High-dimensional, multiscale online changepoint detection
This work addresses the need for efficient online changepoint detection in high-dimensional settings, such as seismology, but is incremental as it builds on existing likelihood ratio test frameworks.
The authors tackled the problem of detecting changes in the mean of high-dimensional Gaussian data streams online, introducing a method that aggregates likelihood ratio tests across scales and coordinates, with proven guarantees on patience and response delay, and demonstrated effectiveness in simulations and a seismology dataset.
We introduce a new method for high-dimensional, online changepoint detection in settings where a $p$-variate Gaussian data stream may undergo a change in mean. The procedure works by performing likelihood ratio tests against simple alternatives of different scales in each coordinate, and then aggregating test statistics across scales and coordinates. The algorithm is online in the sense that both its storage requirements and worst-case computational complexity per new observation are independent of the number of previous observations; in practice, it may even be significantly faster than this. We prove that the patience, or average run length under the null, of our procedure is at least at the desired nominal level, and provide guarantees on its response delay under the alternative that depend on the sparsity of the vector of mean change. Simulations confirm the practical effectiveness of our proposal, which is implemented in the R package 'ocd', and we also demonstrate its utility on a seismology data set.