Optimal high-dimensional and nonparametric distributed testing under communication constraints
研究了数据分散在多台机器且通信受限时，如何设计最优的分布式假设检验方法，发现分布式检验有不同于分布式估计的新现象，且一致非参数检验即使只有1比特通信也能实现。
We derive minimax testing errors in a distributed framework where the data is split over multiple machines and their communication to a central machine is limited to b bits. We investigate both the d- and infinite-dimensional signal detection problem under Gaussian white noise. We also derive distributed testing algorithms reaching the theoretical lower bounds. Our results show that distributed testing is subject to fundamentally different phenomena that are not observed in distributed estimation. Among our findings we show that testing protocols that have access to shared randomness can perform strictly better in some regimes than those that do not. We also observe that consistent nonparametric distributed testing is always possible, 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.