Robust Quickest Change Detection in Multi-Stream Non-Stationary Processes

TL;DR

This paper develops a robust quickest change detection algorithm for multi-stream non-stationary processes, ensuring optimal detection performance even when data distributions vary over time and are not fully known.

Contribution

It introduces a novel approach using least favorable laws for robust detection in non-stationary multi-stream data, extending classical QCD theory.

Findings

Algorithm achieves robustness in non-stationary settings

Effective on simulated data

Validated on real-world public health and aviation data

Abstract

The problem of robust quickest change detection (QCD) in non-stationary processes under a multi-stream setting is studied. In classical QCD theory, optimal solutions are developed to detect a sudden change in the distribution of stationary data. Most studies have focused on single-stream data. In non-stationary processes, the data distribution both before and after change varies with time and is not precisely known. The multi-dimension data even complicates such issues. It is shown that if the non-stationary family for each dimension or stream has a least favorable law (LFL) or distribution in a well-defined sense, then the algorithm designed using the LFLs is robust optimal. The notion of LFL defined in this work differs from the classical definitions due to the dependence of the post-change model on the change point. Examples of multi-stream non-stationary processes encountered in public health monitoring and aviation applications are provided. Our robust algorithm is applied to simulated and real data to show its effectiveness.