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.

在处理真实世界的不规则时间序列数据中，由于不连续的采样间隔和缺失值，神经随机微分方程（Neural SDEs）的良好性能依赖于漂移和扩散函数的巧妙选择，本研究通过提出三个稳定的 Neural SDE 类别： Langevin 型 SDE、线性噪声 SDE 和几何 SDE，并通过广泛的实验验证了这些方法在分布转移和不同缺失率下的鲁棒性，展示了该方法在处理真实世界不规则时间序列数据中的有效性。

分析非规则时间序列数据的稳定神经随机微分方程

Stable Neural Stochastic Differential Equations in Analyzing Irregular  Time Series Data

Discovering the underlying relationships among variables from temporal
observations has been a longstanding challenge in numerous scientific
disciplines, including biology, finance, and climate science. The dynamics of
such systems are often best described using continuous-time stochastic
processes. Unfortunately, most existing structure learning approaches assume
that the underlying process evolves in discrete-time and/or observations occur
at regular time intervals. These mismatched assumptions can often lead to
incorrect learned structures and models. In this work, we introduce a novel
structure learning method, SCOTCH, which combines neural stochastic
differential equations (SDE) with variational inference to infer a posterior
distribution over possible structures. This continuous-time approach can
naturally handle both learning from and predicting observations at arbitrary
time points. Theoretically, we establish sufficient conditions for an SDE and
SCOTCH to be structurally identifiable, and prove its consistency under
infinite data limits. Empirically, we demonstrate that our approach leads to
improved structure learning performance on both synthetic and real-world
datasets compared to relevant baselines under regular and irregular sampling
intervals.

基于连续时间随机微分方程和变分推断，我们提出了一种新的结构学习方法 SCOTCH，可以自然地处理任意时间点的学习和预测观测，并在合规和非合规采样间隔下，在合成和真实数据集上表现出较好的结构学习性能。