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

Wuxia Chen, Sean Moushegian, Vahid Tarokh, Taposh Banerjee

TL;DR

This work tackles multi-stream quickest change detection when pre- and post-change densities are unknown and may be unnormalized. It introduces min-SCUSUM, a Hyvärinen-score-based extension of min-CUSUM that uses score differences to form per-channel statistics and a unified stopping rule, with a diagnosis rule that selects the most active channel at stopping. The authors prove consistency, derive a false-alarm lower bound, and establish delay and miss-identification guarantees that scale with the Fisher divergence $D_F(g_i||f_i)$; a single threshold $b=\log(|\mathcal{I}|/α)$ balances false alarms and false isolations. Empirically, the method shows provable performance on synthesized high-dimensional data and demonstrates effective detection and fault isolation in real video streams, highlighting its practicality for high-dimensional, score-based 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.

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

TL;DR

This work tackles multi-stream quickest change detection when pre- and post-change densities are unknown and may be unnormalized. It introduces min-SCUSUM, a Hyvärinen-score-based extension of min-CUSUM that uses score differences to form per-channel statistics and a unified stopping rule, with a diagnosis rule that selects the most active channel at stopping. The authors prove consistency, derive a false-alarm lower bound, and establish delay and miss-identification guarantees that scale with the Fisher divergence ; a single threshold balances false alarms and false isolations. Empirically, the method shows provable performance on synthesized high-dimensional data and demonstrates effective detection and fault isolation in real video streams, highlighting its practicality for high-dimensional, score-based 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.

Paper Structure

This paper contains 21 sections, 8 theorems, 98 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Related Work
  3. Problem Formulation
  4. Hyvärinen score and Score Based Change Detection
  5. Hyvärinen Score
  6. Score-Based Quickest Change Detection
  7. min-SCUSUM Stopping and Diagnosis Algorithm
  8. Analysis of the min-SCUSUM Algorithm
  9. Consistency
  10. False Alarm Analysis
  11. Delay Analysis
  12. Probability of False Isolation
  13. Numerical Results
  14. Validating the Upper Bound on the Probability of Misidentification Using Synthesized Data
  15. Detection on Real-World Video Streams
  16. ...and 6 more sections

Key Result

Lemma 5.1

(Existence of positive $\lambda_i$) Define $h(\lambda_i) \triangleq \mathbb{E}_{\infty}\left[ e^{\lambda_i \cdot \left( S_H(X_{i,n}, f_i) - S_H(X_{i,n}, g_i) \right)} \right]-1$, we have either case (a) or case (b).

Figures (5)

  • Figure 1: The evolution of the SCUSUM statistics for the three streams.
  • Figure 2: The plots of the probability of misidentification for three possible change points $\nu=0,20,100$ as a function of the stopping threshold $b$.
  • Figure 3: Sample video frames before and after change.
  • Figure 4: SCUSUM statistics across three streams.
  • Figure 5: Negative drift before change, positive drift after.

Theorems & Definitions (19)

  • Definition 3.1
  • Definition 3.2
  • Definition 3.4
  • Lemma 5.1
  • proof
  • Theorem 5.2
  • proof
  • Theorem 5.3
  • proof
  • Theorem 5.4
  • ...and 9 more