Discussion of: “Nonparametric regression using deep neural networks with ReLU activation function”

Kutyniok, Gitta (2020): Discussion of: “Nonparametric regression using deep neural networks with ReLU activation function”. In: Annals of Statistics, Vol. 48, No. 4: pp. 1902-1905

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.

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Mathematics > Bavarian Chair for Mathematical Foundations of Artificial Intelligence
• Subjects: 500 Science > 510 Mathematics
• ISSN: 0090-5364
• Language: English