Measuring Orthogonality as the Blind-Spot of Uncertainty Disentanglement

TL;DR

This paper introduces a new metric called Uncertainty Disentanglement Error to evaluate the orthogonality of aleatoric and epistemic uncertainties, highlighting the importance of orthogonality for proper uncertainty disentanglement in models.

Contribution

It formalizes orthogonality as a key criterion for uncertainty disentanglement, proves its necessity and sufficiency, and develops a metric to measure it, with empirical validation on deep ensemble models.

Findings

Orthogonality and consistency are necessary and sufficient for disentanglement.

Deep Ensembles trained from scratch can achieve orthogonal epistemic uncertainty estimates.

Current models still struggle with orthogonal aleatoric uncertainty estimates.

Abstract

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.