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

By Behrooz Ghorbani, Song Mei, Theodor Misiakiewicz, Andrea Montanari. 2020

27 citations recorded by the source corpus.

for g,gl1, . . . , gl1,...,lr : R → R (p,C)-smooth functions and x1r single components of x ∈ R (not necessarily different for two different indices (l1, . . . , lr )). With the use of a penalized least squares estimate for smoothing splines, they proved the rate n−2p/(2p+1). Kohler and Krzyżak (2017) extended this function class in form of the so-called generalized hierarchical interaction models introduced as follows:

Subfields: Artificial Intelligence, Computer Vision and Pattern Recognition, Statistics and Probability

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Sanjog Misra
2. Max H. Farrell
3. Tengyuan Liang
4. Simon Lacoste-Julien

In Computer Vision and Pattern Recognition

1. Max H. Farrell
2. Sanjog Misra
3. Tengyuan Liang

In Statistics and Probability

1. Tengyuan Liang
2. Sanjog Misra
3. Max H. Farrell
4. M. D. Cattaneo
5. Zhiqiang Tan
6. Stefan Wager
7. Sebastian Calonico
8. Susan Athey

Citations in the corpus

• Deep Neural Networks for Estimation and Inference: Application to Causal Effects and Other Semiparametric Estimands (2018, background): “For more on the results and limitations of Schmidt-Hieber (2019), see the published discussions (Ghorbani et al., 2019; Shamir, 2019; Kutyniok, 2019).”