High-dimensional online changepoint detection and inference

Changepoint detection is a classical statistical problem, dating back at least to 1954 in the univariate case. However, modern applications in internet traffic monitoring, fMRI and finance, to name just a few, have motivated a resurgence of interest in the topic, from a high-dimensional perspective. One interesting model is where changes occur only in a sparse subset of coordinates (e.g. only a few voxels or a few stocks undergo a change in data generating mechanism), and the aim is to borrow strength across the different components to detect smaller changes than would be possible through only seeing any one of the individual series.

The large majority of the work in this area has focused on the ‘offline’ problem, where one sees the entire data set in advance of trying to ascertain where change(s) occurred. However, the corresponding online problem, where one sees the data coming in over time and seeks to declare a change as soon as possible after it has occurred (with a small probability of false alarm), is at least as important from the point of view of applications.

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