Unified lower bounds for interactive high-dimensional estimation under information constraints

• URL: http://arxiv.org/abs/2010.06562v5
• Date: Thu, 26 Aug 2021 17:57:31 GMT
• Title: Unified lower bounds for interactive high-dimensional estimation under information constraints
• Authors: Jayadev Acharya, Cl\'ement L. Canonne, Ziteng Sun, and Himanshu Tyagi
• Abstract summary: We provide a unified framework enabling us to derive a variety of (tight) minimax lower bounds for different parametric families of distributions. Our lower bound framework is versatile and yields "plug-and-play" bounds that are widely applicable to a large range of estimation problems.
• Score: 40.339506154827106
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We consider the task of distributed parameter estimation using interactive protocols subject to local information constraints such as bandwidth limitations, local differential privacy, and restricted measurements. We provide a unified framework enabling us to derive a variety of (tight) minimax lower bounds for different parametric families of distributions, both continuous and discrete, under any $\ell_p$ loss. Our lower bound framework is versatile and yields "plug-and-play" bounds that are widely applicable to a large range of estimation problems. In particular, our approach recovers bounds obtained using data processing inequalities and Cram\'er--Rao bounds, two other alternative approaches for proving lower bounds in our setting of interest. Further, for the families considered, we complement our lower bounds with matching upper bounds.

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