Round Robin Active Sequential Change Detection for Dependent Multi-Channel Data

Abstract

This paper considers the problem of sequentially detecting a change in the joint distribution of multiple data sources under a sampling constraint. Specifically, the channels or sources generate observations that are independent over time, but not necessarily across channels. The joint distribution of an unknown subset of sources changes at an unknown time instant. Moreover, there is a hard constraint that only a fixed number of sources can be sampled at each time instant, but the sources can be selected dynamically based on the already collected data. The goal is to sequentially observe the sources according to the constraint, and stop sampling as quickly as possible after the change while controlling the false alarm rate below a user-specified level. Thus, a policy for this problem consists of a joint sampling and change-detection rule. A non-randomized policy is studied, and an upper bound is established on its worst-case conditional expected detection delay with respect to both the change point and the observations from the affected sources before the change. In certain cases, this rule achieves first-order asymptotic optimality as the false alarm rate tends to zero, simultaneously under every possible post-change distribution and among all schemes that satisfy the same sampling and false alarm constraints. These general results are subsequently applied to the problems of (i) detecting a change in the marginal distributions of (not necessarily independent) information sources, and (ii) detecting a change in the covariance structure of Gaussian information sources.