This paper considers an anomaly detection problem in which a detection algorithm assigns anomaly scores to multi-dimensional data points, such as cellular networks' Key Performance Indicators (KPIs). We propose an optimization framework to refine these anomaly scores by leveraging side information in the form of a causality graph between the various features of the data points. The refinement block builds on causality theory and a proposed notion of confidence scores. After motivating our framework, smoothness properties are proved for the ensuing mathematical expressions. Next, equipped with these results, a gradient descent algorithm is proposed, and a proof of its convergence to a stationary point is provided. Our results hold (i) for any causal anomaly detection algorithm and (ii) for any side information in the form of a directed acyclic graph. Numerical results are provided to illustrate the advantage of our proposed framework in dealing with False Positives (FPs) and False Negatives (FNs). Additionally, the effect of the graph's structure on the expected performance advantage and the various trade-offs that take place are analyzed.

翻译：本文考虑一种异常检测问题，其中检测算法为多维数据点（如蜂窝网络的关键性能指标KPI）分配异常分数。我们提出一个优化框架，通过利用数据点各特征之间因果图形式的辅助信息来优化这些异常分数。该优化模块基于因果理论及提出的置信度概念构建。在阐释框架动机之后，我们证明后续数学表达式的平滑性。接着，基于这些结果，提出梯度下降算法，并证明其收敛至驻点。我们的结论适用于：(i) 任意因果异常检测算法；(ii) 任意有向无环图形式的辅助信息。通过数值结果展示所提框架在处理假阳性（FP）与假阴性（FN）方面的优势，同时分析图结构对预期性能优势的影响及发生的多种权衡关系。