Summary of Minimax Optimal Two-sample Testing Under Local Differential Privacy, by Jongmin Mun et al.
Minimax Optimal Two-Sample Testing under Local Differential Privacy
by Jongmin Mun, Seungwoo Kwak, Ilmun Kim
First submitted to arxiv on: 13 Nov 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Cryptography and Security (cs.CR); Machine Learning (cs.LG)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary The paper explores the trade-off between privacy and statistical utility in private two-sample testing under local differential privacy (LDP) for both multinomial and continuous data. The authors introduce private permutation tests using practical privacy mechanisms such as Laplace, discrete Laplace, and Google’s RAPPOR. They extend this approach to continuous data via binning and study its uniform separation rates under LDP over Hölder and Besov smoothness classes. The proposed tests rigorously control the type I error for any finite sample size, adhere to LDP constraints, and achieve minimax separation rates under LDP. The results reveal inherent privacy-utility trade-offs that are unavoidable in private testing. To address scenarios with unknown smoothness parameters, the authors propose an adaptive test based on a Bonferroni-type approach that ensures robust performance without prior knowledge of the smoothness parameters. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary The paper looks at how to balance privacy and statistical usefulness when doing private two-sample tests. It uses local differential privacy (LDP) for both categorical and continuous data. The authors create new private permutation tests using Laplace, discrete Laplace, and RAPPOR methods. They also show that these tests work well under different types of smoothness classes. The results mean that there are unavoidable trade-offs between privacy and utility in private testing. |
