@inproceedings{
zhang2024trajectory,
title={Trajectory Flow Matching with Applications to Clinical Time Series Modelling},
author={Xi Zhang and Yuan Pu and Yuki Kawamura and Andrew Loza and Yoshua Bengio and Dennis Shung and Alexander Tong},
booktitle={The Thirty-eighth Annual Conference on Neural Information Processing Systems},
year={2024},
url={https://openreview.net/forum?id=fNakQltI1N}
}
Modeling stochastic and irregularly sampled time series is a challenging problem found in a wide range of applications, especially in medicine. Neural stochastic differential equations (Neural SDEs) are an attractive modeling technique for this problem, which parameterize the drift and diffusion terms of an SDE with neural networks. However, current algorithms for training Neural SDEs require backpropagation through the SDE dynamics, greatly limiting their scalability and stability. 
To address this, we propose **Trajectory Flow Matching** (TFM), which trains a Neural SDE in a *simulation-free* manner, bypassing backpropagation through the dynamics. TFM leverages the flow matching technique from generative modeling to model time series. In this work we first establish necessary conditions for TFM to learn time series data. Next, we present a reparameterization trick which improves training stability. Finally, we adapt TFM to the clinical time series setting, demonstrating improved performance on three clinical time series datasets both in terms of absolute performance and uncertainty prediction.
Trajectory Flow Matching with Applications to Clinical Time Series Modelling
Xi Zhang Yuan Pu Yuki Kawamura Andrew Loza Yoshua Bengio Dennis Shung Alexander Tong