Nonparametric Filtering, Estimation and Classification using Neural Jump ODEs

• URL: http://arxiv.org/abs/2412.03271v1
• Date: Wed, 04 Dec 2024 12:31:15 GMT
• Title: Nonparametric Filtering, Estimation and Classification using Neural Jump ODEs
• Authors: Jakob Heiss, Florian Krach, Thorsten Schmidt, Félix B. Tambe-Ndonfack,
• Abstract summary: 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. This work extends the framework to input-output systems, enabling direct applications in online filtering and classification.
• Score: 3.437372707846067
• License:
• 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.

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