Nonparametric Filtering, Estimation and Classification using Neural Jump ODEs

TL;DR

This paper extends Neural Jump ODEs to input-output systems for online filtering and classification, providing theoretical guarantees and demonstrating superior empirical performance in complex, real-time applications.

Contribution

It introduces an extension of Neural Jump ODEs for input-output systems with convergence guarantees, enabling effective online filtering and classification.

Findings

The method outperforms classical parametric approaches in complex distribution scenarios.

Theoretical convergence guarantees for $L^2$-optimal filtering are established.

Empirical results show superior real-time performance in finance and health monitoring.

Abstract

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.