In this work, we explore modeling change points in time-series data using neural stochastic differential equations (neural SDEs). We propose a novel model formulation and training procedure based on the variational autoencoder (VAE) framework for modeling time-series as a neural SDE. Unlike existing algorithms training neural SDEs as VAEs, our proposed algorithm only necessitates a Gaussian prior of the initial state of the latent stochastic process, rather than a Wiener process prior on the entire latent stochastic process. We develop two methodologies for modeling and estimating change points in time-series data with distribution shifts. Our iterative algorithm alternates between updating neural SDE parameters and updating the change points based on either a maximum likelihood-based approach or a change point detection algorithm using the sequential likelihood ratio test. We provide a theoretical analysis of this proposed change point detection scheme. Finally, we present an empirical evaluation that demonstrates the expressive power of our proposed model, showing that it can effectively model both classical parametric SDEs and some real datasets with distribution shifts.

本研究针对时间序列数据中的变换点建模问题，提出了一种基于变分自编码器框架的神经随机微分方程模型及其训练程序。与现有算法不同，我们的方法仅需初始状态的高斯先验，而无需对整个潜在随机过程使用维纳过程先验。实证评估表明，该模型能够有效地模拟经典的参数随机微分方程及具有分布转变的真实数据集。

具有变换点的变分神经随机微分方程