用小波展开提升数值型数据的本地差分隐私分布估计精度。
Consistent Estimation of Numerical Distributions under Local Differential Privacy by Wavelet Expansion
- 通过小波系数在本地差分隐私下估计分布，优先保证宏观层面准确。
- 在Wasserstein和KS距离上显著优于现有方法，误差更低。
- 适合需要保护隐私且关注整体分布形态的数值数据场景。
在本地差分隐私（LDP）下的分布估计是一个基础且具有挑战性的任务。针对类别型数据已有显著进展，但由于评估指标不同，这些方法难以直接应用于数值型数据。特别是需防止概率质量被错误地移至远离真实值的位置。本文提出一种新方法：利用小波展开表示样本分布，并在LDP下估计小波系数。该方法优先估计低阶系数，以确保宏观层面的准确性，从而避免概率质量过度偏移。我们为该方法建立了理论保障。实验表明，该小波展开方法在Wasserstein距离和Kolmogorov-Smirnov（KS）距离上均显著优于现有方案。
原文摘要 · Abstract (English)
Distribution estimation under local differential privacy (LDP) is a fundamental and challenging task. Significant progresses have been made on categorical data. However, due to different evaluation metrics, these methods do not work well when transferred to numerical data. In particular, we need to prevent the probability mass from being misplaced far away. In this paper, we propose a new approach that express the sample distribution using wavelet expansions. The coefficients of wavelet series are estimated under LDP. Our method prioritizes the estimation of low-order coefficients, in order to ensure accurate estimation at macroscopic level. Therefore, the probability mass is prevented from being misplaced too far away from its ground truth. We establish theoretical guarantees for our methods. Experiments show that our wavelet expansion method significantly outperforms existing solutions under Wasserstein and KS distances.
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