  We present a novel model architecture which leverages deep learning tools to
perform exact Bayesian inference on sets of high dimensional, complex
observations. Our model is provably exchangeable, meaning that the joint
distribution over observations is invariant under permutation: this property
lies at the heart of Bayesian inference. The model does not require variational
approximations to train, and new samples can be generated conditional on
previous samples, with cost linear in the size of the conditioning set. The
advantages of our architecture are demonstrated on learning tasks that require
generalisation from short observed sequences while modelling sequence
variability, such as conditional image generation, few-shot learning, and
anomaly detection.
