Year: 2022
Type: preprint
Abstract: In this work, we study local minimax convergence estimation rates subject to $ε$-differential privacy. Unlike worst-case rates, which may be conservative, algorithms that are locally minimax optimal must adapt to easy instances of the problem. We construct locally minimax differentially private estimators for one-parameter exponential families and estimating the tail rate of a distribution. In these cases, we show that optimal algorithms for simple hypothesis testing, namely the recent optimal private testers of Canonne et al. (2019), directly inform the design of locally minimax estimation algorithms.
Source: arXiv (Cornell University)
Authors: McMillan, Audra, Smith, Adam, Ullman, Jon
Institutions: Boston University, Northeastern University
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4307788253