Edward De Brouwer, Jaak Simm, Adam Arany, Yves Moreau
Modeling real-world multidimensional time series can be particularly challenging when these are sporadically observed (i.e., sampling is irregular both in time and across dimensions)-such as in the case of clinical patient data. To address these challenges, we propose (1) a continuous-time version of the Gated Recurrent Unit, building upon the recent Neural Ordinary Differential Equations (Chen et al., 2018), and (2) a Bayesian update network that processes the sporadic observations. We bring these two ideas together in our GRU-ODE-Bayes method. We then demonstrate that the proposed method encodes a continuity prior for the latent process and that it can exactly represent the Fokker-Planck dynamics of complex processes driven by a multidimensional stochastic differential equation. Additionally, empirical evaluation shows that our method outperforms the state of the art on both synthetic data and real-world data with applications in healthcare and climate forecast. What is more, the continuity prior is shown to be well suited for low number of samples settings.
| Task | Dataset | Metric | Value | Model |
|---|---|---|---|---|
| Time Series Forecasting | MIMIC-III | NegLL | 0.83 | GRU-ODE-Bayes |
| Time Series Forecasting | USHCN-Daily | MSE | 0.43 | GRU-ODE-Bayes |
| Time Series Analysis | MIMIC-III | NegLL | 0.83 | GRU-ODE-Bayes |
| Time Series Analysis | USHCN-Daily | MSE | 0.43 | GRU-ODE-Bayes |
| Multivariate Time Series Forecasting | MIMIC-III | NegLL | 0.83 | GRU-ODE-Bayes |
| Multivariate Time Series Forecasting | USHCN-Daily | MSE | 0.43 | GRU-ODE-Bayes |