Conditional Score Learning for Quickest Change Detection in Markov Transition Kernels

TL;DR

This paper introduces a score-based quickest change detection method for high-dimensional Markov processes that learns the transition dynamics directly from data, providing theoretical guarantees and practical algorithms.

Contribution

It develops a novel score-based CUSUM procedure that learns the transition kernel without explicit likelihoods, with proven bounds on false alarms and detection delay.

Findings

Exponential lower bounds on false alarm times.

Asymptotic upper bounds on detection delay.

Practical score-based detection algorithm for high-dimensional data.

Abstract

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.