Detecting Changes in the Scale of Dependent Gaussian Processes: A Large Deviations Approach

This paper devises new hypothesis tests for detecting changes in the scale of interdependent and serially correlated data streams, i.e, proportional changes of the mean and (co-)variance. Such procedures are of great importance in various networking contexts, since they enable automatic detection of changes, e.g. in the network load. Assuming the underlying structure is Gaussian, we compute the log-likelihood ratio test statistic, either as a function of the observations themselves or as a function of the innovations (i.e., a sequence of i.i.d. Gaussians, to be extracted from the observations). An alarm is raised if the test statistic exceeds a certain threshold. Based on large deviations techniques, we demonstrate how the threshold is chosen such that the ratio of false alarms is kept at a predefined (low) level. Numerical experiments validate the procedure, and demonstrate the merits of a multidimensional detection approach (over multiple one-dimensional tests). Also a detailed comparison between the observations-based approach and the innovations-based approach is provided.