Data-Efficient Minimax Quickest Change Detection with Composite Post-Change Distribution

The problem of quickest change detection is studied, where there is an additional constraint on the cost of observations used before the change point and where the post-change distribution is composite. Minimax formulations are proposed for this problem. It is assumed that the post-change family of distributions has a member which is least favorable in some sense. An algorithm is proposed in which on-off observation control is employed using the least favorable distribution, and a generalized likelihood ratio based approach is used for change detection. Under the additional condition that either the post-change family of distributions is finite, or both the pre- and post-change distributions belong to a one parameter exponential family, it is shown that the proposed algorithm is asymptotically optimal, uniformly for all possible post-change distributions.Comment: Submitted to IEEE Transactions on Info. Theory, Oct 2014. Preliminary version presented at ISIT 2014 at Honolulu, Hawai

Quickest Change Detection of a Markov Process Across a Sensor Array

Recent attention in quickest change detection in the multi-sensor setting has been on the case where the densities of the observations change at the same instant at all the sensors due to the disruption. In this work, a more general scenario is considered where the change propagates across the sensors, and its propagation can be modeled as a Markov process. A centralized, Bayesian version of this problem, with a fusion center that has perfect information about the observations and a priori knowledge of the statistics of the change process, is considered. The problem of minimizing the average detection delay subject to false alarm constraints is formulated as a partially observable Markov decision process (POMDP). Insights into the structure of the optimal stopping rule are presented. In the limiting case of rare disruptions, we show that the structure of the optimal test reduces to thresholding the a posteriori probability of the hypothesis that no change has happened. We establish the asymptotic optimality (in the vanishing false alarm probability regime) of this threshold test under a certain condition on the Kullback-Leibler (K-L) divergence between the post- and the pre-change densities. In the special case of near-instantaneous change propagation across the sensors, this condition reduces to the mild condition that the K-L divergence be positive. Numerical studies show that this low complexity threshold test results in a substantial improvement in performance over naive tests such as a single-sensor test or a test that wrongly assumes that the change propagates instantaneously.Comment: 40 pages, 5 figures, Submitted to IEEE Trans. Inform. Theor