Stochastic differential equations (SDEs) have been widely used to model real world random phenomena. Existing works mainly focus on the case where the time series is modeled by a single SDE, which might be restrictive for modeling time series with distributional shift. In this work, we propose a change point detection algorithm for time series modeled as neural SDEs. Given a time series dataset, the proposed method jointly learns the unknown change points and the parameters of distinct neural SDE models corresponding to each change point. Specifically, the SDEs are learned under the framework of generative adversarial networks (GANs) and the change points are detected based on the output of the GAN discriminator in a forward pass. At each step of the proposed algorithm, the change points and the SDE model parameters are updated in an alternating fashion. Numerical results on both synthetic and real datasets are provided to validate the performance of our algorithm in comparison to classical change point detection benchmarks, standard GAN-based neural SDEs, and other state-of-the-art deep generative models for time series data.

翻译：随机微分方程（SDE）被广泛用于对现实世界中的随机现象进行建模。现有研究主要关注由单一SDE建模的时间序列，这在处理存在分布漂移的时间序列时可能具有局限性。本文提出了一种针对神经SDE建模时间序列的变点检测算法。给定时间序列数据集，该方法联合学习未知变点以及各变点对应的不同神经SDE模型参数。具体而言，SDE在生成对抗网络框架下进行学习，并通过前向传播过程中GAN判别器的输出实现变点检测。在算法每一步中，变点与SDE模型参数交替更新。通过合成数据集与真实数据集的数值实验，我们验证了该算法相较于经典变点检测基准方法、基于GAN的标准神经SDE模型以及其它最新时序数据深度生成模型的性能优势。