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.

翻译：本文提出了一种针对未归一化及基于分数的统计模型的多流最快变化检测与故障隔离方法。传统最快变化检测文献中的最优算法需要明确的变化前与变化后分布以计算观测值的似然比，这对于高维数据计算成本较高，有时对于复杂机器学习模型甚至不可行。为解决这些挑战，我们提出了min-SCUSUM方法，这是一种基于Hyvarinen分数的算法，通过计算分数函数差值替代对数似然比。我们对所提算法进行了延迟与误报分析，表明其渐近性能取决于变化前后分布之间的Fisher散度。此外，我们建立了在区分受影响流与未受影响流时故障误识别概率的上界。