Change-point detection, detecting an abrupt change in the data distribution from sequential data, is a fundamental problem in statistics and machine learning. CUSUM is a popular statistical method for online change-point detection due to its efficiency from recursive computation and constant memory requirement, and it enjoys statistical optimality. CUSUM requires knowing the precise pre- and post-change distribution. However, post-change distribution is usually unknown a priori since it represents anomaly and novelty. Classic CUSUM can perform poorly when there is a model mismatch with actual data. While likelihood ratio-based methods encounter challenges facing high dimensional data, neural networks have become an emerging tool for change-point detection with computational efficiency and scalability. In this paper, we introduce a neural network CUSUM (NN-CUSUM) for online change-point detection. We also present a general theoretical condition when the trained neural networks can perform change-point detection and what losses can achieve our goal. We further extend our analysis by combining it with the Neural Tangent Kernel theory to establish learning guarantees for the standard performance metrics, including the average run length (ARL) and expected detection delay (EDD). The strong performance of NN-CUSUM is demonstrated in detecting change-point in high-dimensional data using both synthetic and real-world data.

翻译：变点检测——从序列数据中检测数据分布的突然变化——是统计学和机器学习领域的基本问题。CUSUM因其递归计算的高效性和恒定的内存需求而成为一种流行的在线变点检测统计方法，并具有统计最优性。CUSUM需要精确已知的变点前和变点后分布。然而，变点后分布通常无法先验获知，因为它代表异常和新颖性。当模型与实际数据不匹配时，传统CUSUM方法性能可能不佳。虽然基于似然比的方法在处理高维数据时面临挑战，但神经网络凭借其计算效率和可扩展性已成为变点检测的新兴工具。本文提出了一种用于在线变点检测的神经网络CUSUM（NN-CUSUM）。我们同时给出了一个通用理论条件，阐明何时训练好的神经网络能够执行变点检测，以及哪些损失函数可以实现该目标。我们进一步结合神经正切核理论扩展分析，为包括平均运行长度和期望检测延迟在内的标准性能指标建立了学习保证。通过合成数据和真实数据的高维变点检测实验，验证了NN-CUSUM的优越性能。