The Variational Homoencoder: Learning to Infer High-Capacity Generative Models from Few Examples

Hierarchical Bayesian methods have the potential to unify many related tasks (e.g. k-shot classification, conditional, and unconditional generation) by framing each as inference within a single generative model. We show that existing approaches for learning such models can fail on expressive generative networks such as PixelCNNs, by describing the global distribution with little reliance on latent variables. To address this, we develop a modification of the Variational Autoencoder in which encoded observations are decoded to new elements from the same class; the result, which we call a Variational Homoencoder (VHE), may be understood as training a hierarchical latent variable model which better utilises latent variables in these cases. Using this framework enables us to train a hierarchical PixelCNN for the Omniglot dataset, outperforming all existing models on test set likelihood. With a single model we achieve both strong one-shot generation and near human-level classification, competitive with state-of-the-art discriminative classifiers. The VHE objective extends naturally to richer dataset structures such as factorial or hierarchical categories, as we illustrate by training models to separate character content from simple variations in drawing style, and to generalise the style of an alphabet to new characters.