On Computing Pairwise Statistics with Local Differential Privacy

TL;DR

This paper develops new algorithms for computing pairwise statistics under local differential privacy, enabling privacy-preserving analysis of metrics like Kendall's tau and Gini's measures.

Contribution

It introduces several novel, generic algorithms for pairwise statistics computation in the local DP model, extending existing techniques for linear queries.

Findings

Algorithms successfully compute pairwise statistics with privacy guarantees.

Applicable to metrics like Kendall's tau, AUC, and Gini measures.

Provides theoretical analysis of privacy and accuracy trade-offs.

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.