Nonparametric distributed learning under general designs

Meimei Liu, Zuofeng Shang, Guang Cheng

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


This paper focuses on the distributed learning in nonparamet-ric regression framework. With sufficient computational resources, the ef-ficiency of distributed algorithms improves as the number of machines in-creases. We aim to analyze how the number of machines affects statistical optimality. We establish an upper bound for the number of machines to achieve statistical minimax in two settings: nonparametric estimation and hypothesis testing. Our framework is general compared with existing work. We build a unified frame in distributed inference for various regression problems, including thin-plate splines and additive regression under random design: univariate, multivariate, and diverging-dimensional designs. The main tool to achieve this goal is a tight bound of an empirical process by introducing the Green function for equivalent kernels. Thorough numerical studies back theoretical findings.

Original languageEnglish (US)
Pages (from-to)3070-3102
Number of pages33
JournalElectronic Journal of Statistics
Issue number2
StatePublished - 2020

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


  • Computational limit
  • Divide and conquer
  • Kernel ridge regression
  • Minimax optimality
  • Nonparametric testing


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