Minimax-Optimal Algorithms for Detecting Changes in Statistically Periodic Random Processes

Abstract

Theory and algorithms are developed for detecting changes in the distribution of statistically periodic random processes. The statistical periodicity is modeled using independent and periodically identically distributed processes, a new class of stochastic processes proposed by us. An algorithm is developed that is minimax asymptotically optimal as the false alarm rate goes to zero. Algorithms are also developed for the cases when the post-change distribution is not known or when there are multiple streams of observations. The modeling is inspired by real datasets encountered in cyber-physical systems, biology, and medicine. The developed algorithms are applied to sequences of Instagram counts collected around a 5K run in New York City to detect the run.