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Real-world databases are complex and usually require dealing withheterogeneous and mixed data types making the exploitation of sharedinformation between views a critical issue. For this purpose, recent studiesbased on deep generative models merge all views into a nonlinear complex latentspace, which can share information among views. However, this solution limitsthe model's interpretability, flexibility, and modularity. We propose a novelmethod to overcome these limitations by combining multiple VariationalAutoEncoders (VAE) with a Factor Analysis latent space (FA-VAE). We use VAEs tolearn a private representation of each heterogeneous view in a continuouslatent space. Then, we share the information between views by a low-dimensionallatent space using a linear projection matrix. This way, we create a flexibleand modular hierarchical dependency between private and shared information inwhich new views can be incorporated afterwards. Beyond that, we can conditionpre-trained models, cross-generate data from different domains, and performtransfer learning between generative models.

Multimodal hierarchical Variational AutoEncoders with Factor Analysis latent space