A Bayesian treatment of deep learning allows for the computation of uncertainties associated with the predictions of deep neural networks. We show how the concept of Errors-in-Variables can be used in Bayesian deep regression to also account for the uncertainty associated with the input of the employed neural network. The presented approach thereby exploits a relevant, but generally overlooked, source of uncertainty and yields a decomposition of the predictive uncertainty into an aleatoric and epistemic part that is more complete and, in many cases, more consistent from a statistical perspective. We discuss the approach along various simulated and real examples and observe that using an Errors-in-Variables model leads to an increase in the uncertainty while preserving the prediction performance of models without Errors-in-Variables. For examples with known regression function we observe that this ground truth is substantially better covered by the Errors-in-Variables model, indicating that the presented approach leads to a more reliable uncertainty estimation.

翻译：贝叶斯深度学习方法能够计算深度神经网络预测相关的的不确定性。我们展示了变量含误差（Errors-in-Variables）概念如何应用于贝叶斯深度回归，以同时考虑所采用神经网络输入相关的不确定性。所提出的方法由此利用了相关但通常被忽视的不确定性来源，并将预测不确定性分解为偶然不确定性和认知不确定性两部分，这种分解更加完整，而且在许多情况下从统计角度更加一致。我们通过多种模拟和实际示例讨论了该方法，并观察到使用变量含误差模型在保持无变量含误差模型预测性能的同时，会导致不确定性增加。对于已知回归函数的示例，我们发现变量含误差模型能更好地覆盖真实回归函数，这表明所提出的方法能够产生更可靠的不确定性估计。