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# The LORACs Prior for VAEs: Letting the Trees Speak for the Data

*Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics*, PMLR 89:3292-3301, 2019.

#### Abstract

In variational autoencoders, the prior on the latent codes $z$ is often treated as an afterthought, but the prior shapes the kind of latent representation that the model learns. If the goal is to learn a representation that is interpretable and useful, then the prior should reflect the ways in which the high-level factors that describe the data vary. The “default” prior is a standard normal, but if the natural factors of variation in the dataset exhibit discrete structure or are not independent, then the isotropic-normal prior will actually encourage learning representations that \emph{mask} this structure. To alleviate this problem, we propose using a flexible Bayesian nonparametric hierarchical clustering prior based on the time-marginalized coalescent (TMC). To scale learning to large datasets, we develop a new inducing-point approximation and inference algorithm. We then apply the method without supervision to several datasets and examine the interpretability and practical performance of the inferred hierarchies and learned latent space.