ON DEEP LEARNING AS A REMEDY FOR THE CURSE OF DIMENSIONALITY IN NONPARAMETRIC REGRESSION

• 成果类型: Article
• 署名作者: Bauer, Benedikt; Kohler, Michael
• 署名单位: Technical University of Darmstadt
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/18-AOS1747
• 发表日期: 2019
• 页码: 2261-2285
• 关键词: Approximation; CONVERGENCE; networks; bounds; rates

摘要

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.