Theory of Deep Anomaly Detection

• Applicant: Professor Dr. Marius Kloft
• Subject Area: Image and Language Processing, Computer Graphics and Visualisation, Human Computer Interaction, Ubiquitous and Wearable Computing
• Term: since 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 464252197

Anomaly detection is one of the fundamental problems in machine learning, with applications from computer security to industrial fault detection and early warning systems. With the extensive use of deep learning many complex benchmarks have effectively been solved over the past years. However, there is hardly any theoretical understanding of "deep anomaly detection"; to date, theoretical understanding remains mainly limited to shallow anomaly detection. The goal of this research project is the development of the first learning theory of deep anomaly detection. Achieving this goal would help gain a better understanding of deep anomaly detection, which will eventually aid the development of new algorithms. Developing a learning theory of deep anomaly detection is difficult. Due to lacking characterization of the anomaly distribution, adapting classic generalization analysis is challenging. We will develop a new theoretical path, including finite sample bounds and consistency analysis, to provide theoretical performance guarantees for deep anomaly detection, both in finite data scenarios and under theoretical limits. Key to the new theory will be a fine-grained analysis that also takes the optimization algorithm into account. Modern methods of AD deliberately deviate from on of the fundamental assumption that anomalies are uniformly distributed and still produce exceptional results. For the first time, these distributional discrepancies will be incorporated in anomaly detection theory.

• DFG Programme: Priority Programmes
• Subproject of: SPP 2298: Theoretical Foundations of Deep Learning