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 common approaches that approximate the parameter posterior often fail to deliver reliable estimates of predictive uncertainty. In this paper, we propose a novel criterion for reliable predictive uncertainty: a model's predictive variance should be grounded in the empirical density of the input. That is, the model should produce higher uncertainty for inputs that are improbable in the training data and lower uncertainty for inputs that are more probable. To operationalize this criterion, we develop the density uncertainty layer, a stochastic neural network architecture that satisfies the density uncertain criterion by design. We study density uncertainty layers on the UCI and CIFAR-10/100 uncertainty benchmarks. Compared to existing approaches, density uncertainty layers provide more reliable uncertainty estimates and robust out-of-distribution detection performance.

翻译：评估深度神经网络的预测不确定性对于深度学习在安全相关应用中的部署至关重要。尽管贝叶斯深度学习为估计模型不确定性提供了理论框架，但常见的方法通过近似参数后验分布往往无法提供可靠的预测不确定性估计。本文提出了一种可靠的预测不确定性新准则：模型的预测方差应基于输入的经验密度。即模型应对训练数据中低概率输入产生更高的不确定性，而对高概率输入产生更低的不确定性。为实现这一准则，我们开发了密度不确定性层，这是一种随机神经网络架构，通过设计满足密度不确定性准则。我们在UCI和CIFAR-10/100不确定性基准上研究了密度不确定性层。与现有方法相比，密度不确定性层提供了更可靠的不确定性估计和鲁棒的分布外检测性能。