Data-Driven Approaches for Detecting and Identifying Anomalous Data Streams

This chapter considers the problem of detecting anomalous data streams out of a large number of typical data streams based on their statistical behavior. We are interested in two types of problems: detecting existence of anomalous data streams and then further identifying such anomalous data streams if they exist. While our focus is on the nonparametric scenario with distributions of data streams being unknown, we also introduce parametric and semiparametric models to develop useful understanding toward nonparametric models. We first introduce three data-driven approaches for nonparametric detection, and then describe applications of these approaches to designing tests for the problems of interest here. We then discuss applications of the developed tests in biomedical signal processing. Finally, we conclude with remarks on open problems and future directions.