Conventional Bayesian Neural Networks (BNNs) cannot leverage unlabelled data to improve their predictions. To overcome this limitation, we introduce Self-Supervised Bayesian Neural Networks, which use unlabelled data to learn improved prior predictive distributions by maximising an evidence lower bound during an unsupervised pre-training step. With a novel methodology developed to better understand prior predictive distributions, we then show that self-supervised prior predictives capture image semantics better than conventional BNN priors. In our empirical evaluations, we see that self-supervised BNNs offer the label efficiency of self-supervised methods and the uncertainty estimates of Bayesian methods, particularly outperforming conventional BNNs in low-to-medium data regimes.
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