Nonparametric Filtering, Estimation and Classification using Neural Jump ODEs

2024-12-04

arXiv.org

AI Summary

To address the challenges of filtering, estimation, and classification for irregularly sampled and partially observed online time-series data, this paper proposes the Neural Jump ODE framework. It extends Jump ODEs—previously limited to autonomous systems—to general input-output dynamical systems, enabling nonparametric modeling that jointly captures discontinuous (jump) dynamics, learns conditional expectations nonparametrically, and supports online recursive updates. Theoretically, we prove that the framework achieves optimal L² filtering without assuming specific parametric forms or strong regularity conditions on latent distributions—overcoming key limitations of classical parametric models. Empirically, Neural Jump ODE significantly outperforms Kalman filters, particle filters, and RNN/LSTM classifiers on complex non-Gaussian and multimodal latent processes, while maintaining real-time inference capability. Its efficacy is validated in low-latency critical applications, including financial trading signal prediction and wearable health monitoring.

Technology Category

• Machine Learning: Time-Series/Data Streams
• Intelligent Robots: State Estimation
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs

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.

Problem

• Develops neural ODEs with jumps for irregular time series data
• Extends framework to enable real-time filtering and classification tasks
• Provides theoretical convergence guarantees for L²-optimal filtering solutions

Innovation

• Neural ODEs model conditional expectations between observations
• Extends framework to input-output systems for filtering
• Establishes theoretical convergence for L^2-optimal filtering