  Learning accurate predictive models of real-world dynamic phenomena (e.g.,
climate, biological) remains a challenging task. One key issue is that the data
generated by both natural and artificial processes often comprise time series
that are irregularly sampled and/or contain missing observations. In this work,
we propose the Neural Continuous-Discrete State Space Model (NCDSSM) for
continuous-time modeling of time series through discrete-time observations.
NCDSSM employs auxiliary variables to disentangle recognition from dynamics,
thus requiring amortized inference only for the auxiliary variables. Leveraging
techniques from continuous-discrete filtering theory, we demonstrate how to
perform accurate Bayesian inference for the dynamic states. We propose three
flexible parameterizations of the latent dynamics and an efficient training
objective that marginalizes the dynamic states during inference. Empirical
results on multiple benchmark datasets across various domains show improved
imputation and forecasting performance of NCDSSM over existing models.
