Federated Data and Feature Selection by Generalized CUR Decomposition

With the advance of federated learning (FL) in privacy-sensitive domains, the need for efficient and robust training becomes increasingly urgent. Communication bottlenecks, heterogeneous client distributions, and fairness requirements make it essential to select the “right” data and features for model training. Yet existing FL research often addresses feature selection and data selection separately, ignoring their interplay in real-world high-dimensional and noisy datasets, leading to suboptimal performance. In this paper, we propose a unified framework for data and feature selection by formulating the problem as a generalized CUR decomposition problem. We introduce FedGCUR, a practical framework that integrates a federated column-pivoted QR (FedCPQR) decomposition routine with per-silo row selection. We prove that FedCPQR produces exactly the same decomposition results as centralized CPQR and establish an upper bound of the reconstruction error of FedGCUR. Experiments on tabular tasks and vision benchmarks show strong downstream accuracy and absolute CUR reconstruction quality compared with representative data and feature selection baselines.