Accurate, private, secure, federated U-statistics with higher degree

TL;DR

This paper introduces a secure, privacy-preserving protocol for computing high-degree U-statistics in federated learning, significantly improving accuracy over previous methods while maintaining efficiency.

Contribution

It presents a novel protocol leveraging MPC for central differential privacy in federated U-statistics of degree k ≥ 2, with theoretical analysis and empirical validation.

Findings

Reduces Mean Squared Error for Kendall's τ by up to four orders of magnitude.

Provides a scalable, accurate method for high-degree U-statistics under privacy constraints.

Achieves favorable performance in empirical evaluations compared to existing solutions.

Abstract

We study the problem of computing a U-statistic with a kernel function f of degree k $\ge$ 2, i.e., the average of some function f over all k-tuples of instances, in a federated learning setting. Ustatistics of degree 2 include several useful statistics such as Kendall's $\tau$ coefficient, the Area under the Receiver-Operator Curve and the Gini mean difference. Existing methods provide solutions only under the lower-utility local differential privacy model and/or scale poorly in the size of the domain discretization. In this work, we propose a protocol that securely computes U-statistics of degree k $\ge$ 2 under central differential privacy by leveraging Multi Party Computation (MPC). Our method substantially improves accuracy when compared to prior solutions. We provide a detailed theoretical analysis of its accuracy, communication and computational properties. We evaluate its performance empirically, obtaining favorable results, e.g., for Kendall's $\tau$ coefficient, our approach reduces the Mean Squared Error by up to four orders of magnitude over existing baselines.