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

I would like to commend Johannes Schmidt-Hieber for a very interesting and timely paper which studies nonparametric regression using deep neural networks. In recent years, the area of deep learning has seen an explosive growth within machine learning, leading to impressive leaps in performance across a wide range of important applications. However, our theoretical understanding of deep learning systems is still very limited, with many unresolved questions about their computational tractability and statistical performance. I believe that the statistics community can play a crucial role in tackling these challenging questions and hope that Schmidt-Hieber’s paper will spur additional research. Being a computer scientist rather than a statistician, I am happy for the opportunity to provide an “outsider’s” viewpoint on this paper (of course, any opinions expressed are solely my own).