Contextual anomaly detection (CAD) aims to identify anomalies in a target (behavioral) variable conditioned on a set of contextual variables that influence the normalcy of the target variable but are not themselves indicators of anomaly. In many anomaly detection tasks, there exist contextual variables that influence the normalcy of the target variable but are not themselves indicators of anomaly. In this work, we propose a novel framework for CAD, normalcy score (NS), that explicitly models both the aleatoric and epistemic uncertainties. Built on heteroscedastic Gaussian process regression, our method regards the Z-score as a random variable, providing confidence intervals that reflect the reliability of the anomaly assessment. Through experiments on benchmark datasets and a real-world application in cardiology, we demonstrate that NS outperforms state-of-the-art CAD methods in both detection accuracy and interpretability. Moreover, confidence intervals enable an adaptive, uncertainty-driven decision-making process, which may be very important in domains such as healthcare.

翻译：上下文异常检测旨在识别目标（行为）变量中的异常，这些异常是在一组上下文变量的条件下发生的，这些变量影响目标变量的正常性，但其本身并非异常的指标。在许多异常检测任务中，确实存在影响目标变量正常性但自身并非异常指标的上下文变量。在本工作中，我们提出了一种新颖的上下文异常检测框架——正常性评分，该框架明确地对偶然不确定性和认知不确定性进行建模。基于异方差高斯过程回归，我们的方法将Z分数视为一个随机变量，提供反映异常评估可靠性的置信区间。通过在基准数据集上的实验以及心脏病学中的一个真实世界应用，我们证明正常性评分在检测准确性和可解释性方面均优于最先进的上下文异常检测方法。此外，置信区间支持一种自适应的、不确定性驱动的决策过程，这在医疗保健等领域可能至关重要。