  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.
