We study the problem of computing pairwise statistics, i.e., ones of the form $\binom{n}{2}^{-1} \sum_{i \ne j} f(x_i, x_j)$, where $x_i$ denotes the input to the $i$th user, with differential privacy (DP) in the local model. This formulation captures important metrics such as Kendall's $\tau$ coefficient, Area Under Curve, Gini's mean difference, Gini's entropy, etc. We give several novel and generic algorithms for the problem, leveraging techniques from DP algorithms for linear queries.

翻译：本文研究在本地差分隐私（DP）模型下计算成对统计量的问题，即形如$\binom{n}{2}^{-1} \sum_{i \ne j} f(x_i, x_j)$的统计量，其中$x_i$表示第$i$个用户的输入。该数学框架涵盖了肯德尔$\tau$系数、曲线下面积、基尼平均差、基尼熵等重要度量指标。通过借鉴线性查询的差分隐私算法技术，我们针对该问题提出了多种新颖且通用的算法。