FedWNNM: A Federated Framework for Matrix Completion with Provable Privacy-Accuracy Trade-offs

Jiale Yao, Fang Li

Keywords: Federated Learning, Matrix Completion, Privacy-Preserving SVD, Weighted Nuclear Norm Minimization

TL;DR: We propose a privacy-preserving federated SVD method that enables the WNNM algorithm for federated matrix completion, achieving state-of-the-art performance.

Abstract: Federated learning prevents raw data aggregation on a central server, posing challenges for matrix completion. While matrix factorization methods are suitable for federated settings, Weighted Nuclear Norm Minimization (WNNM) outperforms them in centralized contexts by recovering low-rank and nearly low-rank matrices with rapidly decaying singular values. However, WNNM relies on Singular Value Decomposition (SVD), a global operation requiring full data access, which violates federated learning’s privacy principles. To address this, we propose Federated WNNM (FedWNNM), a privacy-preserving solver for federated matrix completion. Our key contribution is a Privacy-Preserving Federated SVD (PPF-SVD) subroutine, where clients generate low-dimensional, privacy-preserving sketches of local data using structured random projections. These sketches are aggregated on a central server to approximate global singular values and right singular vectors without accessing raw data. Theoretical analysis provides upper and lower bounds on approximation error, quantifying the privacy-accuracy trade-off. Experiments demonstrate that FedWNNM achieves state-of-the-art recovery performance with formal privacy guarantees.

Primary Area: alignment, fairness, safety, privacy, and societal considerations

Submission Number: 7365