Anomaly detection challenges in monitoring applications

Monitoring physical systems has become pervasive, particularly in critical applications where ensuring operational integrity is paramount. A fundamental task in this context is identifying anomalous behaviors, commonly referred to as anomaly detection. Over the past years, significant attention has been devoted to anomaly detection, leading to the development of more accurate and robust algorithms capable of processing complex data. However, several fundamental challenges remain. Firstly, anomaly detection is inherently unsupervised, making it difficult to exploit prior knowledge about possible anomalies during the design phase. Secondly, despite advances in related fields, anomaly detection has not been thoroughly analyzed from an information-theoretic perspective. This lack of exploration complicates its integration with other well-established tasks, such as signal compression. This dissertation aims to address these challenges by presenting both practical and information-theoretic frameworks for anomaly detection. In the first part, we design a tool designed to mitigate the challenge of evaluating anomaly detection performance in the absence of real anomalies. To this end, we develop robust mathematical models that emulate possible anomalies in time series data and propose a procedure for generating synthetic anomalies. Furthermore, we establish a theoretical framework for performance assessment based on a novel concept of distinguishability. In the second part, we employ these assessment tools to study the interaction between compression and anomaly detection from an information-theoretic standpoint. We demonstrate that common lossy compression algorithms can compromise the effectiveness of anomaly detection performed on compressed data. We then study how these tasks can be jointly optimized and offer insights for developing practical systems that integrate both functions. In a similar spirit, we design an autoencoder-based compression scheme that not only minimizes distortion but also preserves information critical for anomaly detection.