Sketching for Sequential Change-Point Detection

We study sequential change-point detection using sketches (or linear projections) of the high-dimensional data vectors, and present a new sketching procedure, which is based on the generalized likelihood ratio statistic. We derive theoretical approximations to two fundamental performance metrics for the sketching procedures: the average run length (ARL) and the expected detection delay (EDD), and these approximations are shown to be highly accurate by numerical simulations. We also analyze the ratio of EDD between the sketching procedure and a procedure using the original data, when the sketching matrix $A$ is a random Gaussian matrix and a sparse 0-1 matrix (in particular, an expander graph), respectively. Finally, numerical examples demonstrate that the sketching procedure can approach the performance of the procedure using the original data, even when the post-change mean vector is not sparse.