[Paper Review] Measuring Orthogonality as the Blind-Spot of Uncertainty Disentanglement

Ivo Pascal de Jong, Andreea Ioana Sburlea+2 more|ArXiv.org|Aug 22, 2024

Clinical Laboratory Practices and Quality ControlMedicine3 citations

TL;DR

This paper proposes a comprehensive experimental framework to evaluate the disentanglement of aleatoric and epistemic uncertainty in uncertainty quantification (UQ) methods. Using controlled data manipulations—dataset size, OoD samples, and label noise—it demonstrates that both the Information Theoretic and Gaussian Logits approaches fail to fully separate the two uncertainty types, with the former showing better but still imperfect disentanglement.

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.

Motivation & Objective

• To address the lack of empirical validation for whether aleatoric and epistemic uncertainties are truly disentangled in current UQ methods.
• To identify whether existing uncertainty quantification approaches reliably separate the sources of uncertainty as required for downstream decision-making.
• To establish a standardized, theoretically grounded experimental benchmark for assessing disentanglement quality in future UQ methods.
• To investigate whether theoretical limitations in uncertainty disentanglement manifest in practical model behavior on real and synthetic data.

Proposed method

• Design a set of controlled experiments manipulating dataset size, out-of-distribution (OoD) inputs, and label noise to isolate changes in aleatoric or epistemic uncertainty.
• Apply two leading UQ approaches—Information Theoretic and Gaussian Logits—to Bayesian Neural Networks and measure predicted uncertainty responses.
• Use MC-Dropout, MC-DropConnect, and Deep Ensembles as inference methods to evaluate uncertainty estimation across different model variants.
• Evaluate disentanglement by measuring whether predicted aleatoric uncertainty changes in response to epistemic uncertainty manipulations (and vice versa), under controlled ground-truth conditions.
• Define disentanglement as the absence of correlation between predicted uncertainties when the true underlying uncertainties are uncorrelated.
• Apply the framework to both synthetic and real-world datasets to test generalizability and robustness of the evaluation protocol.

(a) Aleatoric

Experimental results

Research questions

• RQ1 To what extent do current UQ methods disentangle aleatoric and epistemic uncertainty in practice?
• RQ2 How do the Information Theoretic and Gaussian Logits approaches perform under controlled manipulations of dataset size and label noise?
• RQ3 Does predicted aleatoric uncertainty increase on OoD samples, contrary to theoretical expectations?
• RQ4 Are predicted epistemic uncertainties affected by changes in aleatoric uncertainty when the true epistemic uncertainty is unchanged?
• RQ5 Can the proposed experimental framework serve as a reliable benchmark for future disentangled uncertainty methods?

Key findings

• The Information Theoretic approach achieves better disentanglement than the Gaussian Logits approach, but neither method fully separates aleatoric and epistemic uncertainty.
• Both methods exhibit significant cross-contamination: predicted epistemic uncertainty increases when only aleatoric uncertainty is manipulated, and vice versa.
• The Gaussian Logits approach fails to properly reflect changes in epistemic uncertainty with MC-Dropout and MC-DropConnect, though it performs better with Deep Ensembles.
• Aleatoric uncertainty increases on OoD samples for both methods, contradicting theoretical expectations that it should remain stable.
• Theoretical limitations from Wimmer et al. (2023) manifest in practice: under maximum aleatoric uncertainty, epistemic uncertainty prediction breaks down.
• The proposed experimental framework provides a robust, standardized benchmark for evaluating disentanglement quality in any UQ method aiming to separate uncertainty sources.

(b) Epistemic