Conditional Score Learning for Quickest Change Detection in Markov Transition Kernels
This provides a practical method for detecting changes in transition kernels of high-dimensional Markov processes, which is important for applications like anomaly detection in complex systems.
The paper tackles quickest change detection in high-dimensional Markov processes with unknown transition kernels by learning conditional scores directly from sample pairs, avoiding explicit likelihood evaluation. They develop a score-based CUSUM procedure with theoretical guarantees including exponential lower bounds on false alarm time and asymptotic upper bounds on detection delay.
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.