发表机构
Inria; University of Oxford; National University of Singapore; Mohamed bin Zayed University of Artificial Intelligence（法国国家信息与自动化研究所; 牛津大学; 新加坡国立大学; 穆罕默德·本·扎耶德人工智能大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出BetweenCut算法，在树高为h时实现双重对数加性误差的差分隐私重节点分类，改进现有界并独立于数据库大小。
AI 中文摘要
在树中寻找重节点——即计数超过给定阈值的节点——是对结构化数据进行分析和学习的基础模块。在不牺牲准确性的情况下实现记录级差分隐私（DP）具有挑战性，因为每条记录会沿着从根到叶的整个路径对计数做出贡献，导致隐私成本在各级累积。现有方法针对每条记录的多重阈值比较，在树高为$h$时会产生$\u03a9_{\u03b5,\u03b4}(\u03bbog h)$或$\u03a9_{\u03b5,\u03b4}(\u221a\u03bbog h)$的加性误差界。我们引入了\textsc{BetweenCut}，一种$(\u03b5,\u03b4)$-DP算法，其加性误差界为$O_{\u03b5,\u03b4}(\u03bbog\u03bbog h)$，改进了现有针对深树的界。该误差界同时适用于所有节点，且与输入数据库大小无关。
英文摘要
Finding heavy nodes in a tree---those whose counts exceed a given threshold---is a building block for analysis and learning over structured data. Achieving record-level differential privacy (DP) without sacrificing accuracy is challenging because each record contributes to counts along an entire root-to-leaf path, allowing privacy costs to accumulate across levels. Existing methods account for the multiple threshold comparisons for each record incur additive error margins of $Ω_{\varepsilon,δ}(\log h)$ or $Ω_{\varepsilon,δ}(\sqrt{\log h})$ for tree height $h$. We introduce \textsc{BetweenCut}, an $(\varepsilon,δ)$-DP algorithm with an additive error margin of $O_{\varepsilon,δ}(\log\log h)$, improving the existing bounds for deep trees. This error holds simultaneously for all nodes and is independent of the input database size.
