Neural Jump Ordinary Differential Equations: Consistent Continuous-Time Prediction and Filtering
METADATA ONLY
Loading...
Author / Producer
Date
2021
Publication Type
Conference Paper
ETH Bibliography
yes
Citations
Altmetric
METADATA ONLY
Data
Rights / License
Abstract
Combinations of neural ODEs with recurrent neural networks (RNN), like GRU-ODE-Bayes or ODE-RNN are well suited to model irregularly observed time series. While those models outperform existing discrete-time approaches, no theoretical guarantees for their predictive capabilities are available. Assuming that the irregularly-sampled time series data originates from a continuous stochastic process, the L2-optimal online prediction is the conditional expectation given the currently available information. We introduce the Neural Jump ODE (NJ-ODE) that provides a data-driven approach to learn, continuously in time, the conditional expectation of a stochastic process. Our approach models the conditional expectation between two observations with a neural ODE and jumps whenever a new observation is made. We define a novel training framework, which allows us to prove theoretical guarantees for the first time. In particular, we show that the output of our model converges to the L2-optimal prediction. This can be interpreted as solution to a special filtering problem. We provide experiments showing that the theoretical results also hold empirically. Moreover, we experimentally show that our model outperforms the baselines in more complex learning tasks and give comparisons on real-world datasets.
Permanent link
Publication status
published
External links
Editor
Book title
International Conference on Learning Representations (ICLR 2021)
Journal / series
Volume
Pages / Article No.
Publisher
OpenReview
Event
9th International Conference on Learning Representations (ICLR 2021)
Edition / version
Methods
Software
Geographic location
Date collected
Date created
Subject
Neural ODE; conditional expectation; irregular-observed data modelling
Organisational unit
03845 - Teichmann, Josef / Teichmann, Josef
02000 - Dep. Mathematik / Dep. of Mathematics