A supervised deep learning method for nonparametric density estimation

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Abstract

Nonparametric density estimation is an unsupervised learning problem. In this work we propose a two-step procedure that casts the density estimation problem in the first step into a supervised regression prob-lem. The advantage is that we can afterwards apply supervised learning methods. Compared to the standard nonparametric regression setting, the proposed procedure creates, however, dependence among the training sam-ples. To derive statistical risk bounds, one can therefore not rely on the well-developed theory for i.i.d. data. To overcome this, we prove an oracle inequality for this specific form of data dependence. As an application, it is shown that under a compositional structure assumption on the underlying density, the proposed two-step method achieves convergence rates that are faster than the standard nonparametric rates. A simulation study illus-trates the finite sample performance.

Original languageEnglish
Pages (from-to)5601-5658
Number of pages58
JournalElectronic Journal of Statistics
Volume18
Issue number2
DOIs
Publication statusPublished - 2024

Keywords

  • (Un)supervised learning
  • Neural networks
  • Nonparametric density esti-mation
  • Statistical estimation rates

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