Detecting the presence of anomalies in regression models is a crucial task in machine learning, as anomalies can significantly impact the accuracy and reliability of predictions. Random Sample Consensus (RANSAC) is one of the most popular robust regression methods for addressing this challenge. However, this method lacks the capability to guarantee the reliability of the anomaly detection (AD) results. In this paper, we propose a novel statistical method for testing the AD results obtained by RANSAC, named CTRL-RANSAC (controllable RANSAC). The key strength of the proposed method lies in its ability to control the probability of misidentifying anomalies below a pre-specified level $\alpha$ (e.g., $\alpha = 0.05$). By examining the selection strategy of RANSAC and leveraging the Selective Inference (SI) framework, we prove that achieving controllable RANSAC is indeed feasible. Furthermore, we introduce a more strategic and computationally efficient approach to enhance the true detection rate and overall performance of the CTRL-RANSAC. Experiments conducted on synthetic and real-world datasets robustly support our theoretical results, showcasing the superior performance of the proposed method.

翻译：在回归模型中检测异常值的存在是机器学习中的一项关键任务，因为异常值会显著影响预测的准确性和可靠性。随机抽样一致性（RANSAC）是应对这一挑战最常用的稳健回归方法之一。然而，该方法无法保证异常检测（AD）结果的可靠性。本文提出了一种新颖的统计方法来检验RANSAC所得的AD结果，称为CTRL-RANSAC（可控RANSAC）。所提方法的核心优势在于能够将误判异常值的概率控制在预先设定的水平$\alpha$以下（例如$\alpha = 0.05$）。通过分析RANSAC的选择策略并利用选择性推断（SI）框架，我们证明了实现可控RANSAC确实是可行的。此外，我们引入了一种更具策略性且计算效率更高的方法，以提升CTRL-RANSAC的真实检测率和整体性能。在合成数据集和真实数据集上进行的实验有力地支持了我们的理论结果，展示了所提方法的优越性能。