论文标题
信息约束下的互动推论
Interactive Inference under Information Constraints
论文作者
论文摘要
我们研究了在信息限制（例如，通信约束和当地差异隐私）下，交互性在分布式统计推断中的作用。我们专注于合适性测试的任务和离散分布的估计。从先前的工作中，这些任务在非相互作用协议下得到了充分的理解。由于相关性可以由于交互性而建立，因此很难直接扩展这些方法以进行交互式协议。实际上，可以在先前使用交互式协议的分布估计的紧密范围内找到差距。 我们提出了一种处理这种相关性的新方法，并建立了一种统一的方法来建立这两个任务的下限。作为应用程序，我们在当地差异隐私和通信约束下获得了估计和测试的最佳界限。我们还提供了一个自然测试问题的示例，其中交互作用有所帮助。
We study the role of interactivity in distributed statistical inference under information constraints, e.g., communication constraints and local differential privacy. We focus on the tasks of goodness-of-fit testing and estimation of discrete distributions. From prior work, these tasks are well understood under noninteractive protocols. Extending these approaches directly for interactive protocols is difficult due to correlations that can build due to interactivity; in fact, gaps can be found in prior claims of tight bounds of distribution estimation using interactive protocols. We propose a new approach to handle this correlation and establish a unified method to establish lower bounds for both tasks. As an application, we obtain optimal bounds for both estimation and testing under local differential privacy and communication constraints. We also provide an example of a natural testing problem where interactivity helps.
