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Because of the widespread existence of noise and data corruption, recoveringthe true regression parameters with a certain proportion of corrupted responsevariables is an essential task. Methods to overcome this problem often involverobust least-squares regression, but few methods perform well when confrontedwith severe adaptive adversarial attacks. In many applications, prior knowledgeis often available from historical data or engineering experience, and byincorporating prior information into a robust regression method, we develop aneffective robust regression method that can resist adaptive adversarialattacks. First, we propose the novel TRIP (hard Thresholding approach to Robustregression with sImple Prior) algorithm, which improves the breakdown pointwhen facing adaptive adversarial attacks. Then, to improve the robustness andreduce the estimation error caused by the inclusion of priors, we use the ideaof Bayesian reweighting to construct the more robust BRHT (robust BayesianReweighting regression via Hard Thresholding) algorithm. We prove thetheoretical convergence of the proposed algorithms under mild conditions, andextensive experiments show that under different types of dataset attacks, ouralgorithms outperform other benchmark ones. Finally, we apply our methods to adata-recovery problem in a real-world application involving a space solararray, demonstrating their good applicability.

A Bayesian Robust Regression Method for Corrupted Data Reconstruction