Robust Quickest Change Detection for Unnormalized Models

TL;DR

This paper introduces RSCUSUM, a robust score-based change detection algorithm that efficiently detects distribution changes in online data streams, especially for unnormalized models with unknown post-change distributions.

Contribution

It proposes a novel RSCUSUM algorithm that uses Fisher divergence for robust and efficient change detection in unnormalized models, addressing unknown post-change distributions.

Findings

RSCUSUM effectively detects changes in simulated data streams.

Theoretical analysis confirms the robustness and efficiency of RSCUSUM.

Simulation results demonstrate superior performance over existing methods.

Abstract

Detecting an abrupt and persistent change in the underlying distribution of online data streams is an important problem in many applications. This paper proposes a new robust score-based algorithm called RSCUSUM, which can be applied to unnormalized models and addresses the issue of unknown post-change distributions. RSCUSUM replaces the Kullback-Leibler divergence with the Fisher divergence between pre- and post-change distributions for computational efficiency in unnormalized statistical models and introduces a notion of the ``least favorable'' distribution for robust change detection. The algorithm and its theoretical analysis are demonstrated through simulation studies.