  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.
