Interactive Inference Under Information Constraints
Interactive Inference Under Information Constraints
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DOI：
10.1109/tit.2021.3123905
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发表时间：
2020-07
影响因子：
2.5
通讯作者：
Jayadev Acharya;C. Canonne;Yuhan Liu;Ziteng Sun;Himanshu Tyagi
中科院分区：
文献类型：
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作者：
Jayadev Acharya;C. Canonne;Yuhan Liu;Ziteng Sun;Himanshu Tyagi
我们研究了交互性在信息约束下的分布式统计推断中的作用，例如，通信约束和局部差分隐私。我们专注于拟合优度测试和离散分布估计的任务。从以前的工作中，这些任务在非交互式协议下得到了很好的理解。扩展这些方法直接用于交互式协议是困难的，由于相关性，可以建立由于交互性;事实上，差距可以发现在以前的索赔的紧边界的分布估计使用交互式协议。我们提出了一种新的方法来处理这种相关性，并建立一个统一的方法来建立这两个任务的下限。作为一个应用，我们得到了最优的边界估计和测试下的局部差分隐私和通信约束。我们还提供了一个自然测试问题的例子，其中交互性有助于。
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.