Score-Based Quickest Change Detection and Fault Identification for Multi-Stream Signals

TL;DR

This paper presents a novel score-based method for quick detection and fault identification in multi-stream signals, reducing computational complexity compared to traditional likelihood-based approaches.

Contribution

The paper introduces the min-SCUSUM algorithm using Hyvarinen scores for efficient change detection without explicit likelihoods, applicable to complex models.

Findings

Asymptotic performance depends on Fisher divergence.

Provides bounds on fault misidentification probability.

Effective for high-dimensional and complex models.

Abstract

This paper introduces an approach to multi-stream quickest change detection and fault isolation for unnormalized and score-based statistical models. Traditional optimal algorithms in the quickest change detection literature require explicit pre-change and post-change distributions to calculate the likelihood ratio of the observations, which can be computationally expensive for higher-dimensional data and sometimes even infeasible for complex machine learning models. To address these challenges, we propose the min-SCUSUM method, a Hyvarinen score-based algorithm that computes the difference of score functions in place of log-likelihood ratios. We provide a delay and false alarm analysis of the proposed algorithm, showing that its asymptotic performance depends on the Fisher divergence between the pre- and post-change distributions. Furthermore, we establish an upper bound on the probability of fault misidentification in distinguishing the affected stream from the unaffected ones.