OPTIMAL HIGH-DIMENSIONAL AND NONPARAMETRIC DISTRIBUTED TESTING UNDER COMMUNICATION CONSTRAINTS

• 成果类型: Article
• 署名作者: Szabo, Botond; Vuursteen, Lasse; van Zanten, Harry
• 署名单位: Bocconi University; Delft University of Technology; Vrije Universiteit Amsterdam
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/23-AOS2269
• 发表日期: 2023
• 页码: 909-934
• 关键词: inference

摘要

We derive minimax testing errors in a distributed framework where the data is split over multiple machines and their communication to a central ma-chine is limited to b bits. We investigate both the d- and infinite-dimensional signal detection problem under Gaussian white noise. We also derive dis-tributed testing algorithms reaching the theoretical lower bounds. Our results show that distributed testing is subject to fundamentally dif-ferent phenomena that are not observed in distributed estimation. Among our findings we show that testing protocols that have access to shared random-ness can perform strictly better in some regimes than those that do not. We also observe that consistent nonparametric distributed testing is always pos-sible, even with as little as one bit of communication, and the corresponding test outperforms the best local test using only the information available at a single local machine. Furthermore, we also derive adaptive nonparametric distributed testing strategies and the corresponding theoretical lower bounds.