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MuSyAD on Anomaly Detection
Anomaly detection is an interdisciplinary domain, borrowing elements from mathematics, computer science, and engineering. The main aim is to develop efficient techniques for detecting anomalous behaviour of systems. In the classical scenario a monitor receives data from a system and compares this data to a reference system with some single normal behaviour. Ideally no strong assumptions are made on the nature of anomalous behaviours, so the problem of anomaly detection is by essence a non parametric problem. Here I propose to study a more complex scenario, which will be referred to as multisystem anomaly detection. In this setting, reference systems can have a variety of normal behaviours, and moreover, there are many systems under the monitor s surveillance, and the monitor must allocate its resources wisely among them. In this situation new theoretical and computational challenges arise. The overall objective of this proposal is to find efficient methods to solve the problem of multi-system anomaly detection. This aim will be reached by addressing the following sub-objectives. First, we will generalise the theoretical framework of anomaly detection to the broader setting of multi-system anomaly detection. Second, multi-system anomaly detection methods will be developed, by taking ideas from the non parametric testing field and applying them to the new framework. Third, we will study optimal monitoring strategies for cases where the multiple systems cannot be monitored simultaneously. Here, it is important that the monitor allocates its resources among the systems in a way that is as efficient as possible. To this end, sequential and adaptive sampling methods that target the anomaly detection problem will be designed. Since anomaly detection is a non parametric problem, elements in the theory of non parametric confidence sets will be used. Finally, the newly developed methods will be applied to practical problems: a methodological example in extreme value theory, an econometric application for speculative bubble detection and two applications in a Brain Computer Interface framework.
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