Integral probability metric-guided CUSUM-Net for nonparametric changepoint detection

• 成果类型: Article
• 署名作者: Li, Yunchen; Wang, Guanghui; Xu, Shuntuo; Yu, Zhou
• 署名单位: East China Normal University; Nankai University; Nankai University
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444; 1464-3510
• DOI: 10.1093/biomet/asag046
• 发表日期: 2026
• 页码: asag046
• 关键词: changepoint detection; Cumulative sum; Deep ReLU network; Integral probability metric; regression

摘要

We propose CUSUM-Net, a nonparametric method for changepoint detection based on integral probability metrics and deep neural networks. Our approach learns a critic function by maximizing an aggregate CUSUM objective over candidate changepoints, thereby linking changepoint detection to optimization of two-sample integral probability metrics. The learned critic induces a one-dimensional representation on which changepoints are localized by a classical CUSUM scan. Unlike parametric procedures, CUSUM-Net accommodates complex, high-dimensional distributional changes and applies to a range of data modalities, including Euclidean data, symmetric positive-definite matrices, images and graphs. We establish excess-risk bounds for the learned critic under H & ouml;lder smoothness assumptions, with faster rates when the data exhibit low-dimensional manifold structure, and derive corresponding changepoint localization guarantees. Numerical experiments demonstrate the flexibility and effectiveness of the proposed method.