Learning Hierarchical Priors in VAEs

Abstract

We propose to learn a hierarchical prior in the context of variational autoencoders to avoid the over-regularisation resulting from a standard normal prior distribution. To incentivise an informative latent representation of the data by learning a rich hierarchical prior, we formulate the objective function as the Lagrangian of a constrainedoptimisation problem and propose an optimisation algorithm inspired by Taming VAEs. We introduce a graph-based interpolation method, which shows that the topology of the learned latent representation corresponds to the topology of the data manifold-and present several examples, where desired properties of latent representation such as smoothness and simple explanatory factors are learned by the prior. Furthermore, we validate our approach on standard datasets, obtaining state-ofthe-art test log-likelihoods.

Multi-Task Neural Processes

“…Hierarchical modeling in the Bayesian framework has been successful to design the form of the prior (Daumé III, 2009;Zhao et al, 2017;Klushyn et al, 2019;Wang & Van Hoof, 2020) and posterior distributions (Ranganath et al, 2016;Krueger et al, 2017;Zhen et al, 2020) based on many observations. It allows the latent variable to follow a complicated distribution and forms a highly flexible approximation (Krueger et al, 2017).…”