Change-point analysis in high dimensions

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Modern applications routinely generate time-ordered datasets, where many covariates are simultaneously measured over time. Examples include wearable technologies recording the health state of individuals from multi-sensor feedbacks, internet traffic data collected by tens of thousands of routers and functional magnetic resonance imaging (fMRI) scans that record the evolution of certain chemical contrast in different areas of the brain. The explosion in number of such high-dimensional data streams calls for methodological advances for their analysis. Change-point analysis is an essential statistical technique used in identifying abrupt changes in such data streams. The identified 'change-points' often signal interesting or abnormal events, and can be used to carve up the data streams into shorter segments that are easier to analyse.Classical change-point analysis methods identify changes in a single variable over time. However, they often suffer from significant performance loss in high-dimensional datasets when applied componentwise. The area of high-dimensional change-point analysis grew out of the need to respond to the challenge created by high-dimensional data streams. A few methods have been proposed in this relatively new area. However, they often require simplifying assumptions that restrict their usefulness in many applications. In this proposal, I will develop new methods that can handle more realistic data settings. Specifically, I will develop (1) an algorithm that can monitor the data stream 'online' as data points are observed one after another, so that it responds to changes as quickly as possible while maintaining a low rate of false alarms; (2) a change-point procedure that can handle highly correlated component series, a situation that is very common in multi-sensor measurements; (3) a robust method for change-point estimation in the presence of missing or contaminated data. I will provide theoretical performance guarantees for the developed methods and implement them in open-source R packages.