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.

翻译：评估深度神经网络的预测不确定性对于深度学习的安全相关应用至关重要。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，但常用的后验近似方法往往无法提供可靠的预测不确定性估计。本文提出一种新的预测不确定性准则：模型的预测方差应建立在输入数据的经验密度基础上——对训练数据中出现的低概率输入应产生更高不确定性，而对高概率输入则应产生较低不确定性。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的架构组件，可确保满足密度不确定性准则。我们在CIFAR-10和CIFAR-100不确定性基准上研究了带有密度不确定性层的神经网络。与现有方法相比，我们发现密度不确定性层能提供可靠的不确定性估计和稳健的分布外检测性能。