  Integrating deep learning with latent state space models has the potential to
yield temporal models that are powerful, yet tractable and interpretable.
Unfortunately, current models are not designed to handle missing data or
multiple data modalities, which are both prevalent in real-world data. In this
work, we introduce a factorized inference method for Multimodal Deep Markov
Models (MDMMs), allowing us to filter and smooth in the presence of missing
data, while also performing uncertainty-aware multimodal fusion. We derive this
method by factorizing the posterior p(z|x) for non-linear state space models,
and develop a variational backward-forward algorithm for inference. Because our
method handles incompleteness over both time and modalities, it is capable of
interpolation, extrapolation, conditional generation, label prediction, and
weakly supervised learning of multimodal time series. We demonstrate these
capabilities on both synthetic and real-world multimodal data under high levels
of data deletion. Our method performs well even with more than 50% missing
data, and outperforms existing deep approaches to inference in latent time
series.
