  Learning continuous-time stochastic dynamics is a fundamental and essential
problem in modeling sporadic time series, whose observations are irregular and
sparse in both time and dimension. For a given system whose latent states and
observed data are high-dimensional, it is generally impossible to derive a
precise continuous-time stochastic process to describe the system behaviors. To
solve the above problem, we apply Variational Bayesian method and propose a
flexible continuous-time stochastic recurrent neural network named Variational
Stochastic Differential Networks (VSDN), which embeds the complicated dynamics
of the sporadic time series by neural Stochastic Differential Equations (SDE).
VSDNs capture the stochastic dependency among latent states and observations by
deep neural networks. We also incorporate two differential Evidence Lower
Bounds to efficiently train the models. Through comprehensive experiments, we
show that VSDNs outperform state-of-the-art continuous-time deep learning
models and achieve remarkable performance on prediction and interpolation tasks
for sporadic time series.
