Compressed Change Detection

In traditional sparse recovery problems, the goal is to identify the support of compressible signals using a small number of measurements. In contrast, in this paper the problem of identification of a sparse number of statistical changes in stochastic phenomena is considered. This framework, which is newly introduced herein, is termed Compressed Change Detection. In particular, given a large number N of features, the goal is to detect a small set of features that undergoes a statistical change using a small number of measurements. The main approach relies on integrating ideas from the theory of identifying codes with change point detection in sequential analysis. If the stochastic properties of certain features change, then the changes can be detected by examining the covering set of an identifying code. Sufficient conditions are derived for the probability of detection to approach 1 in the asymptotic regime where N is large. Several applications and generalizations of the proposed framework are presented.