We present an effective framework for improving the breakdown point of robust regression algorithms. Robust regression has attracted widespread attention due to the ubiquity of outliers, which significantly affect the estimation results. However, many existing robust least-squares regression algorithms suffer from a low breakdown point, as they become stuck around local optima when facing severe attacks. By expanding on the previous work, we propose a novel framework that enhances the breakdown point of these algorithms by inserting a prior distribution in each iteration step, and adjusting the prior distribution according to historical information. We apply this framework to a specific algorithm and derive the consistent robust regression algorithm with iterative local search (CORALS). The relationship between CORALS and momentum gradient descent is described, and a detailed proof of the theoretical convergence of CORALS is presented. Finally, we demonstrate that the breakdown point of CORALS is indeed higher than that of the algorithm from which it is derived. We apply the proposed framework to other robust algorithms, and show that the improved algorithms achieve better results than the original algorithms, indicating the effectiveness of the proposed framework.

提出了一个新的框架来改善健壮回归算法的断点，从而提高算法对于异常点的容错能力。该框架通过在每一次迭代步骤中插入一个先验分布，并根据历史信息调整先验分布，增强了这些算法的断点。将这个框架应用于一个特定的算法，并推导出了一种稳健的针对迭代局部搜索的回归算法（CORALS）。最后，将该框架应用于其他健壮回归算法，并展示了改进的算法比原始算法产生了更好的结果。

一种提高鲁棒回归算法断点的新框架