We developed a novel approximate Bayesian computation (ABC) framework, ABCDP, which produces differentially private (DP) and approximate posterior samples. Our framework takes advantage of the sparse vector technique (SVT), widely studied in the differential privacy literature. SVT incurs the privacy cost only when a condition (whether a quantity of interest is above/below a threshold) is met. If the condition is sparsely met during the repeated queries, SVT can drastically reduce the cumulative privacy loss, unlike the usual case where every query incurs the privacy loss. In ABC, the quantity of interest is the distance between observed and simulated data, and only when the distance is below a threshold can we take the corresponding prior sample as a posterior sample. Hence, applying SVT to ABC is an organic way to transform an ABC algorithm to a privacy-preserving variant with minimal modification, but yields the posterior samples with a high privacy level. We theoretically analyzed the interplay between the noise added for privacy and the accuracy of the posterior samples. We apply ABCDP to several data simulators and show the efficacy of the proposed framework.

中文翻译：

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ABCDP：具有差分隐私的近似贝叶斯计算


我们开发了一种新颖的近似贝叶斯计算（ABC）框架ABCDP ，它可以生成差分隐私（DP）和近似后验样本。我们的框架利用了差分隐私文献中广泛研究的稀疏向量技术（SVT）。仅当满足条件（兴趣数量是否高于/低于阈值）时，SVT 才会产生隐私成本。如果在重复查询过程中很少满足条件，SVT 可以大大减少累积的隐私损失，这与通常情况下每次查询都会导致隐私损失不同。在ABC中，感兴趣的数量是观测数据与模拟数据之间的距离，只有当距离低于阈值时，我们才能将相应的先验样本作为后验样本。因此，将 SVT 应用于 ABC 是一种将 ABC 算法转变为隐私保护变体的有机方法，只需进行最小的修改，但会产生具有高隐私级别的后验样本。我们从理论上分析了为隐私而添加的噪声与后验样本的准确性之间的相互作用。我们将 ABCDP 应用于多个数据模拟器，并展示了所提出框架的有效性。