Asymptotically Optimal Quickest Change Detection in Multistream Data—Part 1: General Stochastic Models

Abstract

Assume that there are multiple data streams (channels, sensors) and in each stream the process of interest produces generally dependent and nonidentically distributed observations. When the process is in a normal mode (in-control), the (pre-change) distribution is known, but when the process becomes abnormal there is a parametric uncertainty, i.e., the post-change (out-of-control) distribution is known only partially up to a parameter. Both the change point and the post-change parameter are unknown. Moreover, the change affects an unknown subset of streams, so that the number of affected streams and their location are unknown in advance. A good changepoint detection procedure should detect the change as soon as possible after its occurrence while controlling for a risk of false alarms. We consider a Bayesian setup with a given prior distribution of the change point and propose two sequential mixture-based change detection rules, one mixes a Shiryaev-type statistic over both the unknown subset of affected streams and the unknown post-change parameter and another mixes a Shiryaev-Robertstype statistic. These rules generalize the mixture detection procedures studied by Tartakovsky ( 2018) in a single-stream case. We provide sufficient conditions under which the proposed multistream change detection procedures are first-order asymptotically optimal with respect to moments of the delay to detection as the probability of false alarm approaches zero.

On Matched Filtering for Statistical Change Point Detection

“…Early applications of change point detection in failure detection focused on metrics such as average run length and detection delay as key metrics of CPD [42], [43]. Recent applications frame the problem of multiple CPD as a classification problem at each time step (change point vs. no change point) where there is a severe class imbalance as only a small fraction of time steps is regarded as true change points.…”

Optimal Bayesian Quickest Detection for Hidden Markov Models and Structured Generalisations

“…In [21] they consider this multistream data problem with parametric uncertainty in the post change parameters and provide sufficient conditions under which the proposed multistream change detection procedures are first-order asymptotically optimal.…”

“…A contribution of this paper is establishing that the optimal rule for QCD in multistream data is a simple threshold test (a variation of the problem considered in [21] which established asymptotic optimality).…”

“…Similar to the problems considered in [20], [21] (however we do not consider here the case with post-change uncertainty rather we assume post-change model is known) we now formulate the problem of QCD in multistream data. Consider D data streams denoted by D = {1, .…”

On the informativeness of measurements in Shiryaev’s Bayesian quickest change detection

“…Quickest change detection (QCD) problems consider the detection of a change in the statistical properties of an observed process and occur in a wide variety of applications including quality control [1], anomaly detection [2], statistics [3], target detection [4] and fault detection [1]. In such problems, a sequence of quantitative measurements are monitored to extract information of the current properties of an observed process with the desire to detect a change as quickly as possible after it occurs subject to a false alarm constraint [5].…”