Minimax Optimal Two-Sample Testing under Local Differential Privacy

2024-12-31 · Source: JMLR · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Data Science & Analytics, Cybersecurity & Data Privacy · Depth: Expert, quick

Summary

A new study introduces minimax optimal two-sample testing methods under local differential privacy (LDP) for both multinomial and continuous data. For multinomial data, the research proposes private permutation tests utilizing privacy mechanisms like Laplace, discrete Laplace, and Google's RAPPOR. This methodology is extended to continuous data through binning, with its uniform separation analyzed under LDP across Hölder and Besov smoothness classes. The proposed tests for both data types rigorously control type I error for any finite sample size, strictly adhere to LDP constraints, and achieve minimax optimality. The study also presents a Bonferroni-type adaptive test for density testing scenarios with unknown smoothness parameters, ensuring robust performance. Numerical experiments validate the theoretical findings and demonstrate the practical effectiveness of these methods.

Key takeaway

For research scientists developing privacy-preserving statistical tests, you should consider integrating these minimax optimal LDP two-sample tests. Your work can benefit from the rigorous type I error control and the demonstrated practical effectiveness, especially when dealing with both multinomial and continuous datasets under strict privacy constraints. The adaptive test for unknown smoothness parameters offers a robust solution for real-world applications.

Key insights

Minimax optimal two-sample tests under LDP are developed for multinomial and continuous data.

Principles

• LDP introduces unavoidable privacy-utility trade-offs.
• Type I error can be controlled for finite sample sizes.
• Binning extends discrete methods to continuous data.

Method

Private permutation tests are used with Laplace, discrete Laplace, or RAPPOR mechanisms. This is extended to continuous data via binning, with a Bonferroni-type adaptive test for unknown smoothness.

In practice

• Use Laplace/RAPPOR for private permutation tests.
• Apply binning for continuous data under LDP.
• Employ adaptive tests for unknown smoothness parameters.

Topics

• Minimax Optimal Testing
• Local Differential Privacy
• Two-Sample Testing
• Privacy-Utility Trade-off
• Smoothness Classes

Code references

• Jong-Min-Moon/optimal-local-dp-two-sample

Best for: Research Scientist, AI Researcher, AI Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by JMLR.