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

arXiv: https://arxiv.org/abs/2603.01986 · HTML: https://mlsanity.com/paper/2603.01986/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 33 references that are in the map.
- First posted on arXiv 2 Mar 2026.

## Builds on (most cited first, 7 of 7)

- [The Discrete Gaussian for Differential Privacy](https://mlsanity.com/paper/2004.00010/) (2020)
- [Private Summation in the Multi-Message Shuffle Model](https://mlsanity.com/paper/2002.00817/) (2020)
- [An Accurate, Scalable and Verifiable Protocol for Federated Differentially Private Averaging](https://mlsanity.com/paper/2006.07218/) (2020)
- [Towards Instance-Optimal Private Query Release](https://mlsanity.com/paper/1811.03763/) (2018)
- [Private Protocols for U-Statistics in the Local Model and Beyond](https://mlsanity.com/paper/1910.03861/) (2019)
- [On Computing Pairwise Statistics with Local Differential Privacy](https://mlsanity.com/paper/2406.16305/) (2024)
- [Correlated Pseudorandomness from the Hardness of Quasi-Abelian Decoding](https://mlsanity.com/paper/2306.03488/) (2023)

## Abstract (arXiv)

We study the problem of computing a U-statistic with a kernel function f of degree k ≥ 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 ≥ 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.