On the rate of convergence of fully connected deep neural network regression estimates

Sophie Langer, Michael Kohler

Research output: Contribution to journalArticleAcademicpeer-review

2 Citations (Scopus)
4 Downloads (Pure)

Abstract

Recent results in nonparametric regression show that deep learning, that is, neural network estimates with many hidden layers, are able to circumvent the so-called curse of dimensionality in case that suitable restrictions on the structure of the regression function hold. One key feature of the neural networks used in these results is that their network architecture has a further constraint, namely the network sparsity. In this paper, we show that we can get similar results also for least squares estimates based on simple fully connected neural networks with ReLU activation functions. Here, either the number of neurons per hidden layer is fixed and the number of hidden layers tends to infinity suitably fast for sample size tending to infinity, or the number of hidden layers is bounded by some logarithmic factor in the sample size and the number of neurons per hidden layer tends to infinity suitably fast for sample size tending to infinity. The proof is based on new approximation results concerning deep neural networks.
Original languageEnglish
Pages (from-to)2231-2249
Number of pages19
JournalAnnals of statistics
Volume49
Issue number4
DOIs
Publication statusPublished - 1 Aug 2021
Externally publishedYes

Fingerprint

Dive into the research topics of 'On the rate of convergence of fully connected deep neural network regression estimates'. Together they form a unique fingerprint.

Cite this