The DOI matches its Crossref record; 40 of the 40 references it cites were found in a registry or an index.
Nonparametric regression using deep neural networks with ReLU activation function
Open accessAbstract
Consider the multivariate nonparametric regression model. It is shown that estimators based on sparsely connected deep neural networks with ReLU activation function and properly chosen network architecture achieve the minimax rates of convergence (up to $\log n$-factors) under a general composition assumption on the regression function. The framework includes many well-studied structural constraints such as (generalized) additive models. While there is a lot of flexibility in the network architecture, the tuning parameter is the sparsity of the network. Specifically, we consider large networks with number of potential network parameters exceeding the sample size. The analysis gives some insights into why multilayer feedforward neural networks perform well in practice. Interestingly, for ReLU activation function the depth (number of layers) of the neural network architectures plays an important role, and our theory suggests that for nonparametric regression, scaling the network depth with the sample size is natural. It is also shown that under the composition assumption wavelet estimators can only achieve suboptimal rates.
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Cites
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Cited by
Debiased machine learning of conditional average treatment effects and other causal functions
Semenova, V., & Chernozhukov, V. (2021) · The Econometrics Journal · doi:10.1093/ectj/utaa027 · Cited by 167
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A Tale of Tails: Model Collapse as a Change of Scaling Laws
Dohmatob, E., Feng, Y., Yang, P., Charton, F., & Kempe, J. (2024) · arXiv · doi:10.48550/arxiv.2402.07043 · Cited by 20
Berrevoets, J., Kacprzyk, K., Qian, Z., & van der Schaar, M. (2023) · arXiv · doi:10.48550/arxiv.2303.02186 · Cited by 8
“In fact, it has been shown that neural networks 5 have a connection to non-parametric regression, leading to high performance models [72].”
Background
Metadata
- Authors
- Schmidt-Hieber, J.
- Venue
- The Annals of Statistics
- Publisher
- Institute of Mathematical Statistics
- Published
- 2020-08-01
- Volume
- 48
- Issue
- 4
- Pages
- 1875-1897
- ISSN
- 0090-5364 (ISSN-L)
- OpenAlex
- W2749772809
- Cited by
- 292
- References
- 40
- FWCI
- 11.74
- Type
- journal article
- Language
- en
- Open access
- bronze
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