This work proposes a class of differentially private mechanisms for linear queries, in particular range queries, that leverages correlated input perturbation to simultaneously achieve unbiasedness, consistency, statistical transparency, and control over utility requirements in terms of accuracy targets expressed either in certain query margins or as implied by the hierarchical database structure. The proposed Cascade Sampling algorithm instantiates the mechanism exactly and efficiently. Our theoretical and empirical analysis demonstrates that we achieve near-optimal utility, effectively compete with other methods, and retain all the favorable statistical properties discussed earlier.

翻译：本研究提出一类用于线性查询（特别是范围查询）的差分隐私机制，该机制利用相关输入扰动技术，在满足以特定查询边界或层次化数据库结构隐含的精度目标所表达的效用要求的同时，实现了无偏性、一致性、统计透明性及效用可控性。所提出的Cascade Sampling算法能够精确且高效地实例化该机制。理论与实证分析表明，我们的方法实现了接近最优的效用，能有效与其他方法竞争，并保留了前文讨论的所有优良统计特性。