Nonparametric distributed learning under general designs

Document Type

Article

Publication Date

1-1-2020

Abstract

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.

Identifier

85091658236 (Scopus)

Publication Title

Electronic Journal of Statistics

External Full Text Location

https://doi.org/10.1214/20-EJS1733

ISSN

19357524

First Page

3070

Last Page

3102

Issue

2

Volume

14

Grant

DMS-1712907

Fund Ref

National Science Foundation

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