Anomaly Detection Based on Compressed Data: An Information Theoretic Characterization

Large monitoring systems produce data that is often compressed to be transmitted over the network. For latency or security reasons, compressed data may be processed at the edge, i.e., along the path from sensors to the cloud, for some purposes such as anomaly detection. However, the performance of a detector distinguishing between normal and anomalous behavior may be affected by the loss of information due to compression. We here analyze how lossy compression affects the performance of a generic anomaly detector. This relationship is formalized in terms of information-theoretic quantities. Within such a framework we leverage a Gaussian assumption to derive analytical results regarding the importance of white noise as a representative of both the average and asymptotic anomalies. Moreover, in an anomaly-agnostic scenario, we also show the existence of a level of compression for which an anomaly is undetectable though compression is not completely destructive. Numerical evidence confirms that the proposed information-theoretic quantities anticipate the performance of practical compressors and detectors in the case of Gaussian and non-Gaussian signals allowing an assessment of the tradeoff between compression and detection.