GRU-ODE-Bayes: Continuous modeling of sporadically-observed time series

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.

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Datasets


Task Dataset Model Metric Name Metric Value Global Rank Result Benchmark
Multivariate Time Series Forecasting MIMIC-III GRU-ODE-Bayes MSE 0.480 ± 0.010 # 2
NegLL 0.83 # 1
Multivariate Time Series Forecasting USHCN-Daily GRU-ODE-Bayes MSE 0.43 # 2

Methods


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