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In the era of advanced data collection technologies, safeguarding individual privacy has become paramount. Local Differential Privacy (LDP) provides an effective means of privacy preservation, widely adopted across academia and industry. This paper investigates LDP perturbation mechanisms—specifically focusing on encoding, perturbation, and aggregation—under a sampling scheme without replacement, which differs from traditional approaches that utilize replacement-based sampling. Our work introduces refined variance analyses and proposes enhanced perturbation mechanisms tailored for scenarios involving entire populations. We find that the Improved Simmons mechanism achieves the lowest variance when the privacy budget is below a specific threshold, while the Improved Warner mechanism excels beyond this threshold. These results align closely with real-world contexts. In experiments using actual datasets, the Improved Warner mechanism reduces variance to 28.7% and the Improved Simmons mechanism to 11.7% compared to their original methods. Furthermore, we illustrate practical deployment scenarios for these mechanisms. The source code, data, and supplementary materials are publicly available at https://github.com/ssjhf/LDP-Perturbation-Mechanisms.git .

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Comparing and Improving Perturbation Mechanisms Under Local Differential Privacy

  • 会议论文

  • 发表日期：

    2026年

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  • She Sun,
  • Li Zhou,
  • Xiaoran Yan,
  • Yi Liu,
  • Huiwen Wu,
  • Jian Yang

摘要

In the era of advanced data collection technologies, safeguarding individual privacy has become paramount. Local Differential Privacy (LDP) provides an effective means of privacy preservation, widely adopted across academia and industry. This paper investigates LDP perturbation mechanisms—specifically focusing on encoding, perturbation, and aggregation—under a sampling scheme without replacement, which differs from traditional approaches that utilize replacement-based sampling. Our work introduces refined variance analyses and proposes enhanced perturbation mechanisms tailored for scenarios involving entire populations. We find that the Improved Simmons mechanism achieves the lowest variance when the privacy budget is below a specific threshold, while the Improved Warner mechanism excels beyond this threshold. These results align closely with real-world contexts. In experiments using actual datasets, the Improved Warner mechanism reduces variance to 28.7% and the Improved Simmons mechanism to 11.7% compared to their original methods. Furthermore, we illustrate practical deployment scenarios for these mechanisms. The source code, data, and supplementary materials are publicly available at https://github.com/ssjhf/LDP-Perturbation-Mechanisms.git .