Uncertainty estimation under model misspecification in neural network regression

TL;DR

This paper investigates how model misspecification in neural network regression affects uncertainty estimation, revealing that flexible models may still produce unreliable uncertainty measures under misspecification.

Contribution

It provides a comprehensive analysis of the impact of model assumptions on uncertainty estimation in neural network regression under misspecification.

Findings

Aleatoric uncertainty is not well captured under model misspecification.

Bayesian approaches can lead to unreliable epistemic uncertainty estimates.

Model choice significantly influences uncertainty quantification in regression.

Abstract

Although neural networks are powerful function approximators, the underlying modelling assumptions ultimately define the likelihood and thus the hypothesis class they are parameterizing. In classification, these assumptions are minimal as the commonly employed softmax is capable of representing any categorical distribution. In regression, however, restrictive assumptions on the type of continuous distribution to be realized are typically placed, like the dominant choice of training via mean-squared error and its underlying Gaussianity assumption. Recently, modelling advances allow to be agnostic to the type of continuous distribution to be modelled, granting regression the flexibility of classification models. While past studies stress the benefit of such flexible regression models in terms of performance, here we study the effect of the model choice on uncertainty estimation. We highlight that under model misspecification, aleatoric uncertainty is not properly captured, and that a Bayesian treatment of a misspecified model leads to unreliable epistemic uncertainty estimates. Overall, our study provides an overview on how modelling choices in regression may influence uncertainty estimation and thus any downstream decision making process.