Differential privacy (DP) has become the de facto standard for protecting sensitive data, providing strong guarantees that published statistics or models reveal limited information about any individual. However, privacy noise and restricted data access make it increasingly difficult to assess the fairness and reliability of private datasets. In this paper, we propose a formal framework for quantifying data unfairness under DP. We identify three core desiderata for unfairness measures based on previous work: positivity, monotonicity, and DP computability. We further instantiate them through three complementary measures: (1) a mutual information-based measure with a total variation distance proxy suitable for DP, (2) a data repair-based measure approximated via a reduction to weighted MaxSAT, and (3) a top-$k$ tuple contribution measure that isolates the most influential records in fairness violations. We design privacy-preserving algorithms and analyze their sensitivity, accuracy, and efficiency. Extensive experiments on multiple real-world datasets demonstrate that our proposed measures faithfully approximate their non-private counterparts, effectively quantify bias under privacy constraints, and provide insights for data management.

翻译：差分隐私（DP）已成为保护敏感数据的事实标准，它能提供强有力的保证，确保所发布的统计结果或模型仅泄露关于任何个体的有限信息。然而，隐私噪声和受限的数据访问使得评估私有数据集的公平性和可靠性愈发困难。本文提出了一种在差分隐私条件下量化数据不公平性的形式化框架。基于先前工作，我们确定了不公平性度量的三个核心需求：积极性、单调性和差分隐私可计算性。我们进一步通过三种互补的度量实例化这些需求：（1）基于互信息的度量，采用适用于差分隐私的全变差距离代理；（2）基于数据修复的度量，通过归约到加权最大可满足性问题进行近似求解；（3）基于前k元组贡献的度量，用于隔离公平性违规中最具影响力的记录。我们设计了隐私保护算法，并分析了其敏感性、准确性和效率。在多个真实数据集上的大量实验表明，我们提出的度量能够忠实地近似非隐私对应物，有效量化隐私约束下的偏差，并为数据管理提供洞见。