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. When there is a model mismatch with actual data, classic CUSUM can perform poorly. While likelihood ratio-based methods encounter challenges in high dimensions, 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（即从序列数据中检测数据分布的突变）是统计学与机器学习领域的核心问题。CUSUM方法作为一种经典的在线变点检测统计方法，凭借其递归计算的效率、恒定内存需求及统计最优性而广泛应用。该方法需预先确知变点前后的分布信息，但作为异常与新颖性表征的变后分布通常难以先验获取。当实际数据存在模型失配时，经典CUSUM方法的性能会显著下降。尽管基于似然比的方法在高维场景中面临挑战，神经网络凭借其计算高效性与可扩展性已成为变点检测领域的新兴工具。本文提出了一种用于在线变点检测的神经网络CUSUM方法（NN-CUSUM），并给出了训练后的神经网络实现变点检测所需满足的一般理论条件，以及能够达成目标的目标损失函数。进一步地，我们结合神经正切核理论拓展了分析框架，为平均运行长度（ARL）和期望检测延迟（EDD）等标准性能指标建立了学习保证。通过合成数据与真实世界数据的高维变点检测实验，充分验证了NN-CUSUM方法的优异性能。