Distributed robust estimation and inference with contaminated data.

We study the problem of robust estimation and inference for contaminated data in distributed learning systems. Existing methods, such as those designed for Byzantine failures, typically assume that contamination is limited to a small subset of machines experiencing complete failure. In contrast, we address distributed partial contamination, where all machines may handle datasets containing some corrupted observations. By generalizing Huber's ϵ -contamination model to distributed settings, we propose a robust framework in which each machine's dataset may be contaminated by a proportion ϵ of observations from an arbitrary distribution. In a linear model setting, we develop a communication-efficient M-estimator that achieves the optimal convergence rate of centralized data. For robust inference, we introduce a distributed multiplier bootstrap method that requires no additional communication post-estimation while maintaining efficiency. To handle high contamination proportions, we present a debiasing procedure to mitigate bias. Extensive simulations demonstrate the robustness and scalability of our methods across diverse contamination scenarios.