Measuring Orthogonality as the Blind-Spot of Uncertainty Disentanglement
This work addresses a foundational issue in uncertainty quantification for machine learning practitioners, though it is incremental in refining evaluation metrics rather than introducing a new paradigm.
The paper tackles the problem of insufficient evaluation methods for disentangling aleatoric and epistemic uncertainty by proposing orthogonality as a necessary condition and introducing Uncertainty Disentanglement Error (UDE) as a metric. It demonstrates that a Deep Ensemble trained from scratch on ImageNet-1k achieves consistent and orthogonal epistemic uncertainty estimates, but aleatoric uncertainty still fails orthogonality.
Aleatoric (data) and epistemic (knowledge) uncertainty are textbook components of Uncertainty Quantification. Jointly estimating these components has been shown to be problematic and non-trivial. As a result, there are multiple ways to disentangle these uncertainties, but current methods to evaluate them are insufficient. We propose that aleatoric and epistemic uncertainty estimates should be orthogonally disentangled - meaning that each uncertainty is not affected by the other - a necessary condition that is often not met. We prove that orthogonality and consistency and necessary and sufficient criteria for disentanglement, and construct Uncertainty Disentanglement Error as a metric to measure these criteria, with further empirical evaluation showing that finetuned models give different orthogonality results than models trained from scratch and that UDE can be optimized for through dropout rate. We demonstrate a Deep Ensemble trained from scratch on ImageNet-1k with Information Theoretic disentangling achieves consistent and orthogonal estimates of epistemic uncertainty, but estimates of aleatoric uncertainty still fail on orthogonality.