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Initial work on variational autoencoders assumed independent latent variableswith simple distributions. Subsequent work has explored incorporating morecomplex distributions and dependency structures: including normalizing flows inthe encoder network allows latent variables to entangle non-linearly, creatinga richer class of distributions for the approximate posterior, and stackinglayers of latent variables allows more complex priors to be specified for thegenerative model. This work explores incorporating arbitrary dependencystructures, as specified by Bayesian networks, into VAEs. This is achieved byextending both the prior and inference network with graphical residual flows -residual flows that encode conditional independence by masking the weightmatrices of the flow's residual blocks. We compare our model's performance onseveral synthetic datasets and show its potential in data-sparse settings.

SIReN-VAE: Leveraging Flows and Amortized Inference for Bayesian Networks