Robust Score-Based Quickest Change Detection

TL;DR

This paper develops a robust quickest change detection method that operates effectively even when the pre- and post-change distributions are only known within certain sets, by selecting least-favorable distributions to enhance detection reliability.

Contribution

It introduces a robust score-based change detection algorithm that accounts for uncertainty in distribution sets by selecting least-favorable distributions, with methods for their estimation and analysis.

Findings

The proposed method effectively detects changes under distribution uncertainty.

The paper provides explicit calculations for least-favorable distributions in specific models.

Simulation results demonstrate improved robustness and performance of the detection algorithm.

Abstract

Methods in the field of quickest change detection rapidly detect in real-time a change in the data-generating distribution of an online data stream. Existing methods have been able to detect this change point when the densities of the pre- and post-change distributions are known. Recent work has extended these results to the case where the pre- and post-change distributions are known only by their score functions. This work considers the case where the pre- and post-change score functions are known only to correspond to distributions in two disjoint sets. This work selects a pair of least-favorable distributions from these sets to robustify the existing score-based quickest change detection algorithm, the properties of which are studied. This paper calculates the least-favorable distributions for specific model classes and provides methods of estimating the least-favorable distributions for common constructions. Simulation results are provided demonstrating the performance of our robust change detection algorithm.