🤖 AI Summary
Real-world time series (e.g., stock prices, meteorological data) often exhibit irregular sampling and pervasive missing values, posing fundamental challenges for continuous-time modeling and robust inference.
Method: We propose three theoretically guaranteed stable neural stochastic differential equations (Neural SDEs): Langevin-type, linear-noise-type, and geometric-type. Grounded in Itô calculus, our framework rigorously ensures strong solution existence, numerical stability, and distributional shift robustness. We further design an adaptive Euler–Maruyama solver and a missingness-aware likelihood optimization scheme to enable continuous latent-space modeling and robust inference.
Results: Our approach achieves significant improvements over baselines—including Neural ODEs and GRU-D—across interpolation, forecasting, and classification tasks on four benchmark datasets. Moreover, extensive evaluation across 30 public datasets under diverse missingness rates confirms consistent generalization performance and strong robustness to missing data.
📝 Abstract
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.