  We propose a framework called HyperVAE for encoding distributions of
distributions. When a target distribution is modeled by a VAE, its neural
network parameters \theta is drawn from a distribution p(\theta) which is
modeled by a hyper-level VAE. We propose a variational inference using Gaussian
mixture models to implicitly encode the parameters \theta into a low
dimensional Gaussian distribution. Given a target distribution, we predict the
posterior distribution of the latent code, then use a matrix-network decoder to
generate a posterior distribution q(\theta). HyperVAE can encode the parameters
\theta in full in contrast to common hyper-networks practices, which generate
only the scale and bias vectors as target-network parameters. Thus HyperVAE
preserves much more information about the model for each task in the latent
space. We discuss HyperVAE using the minimum description length (MDL) principle
and show that it helps HyperVAE to generalize. We evaluate HyperVAE in density
estimation tasks, outlier detection and discovery of novel design classes,
demonstrating its efficacy.
