Aleatoric Uncertainty for Errors-in-Variables Models in Deep Regression

Abstract

AbstractA 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.