Sketching for Sequential Change-Point Detection

We study sequential change-point detection using sketches (linear projections) of high-dimensional signal vectors, by presenting the sketching procedures that are derived based on the generalized likelihood ratio statistic. We consider both fixed and time-varying projections, and derive theoretical approximations to two fundamental performance metrics: the average run length (ARL) and the expected detection delay (EDD); these approximations are shown to be highly accurate by numerical simulations. We also characterize the performance of the procedure when the projection is a Gaussian random projection or a sparse 0-1 matrix (in particular, an expander graph). Finally, we demonstrate the good performance of the sketching performance using simulation and real-data examples on solar flare detection and failure detection in power networks.