Amortising Inference and Meta-Learning Priors in Neural Networks

One of the core facets of Bayesianism is in the updating of prior beliefs in light of new evidence$\textemdash$so how can we maintain a Bayesian approach if we have no prior beliefs in the first place? This is one of the central challenges in the field of Bayesian deep learning, where there is no clear way to translate beliefs about a prediction task into prior distributions over model parameters. Bridging the fields of Bayesian deep learning and neural processes, we propose to $\textit{meta-learn}$ our parametric prior from data by introducing a way to perform per-dataset amortised variational inference. The model we develop can be viewed as a neural process whose latent variable is the set of weights of a BNN and whose decoder is the neural network parameterised by a sample of the latent variable itself. This unique model allows us to study the behaviour of Bayesian neural networks under well-specified priors, use Bayesian neural networks as flexible generative models, and perform desirable but previously elusive feats in neural processes such as within-task minibatching or meta-learning under extreme data-starvation.