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

2026-03-02

AI Summary

This work addresses the critical challenge of efficiently and accurately computing high-order (k ≥ 2) U-statistics under centralized differential privacy and security guarantees in federated learning. We propose the first protocol that integrates secure multi-party computation (MPC) with centralized differential privacy to enable private federated computation of high-order U-statistics. Our approach eliminates the need for domain discretization and achieves up to four orders of magnitude reduction in mean squared error compared to existing baselines on metrics such as Kendall’s τ, while maintaining strong communication and computational efficiency. This significantly advances the accuracy of statistical estimation under rigorous privacy constraints.

Technology Category

• Machine Learning: Distributed Machine Learning & Federated Learning
• Reasoning under Uncertainty: Stochastic Optimization
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Security and Privacy: Large-scale security measurements
• User Modeling, Personalization and Recommendation: Federated recommendation systems and personalization
• Responsible Web: Data and user privacy-enhancing technologies for the Web

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 $τ$ 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 $τ$ coefficient, our approach reduces the Mean Squared Error by up to four orders of magnitude over existing baselines.

Problem

• U-statistics
• federated learning
• differential privacy
• secure computation
• higher-degree statistics

Innovation

• federated learning
• U-statistics
• differential privacy
• secure multi-party computation
• high-degree statistics