在用户隐私要求不同时，给出高概率保证的统计估计新方法。
High-Probability Bounds For Heterogeneous Local Differential Privacy
- 针对不同隐私等级用户，设计高概率成立的均值估计方法。
- 在一维和多维情况下，$\ell_2$-误差上界在 $1-β$ 概率下成立。
- 适用于需严格保障隐私与精度的个性化数据采集场景。
研究用户具有异质隐私水平时的局部差分隐私（LDP）统计估计问题，强调在高概率下保证估计精度。不同于常见的期望分析，本文针对一维和多维均值估计，推导出在 $\ell_2$-范数下以至少 $1-β$ 的概率成立的有限样本上界。同时给出匹配的极小极大下界，证明了所提保证在异质LDP设置下的最优性（常数意义下）。进一步研究了 $\ell_\infty$-距离下的分布学习，设计出在异质隐私需求下具有高概率保证的算法。其技术为具用户特定隐私级别的机制设计提供了系统性指导。
原文摘要 · Abstract (English)
We study statistical estimation under local differential privacy (LDP) when users may hold heterogeneous privacy levels and accuracy must be guaranteed with high probability. Departing from the common in-expectation analyses, and for one-dimensional and multi-dimensional mean estimation problems, we develop finite sample upper bounds in $\ell_2$-norm that hold with probability at least $1-β$. We complement these results with matching minimax lower bounds, establishing the optimality (up to constants) of our guarantees in the heterogeneous LDP regime. We further study distribution learning in $\ell_\infty$-distance, designing an algorithm with high-probability guarantees under heterogeneous privacy demands. Our techniques offer principled guidance for designing mechanisms in settings with user-specific privacy levels.
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