让RANSAC异常检测结果可控制，误判率低于预设阈值。
Controllable RANSAC-based Anomaly Detection via Hypothesis Testing
- 基于选择性推断框架，为RANSAC检测结果提供统计检验。
- 可将误判异常的概率控制在α=0.05以下，理论可证。
- 提升真实检测率，适合对可靠性要求高的工业场景。
在回归模型中检测异常是机器学习中的关键任务，因异常会显著影响预测的准确性和可靠性。随机采样一致性（RANSAC）是应对该挑战最流行的鲁棒回归方法之一，但其无法保证异常检测结果的可靠性。本文提出一种新型统计方法——可控RANSAC（CTRL-RANSAC），用于检验RANSAC所得异常检测结果。该方法的核心优势在于可将误判异常的概率控制在预设水平α（如α=0.05）以下。通过分析RANSAC的选择策略并结合选择性推断（Selective Inference, SI）框架，我们证明了实现可控RANSAC在理论上是可行的。此外，我们提出一种更策略性且计算高效的改进方法，以提升CTRL-RANSAC的真实检测率与整体性能。在合成数据和真实世界数据集上的实验结果稳健支持了理论结论，充分展示了所提方法的优越性。
原文摘要 · Abstract (English)
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 $α$ (e.g., $α= 0.05$). 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.
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