Given the growing significance of reliable, trustworthy, and explainable machine learning, the requirement of uncertainty quantification for anomaly detection systems has become increasingly important. In this context, effectively controlling Type I error rates ($\alpha$) without compromising the statistical power ($1-\beta$) of these systems can build trust and reduce costs related to false discoveries, particularly when follow-up procedures are expensive. Leveraging the principles of conformal prediction emerges as a promising approach for providing respective statistical guarantees by calibrating a model's uncertainty. This work introduces a novel framework for anomaly detection, termed cross-conformal anomaly detection, building upon well-known cross-conformal methods designed for prediction tasks. With that, it addresses a natural research gap by extending previous works in the context of inductive conformal anomaly detection, relying on the split-conformal approach for model calibration. Drawing on insights from conformal prediction, we demonstrate that the derived methods for calculating cross-conformal $p$-values strike a practical compromise between statistical efficiency (full-conformal) and computational efficiency (split-conformal) for uncertainty-quantified anomaly detection on benchmark datasets.

翻译：鉴于可靠、可信及可解释机器学习的重要性日益增长，异常检测系统的不确定性量化需求变得日益关键。在此背景下，有效控制第一类错误率（$\alpha$）同时不损害系统统计效能（$1-\beta$），可建立信任并降低由错误发现带来的成本，尤其当后续验证流程成本高昂时。利用共形预测原理，通过校准模型不确定性提供相应统计保证，成为具有前景的方法。本研究提出一种新型异常检测框架——交叉共形异常检测，该框架基于专为预测任务设计的成熟交叉共形方法。由此，本研究弥补了现有学术空白，通过拓展此前基于分裂共形方法进行模型校准的归纳式共形异常检测研究成果。借鉴共形预测的洞见，我们证明所推导的交叉共形$p$值计算方法在基准数据集上实现了统计效率（全共形）与计算效率（分裂共形）之间的实用折中，用于不确定性量化的异常检测。