  Variational Autoencoders for multimodal data hold promise for many tasks in
data analysis, such as representation learning, conditional generation, and
imputation. Current architectures either share the encoder output, decoder
input, or both across modalities to learn a shared representation. Such
architectures impose hard constraints on the model. In this work, we show that
a better latent representation can be obtained by replacing these hard
constraints with a soft constraint. We propose a new mixture-of-experts prior,
softly guiding each modality's latent representation towards a shared aggregate
posterior. This approach results in a superior latent representation and allows
each encoding to preserve information better from its uncompressed original
features. In extensive experiments on multiple benchmark datasets and two
challenging real-world datasets, we show improved learned latent
representations and imputation of missing data modalities compared to existing
methods.
