Sequential Feature Explanations for Anomaly Detection

In many applications, an anomaly detection system presents the most anomalous data instance to a human analyst, who then must determine whether the instance is truly of interest (e.g., a threat in a security setting). Unfortunately, most anomaly detectors provide no explanation about why an instance was considered anomalous, leaving the analyst with no guidance about where to begin the investigation. To address this issue, we study the problems of computing and evaluating sequential feature explanations (SFEs) for anomaly detectors. An SFE of an anomaly is a sequence of features, which are presented to the analyst one at a time (in order) until the information contained in the highlighted features is enough for the analyst to make a confident judgement about the anomaly. Since analyst effort is related to the amount of information that they consider in an investigation, an explanation’s quality is related to the number of features that must be revealed to attain confidence. In this article, we first formulate the problem of optimizing SFEs for a particular density-based anomaly detector. We then present both greedy algorithms and an optimal algorithm, based on branch-and-bound search, for optimizing SFEs. Finally, we provide a large scale quantitative evaluation of these algorithms using a novel framework for evaluating explanations. The results show that our algorithms are quite effective and that our best greedy algorithm is competitive with optimal solutions.