On Computing Pairwise Statistics with Local Differential Privacy

We study the problem of computing pairwise statistics, i.e., ones of the form ${\left(\genfrac{}{}{0px}{}{n}{2}\right)}^{-1}{\sum }_{i\mathrm{\ne }j}f(x_i,x_j)$, 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.