Nonparametric distributed learning under general designs
Nonparametric distributed learning under general designs
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DOI：
10.1214/20-ejs1733
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发表时间：
2020-01-01
影响因子：
1.1
通讯作者：
Cheng, Guang
中科院分区：
文献类型：
--
作者：
Liu, Meimei;Shang, Zuofeng;Cheng, Guang
本文主要研究非参数回归框架下的分布式学习。在计算资源充足的情况下，分布式算法的效率随着机器数量的增加而提高。我们的目标是分析机器数量如何影响统计最优性。我们建立了在非参数估计和假设检验两种情况下实现统计极大极小的机器数量的上界。与现有的工作相比，我们的框架是一般的。我们为各种回归问题建立了一个统一的分布式推理框架，包括薄板样条和随机设计下的加性回归：单变量、多变量和发散维设计。实现这一目标的主要工具是通过引入等效核的格林函数来建立经验过程的紧界。全面的数值研究支持理论发现。
This paper focuses on the distributed learning in nonparametric regression framework. With sufficient computational resources, the efficiency of distributed algorithms improves as the number of machines increases. 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.