Sequential Change Detection of a Correlation Structure under a Sampling Constraint

The problem of sequentially detecting a change in the correlation structure of multiple Gaussian information sources is considered when it is possible to sample only two of them at each time instance. It is assumed that all sources are initially independent and that at least two of them become positively correlated after the change. The problem is to stop sampling as quickly as possible after the change, while controlling the false alarm rate and without assuming any prior information on the number of sources that become correlated. A joint sampling and change-detection rule is proposed and is shown to achieve the smallest possible worst-case conditional expected detection delay among all processes that satisfy the same constraints, to a first order approximation as the false alarm rate goes to 0, for any possible number of post-change correlated sources.