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ON DEEP LEARNING AS A REMEDY FOR THE CURSE OF DIMENSIONALITY IN NONPARAMETRIC REGRESSION
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ON DEEP LEARNING AS A REMEDY FOR THE CURSE OF DIMENSIONALITY IN NONPARAMETRIC REGRESSION
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ON DEEP LEARNING AS A REMEDY FOR THE CURSE OF DIMENSIONALITY IN NONPARAMETRIC REGRESSION
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Journal Article
ON DEEP LEARNING AS A REMEDY FOR THE CURSE OF DIMENSIONALITY IN NONPARAMETRIC REGRESSION
2019
Overview
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.
Publisher
Institute of Mathematical Statistics
