用神经跳跃微分方程实现在线滤波与分类，无需强假设
Nonparametric Filtering, Estimation and Classification using Neural Jump ODEs
- 基于神经微分方程建模观测间条件期望，新数据到来时触发跳跃更新
- 在不规则观测下实现$L^2$最优滤波，实测优于经典参数方法
- 适合金融、健康监测等实时性要求高的场景
神经跳跃微分方程通过神经微分方程建模观测间的条件期望，并在新观测到达时发生跳跃。该方法在不规则和部分观测场景中展现出强大的数据驱动在线预测能力，且无需强正则性假设。本文将框架扩展至输入-输出系统，直接应用于在线滤波与分类任务。我们建立了该方法的理论收敛性保证，提供了一种 $L^2$-最优滤波的稳健解法。实验表明，模型在复杂分布场景下显著优于传统参数方法，凸显其在金融、健康监测等对实时性要求高的领域的应用潜力。
原文摘要 · Abstract (English)
Neural Jump ODEs model the conditional expectation between observations by neural ODEs and jump at arrival of new observations. They have demonstrated effectiveness for fully data-driven online forecasting in settings with irregular and partial observations, operating under weak regularity assumptions. This work extends the framework to input-output systems, enabling direct applications in online filtering and classification. We establish theoretical convergence guarantees for this approach, providing a robust solution to $L^2$-optimal filtering. Empirical experiments highlight the model's superior performance over classical parametric methods, particularly in scenarios with complex underlying distributions. These results emphasise the approach's potential in time-sensitive domains such as finance and health monitoring, where real-time accuracy is crucial.
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