DISCUSSION OF: NONPARAMETRIC REGRESSION USING DEEP NEURAL NETWORKS WITH RELU ACTIVATION FUNCTION

• 成果类型: Editorial Material
• 署名作者: Kutyniok, Gitta
• 署名单位: Technical University of Berlin
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/19-AOS1911
• 发表日期: 2020
• 页码: 1902-1905
• 关键词: Approximation

摘要

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.