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We study the quickest change detection problem with an unknown post-change distribution. In this scenario, the unknown change in the distribution of observations may occur in many ways without much structure, while, before change, an outlier (a false alarm event) is highly structured, following a particular sample path. We first characterize these likely events for the deviation of finite strings and propose a method to test the deviation, relative to the most likely way for it to occur as an outlier. Our method works along with other change detection schemes to substantially reduce the false positive rates associated with the plain scheme used without the heavy computation associated with the generalized likelihood ratio test. Finally, we apply our method on economic market indicators and climate data. Our method successfully captures the regime shifts during times of historical significance and identifies the current climate change phenomenon to be a highly likely regime shift.

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We propose a quickest change detection problem over sensor networks where both the subset of sensors undergoing a change and the local post-change distributions are unknown. Each sensor in the network observes a local discrete time random process over a finite alphabet. Initially, the observations are independent and identically distributed (i.i.d.) with known pre-change distributions independent from other sensors. At a fixed but unknown change point, a fixed but unknown subset of the sensors undergo a change and start observing samples from an unknown distribution. We assume the change can be quantified using concave (or convex) local statistics over the space of distributions. We propose an asymptotically optimal and computationally tractable stopping time for Lorden's criterion. Under this scenario, our proposed method uses a concave global cumulative sum (CUSUM) statistic at the fusion center and suppresses the most likely false alarms using information projection. Finally, we show some numerical results of the simulation of our algorithm for the problem described.