D4R: Communication-Efficient Robust Reduced-Rank Regression for Distributed Data

Large-scale multivariate data are often distributed across multiple machines and contaminated by outliers, which complicates efficient and interpretable modeling of shared low-rank structure. To address both challenges, we propose a **D**istributed **R**obust **R**educed-**R**ank **R**egression (D4R) framework based on a refined surrogate loss. D4R separates local outlier correction from global low-rank estimation while reducing both computation and communication costs. Theoretically, we establish non-asymptotic error bounds showing that D4R reaches the target statistical rate after finite communication rounds. Simulations and real-data studies demonstrate the robustness and efficiency of our method.