Nonparametric Filtering, Estimation and Classification using Neural Jump ODEs
This provides a robust solution for real-time applications like finance and health monitoring, though it is incremental as it builds on an existing framework.
The paper tackled the problem of online filtering and classification with irregular and partial observations by extending Neural Jump ODEs to input-output systems, achieving superior performance over classical parametric methods in scenarios with complex distributions.
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.