A central server needs to perform statistical inference based on samples that are distributed over multiple users who can each send a message of limited length to the center. We study problems of distribution learning and identity testing in this distributed inference setting and examine the role of shared randomness as a resource. We propose a general-purpose simulate-and-infer strategy that uses only private-coin communication protocols and is sample-optimal for distribution learning. This general strategy turns out to be sample-optimal even for distribution testing among private-coin protocols. Interestingly, we propose a public-coin protocol that outperforms simulate-and-infer for distribution testing and is, in fact, sample-optimal. Underlying our public-coin protocol is a random hash that when applied to the samples minimally contracts the chi-squared distance of their distribution to the uniform distribution.

中文翻译：

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信息约束下的推理 II：通信约束和共享随机性

中央服务器需要根据分布在多个用户上的样本进行统计推断，每个用户都可以向中心发送有限长度的消息。我们研究了分布式推理设置中的分布学习和身份测试问题，并研究了共享随机性作为资源的作用。我们提出了一种通用的模拟和推断策略，该策略仅使用私有硬币通信协议，并且对于分布学习是样本最优的。即使对于私有硬币协议之间的分发测试，这种通用策略也证明是样本最优的。有趣的是，我们提出了一种公共硬币协议，该协议在分布测试方面优于模拟和推断，并且实际上是样本最优的。