期刊
ANNALS OF STATISTICS
卷 48, 期 4, 页码 1902-1905出版社
INST MATHEMATICAL STATISTICS-IMS
DOI: 10.1214/19-AOS1911
关键词
Deep neural networks; generalization; nonparametric regression
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.
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