Compound Sequential Change-point Detection in Parallel Data Streams

TL;DR

This paper introduces a Bayesian sequential change-point detection method for multiple parallel data streams, aiming to maximize pre-change operation while controlling post-change stream proportions, with proven optimality and asymptotic analysis.

Contribution

It develops a uniformly optimal Bayesian procedure for change detection in multiple streams and analyzes its asymptotic properties as the number of streams grows.

Findings

The proposed method controls the proportion of post-change streams effectively.

Numerical examples demonstrate the method's superior performance.

Asymptotic analysis confirms the procedure's scalability.

Abstract

We consider sequential change-point detection in parallel data streams, where each stream has its own change point. Once a change is detected in a data stream, this stream is deactivated permanently. The goal is to maximize the normal operation of the pre-change streams, while controlling the proportion of post-change streams among the active streams at all time points. Taking a Bayesian formulation, we develop a compound decision framework for this problem. A procedure is proposed that is uniformly optimal among all sequential procedures which control the expected proportion of postchange streams at all time points. We also investigate the asymptotic behavior of the proposed method when the number of data streams grows large. Numerical examples are provided to illustrate the use and performance of the proposed method.