. 4 • August 2020
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