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

Factorized Inference in Deep Markov Models for Incomplete Multimodal Time Series