Wasserstein Online Change Point Detection with Neural Networks

Online change point detection (CPD) is a fundamental problem in statistics and machine learning. Kernel methods are theoretically principled but are limited by the choice of kernel and lose power in high dimensions. Learning-based approaches, on the other hand, typically lack the same level of theoretical guarantees. To bridge this gap, we propose an online CPD algorithm approximating the Wasserstein distance between two consecutive sliding windows through a Lipschitz-constrained neural network. The network is trained recursively using a small number of gradient iterations per time step, making the detector unsupervised and online. We derive non-asymptotic concentration bounds for the test statistic under the null hypothesis and under the alternative with a partially contaminated window, leveraging a refined analysis with Rademacher complexity bounds. This yields a constant threshold choice that guarantees any prescribed average run length, a logarithmically growing threshold that controls the false alarm probability over an infinite horizon, and an exponential tail bound on the detection delay. These are, to our knowledge, the first results for an online detector whose statistic is computed by a neural network. Simulation results show that the proposed algorithm achieves lower detection delays per average run length than several state-of-the-art detectors.