Answering database queries while preserving privacy is an important problem that has attracted considerable research attention in recent years. A canonical approach to this problem is to use synthetic data. That is, we replace the input database R with a synthetic database R* that preserves the characteristics of R, and use R* to answer queries. Existing solutions for relational data synthesis, however, either fail to provide strong privacy protection, or assume that R contains a single relation. In addition, it is challenging to extend the existing single-relation solutions to the case of multiple relations, because they are unable to model the complex correlations induced by the foreign keys. Therefore, multi-relational data synthesis with strong privacy guarantees is an open problem. In this paper, we address the above open problem by proposing PrivLava, the first solution for synthesizing relational data with foreign keys under differential privacy, a rigorous privacy framework widely adopted in both academia and industry. The key idea of PrivLava is to model the data distribution in R using graphical models, with latent variables included to capture the inter-relational correlations caused by foreign keys. We show that PrivLava supports arbitrary foreign key references that form a directed acyclic graph, and is able to tackle the common case when R contains a mixture of public and private relations. Extensive experiments on census data sets and the TPC-H benchmark demonstrate that PrivLava significantly outperforms its competitors in terms of the accuracy of aggregate queries processed on the synthetic data.

翻译：在保护隐私的前提下回答数据库查询是近年来吸引大量研究关注的重要问题。解决该问题的标准方法是使用合成数据，即用保留原始数据库R特性的合成数据库R*替代输入数据库R，并基于R*回答查询。然而，现有关系数据合成方案要么无法提供强隐私保护，要么假设R仅包含单个关系。此外，由于现有单关系方案无法建模外键引发的复杂关联性，将其扩展至多关系场景极具挑战。因此，在强隐私保障下实现多关系数据合成仍是一个开放问题。本文提出PrivLava，这是首个在差分隐私（被学术界与工业界广泛采用的严格隐私框架）下合成含外键关系数据的解决方案。PrivLava的核心思想是利用包含潜变量的图模型对R中的数据分布进行建模，其中潜变量用于捕获外键导致的跨关系关联性。我们证明PrivLava支持构成有向无环图的任意外键引用，并能处理R同时包含公开关系与私有关系的常见情形。在普查数据集与TPC-H基准上的大量实验表明，PrivLava在合成数据上处理的聚合查询精度显著优于现有方案。