The Annals of Statistics
- Ann. Statist.
- Volume 47, Number 4 (2019), 2261-2285.
On deep learning as a remedy for the curse of dimensionality in nonparametric regression
Assuming that a smoothness condition and a suitable restriction on the structure of the regression function hold, it is shown that least squares estimates based on multilayer feedforward neural networks are able to circumvent the curse of dimensionality in nonparametric regression. The proof is based on new approximation results concerning multilayer feedforward neural networks with bounded weights and a bounded number of hidden neurons. The estimates are compared with various other approaches by using simulated data.
Ann. Statist., Volume 47, Number 4 (2019), 2261-2285.
Received: November 2017
Revised: April 2018
First available in Project Euclid: 21 May 2019
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Bauer, Benedikt; Kohler, Michael. On deep learning as a remedy for the curse of dimensionality in nonparametric regression. Ann. Statist. 47 (2019), no. 4, 2261--2285. doi:10.1214/18-AOS1747. https://projecteuclid.org/euclid.aos/1558425645
- Supplement A: Further proofs. This supplementary file contains the rather technical proofs of several lemmas and assertions in this article.
- Supplement B: Further simulation results. This file contains the results of some experiments with another activation function in the neural network estimates.