Quickest Change Detection for Unnormalized Statistical Models

TL;DR

This paper introduces the SCUSUM algorithm, a novel change detection method based on Fisher divergence and the Hyv"arinen score, enabling effective detection in unnormalized models without explicit distribution modeling.

Contribution

It develops a new change detection algorithm suitable for unnormalized models, overcoming limitations of classical methods that require explicit distribution forms.

Findings

SCUSUM performs well in detecting changes in unnormalized models.

The algorithm is asymptotically optimal under certain conditions.

Numerical results confirm the effectiveness of SCUSUM.

Abstract

Classical quickest change detection algorithms require modeling pre-change and post-change distributions. Such an approach may not be feasible for various machine learning models because of the complexity of computing the explicit distributions. Additionally, these methods may suffer from a lack of robustness to model mismatch and noise. This paper develops a new variant of the classical Cumulative Sum (CUSUM) algorithm for the quickest change detection. This variant is based on Fisher divergence and the Hyv\"arinen score and is called the Score-based CUSUM (SCUSUM) algorithm. The SCUSUM algorithm allows the applications of change detection for unnormalized statistical models, i.e., models for which the probability density function contains an unknown normalization constant. The asymptotic optimality of the proposed algorithm is investigated by deriving expressions for average detection delay and the mean running time to a false alarm. Numerical results are provided to demonstrate the performance of the proposed algorithm.