Interactive Inference under Information Constraints

• URL: http://arxiv.org/abs/2007.10976v5
• Date: Sat, 23 Oct 2021 09:12:58 GMT
• Title: Interactive Inference under Information Constraints
• Authors: Jayadev Acharya, Cl\'ement L. Canonne, Yuhan Liu, Ziteng Sun, and Himanshu Tyagi
• Abstract summary: We study the role of interactivity in distributed statistical inference under information constraints. We focus on the tasks of goodness-of-fit testing and estimation of discrete distributions.
• Score: 45.72264074254599
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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