发表机构
Google Research; The University of Sydney; Max Planck Institute for Security and Privacy（谷歌研究院; 悉尼大学; 马克斯·普朗克安全与隐私研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究系统研究差分隐私图性质测试，为多种图抽样过程开发隐私放大定理，并设计稠密与有界度图模型中的私有测试器，证明超有限图性质可私有测试，查询复杂度与非私有相当。
AI 中文摘要
图性质测试研究的是，仅使用对图的次线性数量查询，判断一个大规模图是否满足给定性质，或是否远离该性质。由于性质测试器通常只检查输入中随机抽样的一个小部分，它们自然与差分隐私以及通过子抽样实现的隐私放大相兼容。尽管如此，很少有研究将这两个领域联系起来。我们启动了对差分隐私图性质测试的系统性研究，目标是在稠密图和有界度图模型中设计具有正式隐私保证的高效测试器。我们为几种广泛使用的图抽样过程（如诱导子图抽样、随机游走和k-碟抽样）开发了新的隐私放大定理。然后，我们利用这些隐私放大技术，在稠密图模型中设计了一个私有规范测试器，以及在稠密图和有界度图模型中的私有二分性测试器和子图自由性测试器。最后，利用新的k-碟抽样隐私放大定理，我们证明了超有限图的每个性质都是可私有测试的。我们私有测试器产生的查询复杂度与其非私有对应物相当。
英文摘要
Graph property testing asks whether a massive graph satisfies a given property, or is far from doing so, using only a sublinear number of queries to the graph. Since property testers typically inspect only a small, randomly sampled portion of the input, they appear naturally compatible with differential privacy and privacy amplification by subsampling. Despite this, few results link these two fields. We initiate a systematic study of differentially private graph property testing with the goal of designing efficient testers with formal privacy guarantees in the dense and bounded-degree graph models. We develop new privacy amplification theorems for several widely used graph-sampling procedures such as induced subgraph sampling, random walks and k-disc sampling. We then leverage these privacy amplification techniques to design a private canonical tester in the dense graph model, as well as private bipartiteness testers and subgraph freeness testers in the dense and bounded-degree graph models. Finally, using the new privacy amplification theorem for k-disc sampling, we prove that every property of hyperfinite graphs is privately testable. The resulting query complexities of our private testers are comparable to those of their non-private counterparts.
Comments46 pages
