用变分框架建模时间序列突变点，更灵活且高效。
Variational Neural Stochastic Differential Equations with Change Points
- 基于变分自编码器设计新模型，仅需初始状态高斯先验
- 通过迭代优化同时学习神经SDE参数与突变点位置
- 适用于分布突变的真实数据，理论分析与实证均有效
本文研究使用神经随机微分方程（neural SDE）建模时间序列中的突变点。提出一种基于变分自编码器（VAE）的新模型与训练方法，将时间序列建模为神经SDE。与现有方法不同，本方法仅需对潜在随机过程的初始状态设定高斯先验，而非整个过程的维纳过程先验。开发了两种方法来建模和估计具有分布变化的时间序列突变点：一种基于最大似然，另一种采用序贯似然比检验的突变点检测算法。提出的迭代算法交替更新神经SDE参数与突变点位置。提供了该突变点检测方案的理论分析。最后的实验评估表明，所提模型能有效拟合经典参数化SDE及存在分布突变的真实数据集。
原文摘要 · Abstract (English)
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.
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