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. 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.
Richard Samworth holds the Professorship of Statistical Science and is Director of the Statistical Laboratory, a sub-department of the Department of Pure Mathematics and Mathematical Statistics (which is part of the Faculty of Mathematics) at the University of Cambridge.