Accurate, private, secure, federated U-statistics with higher degree
This work addresses the need for accurate, private, and secure computation of high-degree U-statistics in federated learning, which is incremental as it builds on existing differential privacy and MPC techniques.
The paper tackles the problem of computing U-statistics with kernel functions of degree k ≥ 2 in a federated learning setting, achieving a reduction in Mean Squared Error by up to four orders of magnitude for Kendall's τ coefficient compared to prior methods.
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.