差分私有矩阵机制下查询集的最优错误
Optimal error of query sets under the differentially-private matrix mechanism
摘要：
隐私研究的一个共同目标是发布满足正式隐私保证的合成数据，并可由分析师使用以代替原始数据。为了达到合理的准确性，必须调整合成数据集以准确地支持指定的查询集，牺牲其他查询的保真度。这项工作认为，在差分隐私下产生合成数据的方法，并调查是什么使一组查询“容易”或“难以”回答。我们考虑使用矩阵机制回答线性计数查询集，这是一种最近的差分私有机制，可以通过添加适应指定工作负载的复杂相关噪声来减少错误。我们的主要结果是一个新的下限的最小总错误所需的同时释放一组工作量查询的答案。该界限揭示了查询工作负载的硬度与工作负载的谱特性有关，当它以矩阵形式表示时。该界限对于$(ε,δ)$ -差分隐私是最具信息性的，但也适用于$ε$ -差分隐私。
英文摘要：
A common goal of privacy research is to release synthetic data that satisfies a formal privacy guarantee and can be used by an analyst in place of the original data. To achieve reasonable accuracy, a synthetic data set must be tuned to support a specified set of queries accurately, sacrificing fidelity for other queries. This work considers methods for producing synthetic data under differential privacy and investigates what makes a set of queries "easy" or "hard" to answer. We consider answering sets of linear counting queries using the matrix mechanism, a recent differentially-private mechanism that can reduce error by adding complex correlated noise adapted to a specified workload. Our main result is a novel lower bound on the minimum total error required to simultaneously release answers to a set of workload queries. The bound reveals that the hardness of a query workload is related to the spectral properties of the workload when it is represented in matrix form. The bound is most informative for $(ε,δ)$-differential privacy but also applies to $ε$-differential privacy.
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