DMS-EPSRC: Change Point Detection and Localization in High-Dimensions: Theory and Methods

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Change point analysis is a well-established topic in statistics that is concerned with detecting and localizing abrupt changes in the data generating distribution in time series and, more broadly, stochastic and spatial processes. A long-studied subject with a rich literature, change point analysis has produced a host of well-established methods for statistical inference available to practitioners. These techniques are widely used in many, diverse applications to address important real life problems, such as security monitoring, neuroimaging, financial trading, ecological statistics, climate change, medical condition monitoring, sensor networks, risk assessment for disease outbreak, flu trend analysis, genetics and many others. However, existing frameworks for statistical analysis of change point problems often rely on traditional modeling assumptions of parametric nature that are inadequate to capture the inherent complexity of modern, high-dimensional datasets. The broad goal of this proposal is to develop novel theories and methods for change point analysis in high-dimensional and nonparametric settings, for both offline and sequential problems.