Privacy and Statistical Risk: Formalisms and Minimax Bounds
arXiv:1412.4451
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 (18)
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- Robust and Differentially Private Mean Estimation
- Covariance-Aware Private Mean Estimation Without Private Covariance Estimation
- Toward Evaluating Re-identification Risks in the Local Privacy Model
- Element Level Differential Privacy: The Right Granularity of Privacy
- A Private and Computationally-Efficient Estimator for Unbounded Gaussians
- Differential privacy and robust statistics in high dimensions
- Optimal Rates of (Locally) Differentially Private Heavy-tailed Multi-Armed Bandits
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- 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
- Learning with User-Level Privacy
- Privately Learning Mixtures of Axis-Aligned Gaussians
- Pointwise adaptive kernel density estimation under local approximate differential privacy