Look beyond labels: Incorporating functional summary information in Bayesian neural networks

Bayesian deep learning offers a principled approach to train neural networks that accounts for both aleatoric and epistemic uncertainty. In variational inference, priors are often specified over the weight parameters, but they do not capture the true prior knowledge in large and complex neural network architectures. We present a simple approach to incorporate summary information about the predicted probability (such as sigmoid or softmax score) outputs in Bayesian neural networks (BNNs). The available summary information is incorporated as augmented data and modeled with a Dirichlet process, and we derive the corresponding \emph{Summary Evidence Lower BOund}. We show how the method can inform the model about task difficulty or class imbalance. Extensive empirical experiments show that, with negligible computational overhead, the proposed method yields a BNN with a better calibration of uncertainty.