Data-Efficient Quickest Change Detection with On-Off Observation Control

In this paper we extend the Shiryaev's quickest change detection formulation by also accounting for the cost of observations used before the change point. The observation cost is captured through the average number of observations used in the detection process before the change occurs. The objective is to select an on-off observation control policy, that decides whether or not to take a given observation, along with the stopping time at which the change is declared, so as to minimize the average detection delay, subject to constraints on both the probability of false alarm and the observation cost. By considering a Lagrangian relaxation of the constraint problem, and using dynamic programming arguments, we obtain an \textit{a posteriori} probability based two-threshold algorithm that is a generalized version of the classical Shiryaev algorithm. We provide an asymptotic analysis of the two-threshold algorithm and show that the algorithm is asymptotically optimal, i.e., the performance of the two-threshold algorithm approaches that of the Shiryaev algorithm, for a fixed observation cost, as the probability of false alarm goes to zero. We also show, using simulations, that the two-threshold algorithm has good observation cost-delay trade-off curves, and provides significant reduction in observation cost as compared to the naive approach of fractional sampling, where samples are skipped randomly. Our analysis reveals that, for practical choices of constraints, the two thresholds can be set independent of each other: one based on the constraint of false alarm and another based on the observation cost constraint alone.Comment: Preliminary version of this paper has been presented at ITA Workshop UCSD 201

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

Data-Efficient Quickest Outlying Sequence Detection in Sensor Networks

A sensor network is considered where at each sensor a sequence of random variables is observed. At each time step, a processed version of the observations is transmitted from the sensors to a common node called the fusion center. At some unknown point in time the distribution of observations at an unknown subset of the sensor nodes changes. The objective is to detect the outlying sequences as quickly as possible, subject to constraints on the false alarm rate, the cost of observations taken at each sensor, and the cost of communication between the sensors and the fusion center. Minimax formulations are proposed for the above problem and algorithms are proposed that are shown to be asymptotically optimal for the proposed formulations, as the false alarm rate goes to zero. It is also shown, via numerical studies, that the proposed algorithms perform significantly better than those based on fractional sampling, in which the classical algorithms from the literature are used and the constraint on the cost of observations is met by using the outcome of a sequence of biased coin tosses, independent of the observation process.Comment: Submitted to IEEE Transactions on Signal Processing, Nov 2014. arXiv admin note: text overlap with arXiv:1408.474