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Interactive Inference under Information Constraints

Acharya, J and Canonne, CL and Liu, Y and Sun, Z and Tyagi, H (2022) Interactive Inference under Information Constraints. In: IEEE Transactions on Information Theory, 68 (1). pp. 502-516.

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Official URL: https://doi.org/10.1109/TIT.2021.3123905


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.

Item Type: Journal Article
Publication: IEEE Transactions on Information Theory
Publisher: Institute of Electrical and Electronics Engineers Inc.
Additional Information: The copyright for this article belongs to the Authors.
Keywords: Communication constraints; Complexity theory; Correlation; Differential privacies; Goodness-of-fit testing; Interactive protocols; Interactivity; Privacy; Statistical inference; Task analysis, Job analysis
Department/Centre: Division of Electrical Sciences > Electrical Communication Engineering
Date Deposited: 08 Jul 2022 05:57
Last Modified: 08 Jul 2022 05:57
URI: https://eprints.iisc.ac.in/id/eprint/74285

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