Stable Neural Stochastic Differential Equations in Analyzing Irregular Time Series Data

Irregular sampling intervals and missing values in real-world time series data present challenges for conventional methods that assume consistent intervals and complete data. Neural Ordinary Differential Equations (Neural ODEs) offer an alternative approach, utilizing neural networks combined with ODE solvers to learn continuous latent representations through parameterized vector fields. Neural Stochastic Differential Equations (Neural SDEs) extend Neural ODEs by incorporating a diffusion term, although this addition is not trivial, particularly when addressing irregular intervals and missing values. Consequently, careful design of drift and diffusion functions is crucial for maintaining stability and enhancing performance, while incautious choices can result in adverse properties such as the absence of strong solutions, stochastic destabilization, or unstable Euler discretizations, significantly affecting Neural SDEs' performance. In this study, we propose three stable classes of Neural SDEs: Langevin-type SDE, Linear Noise SDE, and Geometric SDE. Then, we rigorously demonstrate their robustness in maintaining excellent performance under distribution shift, while effectively preventing overfitting. To assess the effectiveness of our approach, we conduct extensive experiments on four benchmark datasets for interpolation, forecasting, and classification tasks, and analyze the robustness of our methods with 30 public datasets under different missing rates. Our results demonstrate the efficacy of the proposed method in handling real-world irregular time series data.

Invertible Solution of Neural Differential Equations for Analysis of Irregularly-Sampled Time Series

To handle the complexities of irregular and incomplete time series data, we propose an invertible solution of Neural Differential Equations (NDE)-based method. While NDE-based methods are a powerful method for analyzing irregularly-sampled time series, they typically do not guarantee reversible transformations in their standard form. Our method suggests the variation of Neural Controlled Differential Equations (Neural CDEs) with Neural Flow, which ensures invertibility while maintaining a lower computational burden. Additionally, it enables the training of a dual latent space, enhancing the modeling of dynamic temporal dynamics. Our research presents an advanced framework that excels in both classification and interpolation tasks. At the core of our approach is an enhanced dual latent states architecture, carefully designed for high precision across various time series tasks. Empirical analysis demonstrates that our method significantly outperforms existing models. This work significantly advances irregular time series analysis, introducing innovative techniques and offering a versatile tool for diverse practical applications.