Privacy and Statistical Risk: Formalisms and Minimax Bounds

Abstract

We explore and compare a variety of definitions for privacy and disclosure limitation in statistical estimation and data analysis, including (approximate) differential privacy, testing-based definitions of privacy, and posterior guarantees on disclosure risk. We give equivalence results between the definitions, shedding light on the relationships between different formalisms for privacy. We also take an inferential perspective, where---building off of these definitions---we provide minimax risk bounds for several estimation problems, including mean estimation, estimation of the support of a distribution, and nonparametric density estimation. These bounds highlight the statistical consequences of different definitions of privacy and provide a second lens for evaluating the advantages and disadvantages of different techniques for disclosure limitation.

29 pages

Cited by in corpus (8)

• The Cost of Privacy in Generalized Linear Models: Algorithms and Minimax Lower Bounds
• Element Level Differential Privacy: The Right Granularity of Privacy
• Near Instance-Optimality in Differential Privacy
• A Note on Privacy in Constant Function Market Makers
• Adapting to Function Difficulty and Growth Conditions in Private Optimization
• Statistical Inference in the Differential Privacy Model
• Privately Learning Mixtures of Axis-Aligned Gaussians
• Pointwise adaptive kernel density estimation under local approximate differential privacy