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、可信且可解释的机器学习日益重要，异常检测系统的不确定性量化需求也日益凸显。在此背景下，在不损害统计功效（$1-\beta$）的前提下有效控制第一类错误率（$\alpha$），能够建立信任并降低与错误发现相关的成本，尤其是在后续验证流程成本高昂时。基于共形预测的原理，通过校准模型的不确定性来提供相应的统计保证，是一种富有前景的方法。本文提出了一种新颖的异常检测框架，称为交叉共形异常检测，它基于经典的用于预测任务的交叉共形方法。由此，本文填补了一个自然的研究空白，即扩展了先前基于分割共形方法进行模型校准的归纳式共形异常检测工作。借鉴共形预测的见解，我们证明了所推导的交叉共形$p$值计算方法在基准数据集上能够实现不确定性量化的异常检测中统计效率（全共形）和计算效率（分割共形）之间的实用折衷。