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ON DEEP LEARNING AS A REMEDY FOR THE CURSE OF DIMENSIONALITY IN NONPARAMETRIC REGRESSION
Ist Teil von
The Annals of statistics, 2019-08, Vol.47 (4), p.2261-2285
Ort / Verlag
Hayward: Institute of Mathematical Statistics
Erscheinungsjahr
2019
Quelle
Project Euclid Complete
Beschreibungen/Notizen
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.