Density Uncertainty Layers for Reliable Uncertainty Estimation

Assessing the predictive uncertainty of deep neural networks is crucial for safety-related applications of deep learning. Although Bayesian deep learning offers a principled framework for estimating model uncertainty, the approaches that are commonly used to approximate the posterior often fail to deliver reliable estimates of predictive uncertainty. In this paper we propose a novel criterion for predictive uncertainty, that a model's predictive variance should be grounded in the empirical density of the input. It should produce higher uncertainty for inputs that are improbable in the training data and lower uncertainty for those inputs that are more probable. To operationalize this criterion, we develop the density uncertainty layer, an architectural element for a stochastic neural network that guarantees that the density uncertain criterion is satisfied. We study neural networks with density uncertainty layers on the CIFAR-10 and CIFAR-100 uncertainty benchmarks. Compared to existing approaches, we find that density uncertainty layers provide reliable uncertainty estimates and robust out-of-distribution detection performance.