On Computing Pairwise Statistics with Local Differential Privacy

Badih Ghazi, Pritish Kamath, Ravi Kumar, Pasin Manurangsi, Adam Sealfon

Keywords: differential privacy, local differential privacy, pairwise statistics

TL;DR: We give algorithms and lower bounds for computing pairwise statistics and quadratic forms under local differential privacy.

Abstract: 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.

Submission Number: 8198