Integral Probability Metric-Guided CUSUM-Net for Nonparametric Changepoint Detection

Abstract 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 two-sample integral probability metrics optimization. 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 Hölder smoothness assumptions, with faster rates when the data exhibit low-dimensional manifold structure, and we derive corresponding changepoint localization guarantees. Numerical experiments demonstrate the flexibility and effectiveness of the proposed method.