Data-Efficient Quickest Change Detection in Minimax Settings

Abstract

The classical problem of quickest change detection is studied with an additional constraint on the cost of observations used in the detection process. The change point is modeled as an unknown constant, and minimax formulations are proposed for the problem. The objective in these formulations is to find a stopping time and an on-off observation control policy for the observation sequence, to minimize a version of the worst possible average delay, subject to constraints on the false alarm rate and the fraction of time observations are taken before change. An algorithm called DE-CuSum is proposed and is shown to be asymptotically optimal for the proposed formulations, as the false alarm rate goes to zero.Numerical results are used to show that the DE-CuSum algorithm has good trade-off curves and performs significantly better than the approach of fractional sampling, in which the observations are skipped using the outcome of a sequence of coin tosses, independent of the observation process. This work is guided by the insights gained from an earlier study of a Bayesian version of this problem.

Data-efficient quickest change detection in distributed and multi-channel systems

“…In this paper we extend the results from [9], [10] and [11] to study data-efficient quickest change detection (DE-QCD) in a distributed system described above, when the subset of sensors affected by the change is not known at the fusion center. Since, the knowledge of the distribution of the change point is generally not available in practice, we study the problem in minimax settings.…”

“…In [9] and [10] we extended the classical quickest change detection formulations studied in [1], [2] and [3], by putting an additional constraint on the cost of observations used in the detection process. We proposed problem formulations, for the Bayesian setting in [9], and for two minimax settings in [10], in which the objective was to minimize some version of the average delay, subject to constraints on the false alarm rate and a version of the average number of observations taken before the change point.…”

“…We proposed problem formulations, for the Bayesian setting in [9], and for two minimax settings in [10], in which the objective was to minimize some version of the average delay, subject to constraints on the false alarm rate and a version of the average number of observations taken before the change point. For the i.i.d.…”

“…In [11], we used the insights obtained from [9] and [10] to propose data-efficient algorithms for distributed systems when the change affects all the sensors. We showed that the proposed algorithms have good trade-off curves and provide a significant gain in performance as compared to the approach of fractional sampling.…”

Communication-Efficient Decentralized Change Detection for Cognitive Wireless Networks

“…A data-efficient quickest change detection scheme is developed in [16] and [17] based on a minimax formulation, where the cost in taking samples is controlled through a censoring technique. One of the major problems in existing soft combining based algorithms is that unlimited local memory is required to store the sensing history [16]- [17], i.e., all previous observed information and local decisions. In [15], full feedback from the fusion center is additionally assumed to obtain the optimal solution.…”