DeepUQ: Assessing the Aleatoric Uncertainties from two Deep Learning Methods

TL;DR

This paper compares two deep learning methods, Deep Ensembles and Deep Evidential Regression, for estimating aleatoric uncertainty across different data types and noise levels, highlighting calibration issues and the need for further refinement.

Contribution

It systematically evaluates and compares the performance and calibration of DE and DER in estimating aleatoric uncertainty for 0D and 2D data with varying noise levels.

Findings

Uncertainty scales with injected noise level.

Predicted uncertainty is often miscalibrated compared to true uncertainty.

Calibration issues are more pronounced in high-noise and high-dimensional scenarios.

Abstract

Assessing the quality of aleatoric uncertainty estimates from uncertainty quantification (UQ) deep learning methods is important in scientific contexts, where uncertainty is physically meaningful and important to characterize and interpret exactly. We systematically compare aleatoric uncertainty measured by two UQ techniques, Deep Ensembles (DE) and Deep Evidential Regression (DER). Our method focuses on both zero-dimensional (0D) and two-dimensional (2D) data, to explore how the UQ methods function for different data dimensionalities. We investigate uncertainty injected on the input and output variables and include a method to propagate uncertainty in the case of input uncertainty so that we can compare the predicted aleatoric uncertainty to the known values. We experiment with three levels of noise. The aleatoric uncertainty predicted across all models and experiments scales with the injected noise level. However, the predicted uncertainty is miscalibrated to $\rm{std}(\sigma_{\rm al})$ with the true uncertainty for half of the DE experiments and almost all of the DER experiments. The predicted uncertainty is the least accurate for both UQ methods for the 2D input uncertainty experiment and the high-noise level. While these results do not apply to more complex data, they highlight that further research on post-facto calibration for these methods would be beneficial, particularly for high-noise and high-dimensional settings.