无需显式计算似然，用条件得分学习马尔可夫转移核变化。
Conditional Score Learning for Quickest Change Detection in Markov Transition Kernels
- 直接从样本对学习条件得分，避免复杂似然计算。
- 提出基于得分差的CUSUM检测法，实现高维状态下的快速变化检测。
- 理论证明误报间隔与检测延迟均有保障，适合高维动态系统监控。
针对未知转移核的马尔可夫过程中的快速变化检测问题，本文提出直接从样本对 (x, y) 中学习条件得分 ∇_y log p(y|x)，其中 x 与 y 由同一转移核生成。该方法避免了显式似然评估，为学习转移动态提供了实用途径。基于此估计，我们设计了一种基于得分的 CUSUM 检测程序，利用条件 Hyvarinen 得分差异检测核的变化。为保证统计量增量有界，提出截断版本。借助均匀遍历马尔可夫过程的 Hoeffding 不等式，证明了误报均值时间的指数下界，并给出了检测延迟的渐近上界。这些结果同时提供了理论保证与实际可行性，适用于高维马尔可夫模型的得分驱动检测。
原文摘要 · Abstract (English)
We address the problem of quickest change detection in Markov processes with unknown transition kernels. The key idea is to learn the conditional score $\nabla_{\mathbf{y}} \log p(\mathbf{y}|\mathbf{x})$ directly from sample pairs $( \mathbf{x},\mathbf{y})$, where both $\mathbf{x}$ and $\mathbf{y}$ are high-dimensional data generated by the same transition kernel. In this way, we avoid explicit likelihood evaluation and provide a practical way to learn the transition dynamics. Based on this estimation, we develop a score-based CUSUM procedure that uses conditional Hyvarinen score differences to detect changes in the kernel. To ensure bounded increments, we propose a truncated version of the statistic. With Hoeffding's inequality for uniformly ergodic Markov processes, we prove exponential lower bounds on the mean time to false alarm. We also prove asymptotic upper bounds on detection delay. These results give both theoretical guarantees and practical feasibility for score-based detection in high-dimensional Markov models.
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