No Single Metric Tells the Whole Story: A Multi-Dimensional Evaluation Framework for Uncertainty Attributions

Emily Schiller; Teodor Chiaburu; Marco Zullich; Luca Longo

cs.LGMar 25, 2026

No Single Metric Tells the Whole Story: A Multi-Dimensional Evaluation Framework for Uncertainty Attributions

Authors: Emily Schiller, Teodor Chiaburu, Marco Zullich, Luca Longo

Organizations: XITASO GmbH IT & Software Solutions, Augsburg, Germany · The Artificial Intelligence and Cognitive Load Research Lab, University College Cork · Berliner Hochschule für Technik, Berlin, Germany · Faculty of Technology, Policy and Management, Delft University of Technology, Delft, the Netherlands ·

Abstract

Research on explainable AI (XAI) has frequently focused on explaining model predictions. More recently, methods have been proposed to explain prediction uncertainty by attributing it to input features (uncertainty attributions). However, the evaluation of these methods remains inconsistent as studies rely on heterogeneous proxy tasks and metrics, hindering comparability. We address this by aligning uncertainty attributions with the well-established Co-12 framework for XAI evaluation. We propose concrete implementations for the correctness, consistency, continuity, and compactness properties. Additionally, we introduce conveyance, a property tailored to uncertainty attributions that evaluates whether controlled increases in epistemic uncertainty reliably propagate to feature-level attributions. We demonstrate our evaluation framework with eight metrics across combinations of uncertainty quantification and feature attribution methods on tabular and image data. Our experiments show that gradient-based methods consistently outperform perturbation-based approaches in consistency and conveyance, while Monte-Carlo dropconnect outperforms Monte-Carlo dropout in most metrics. Although most metrics rank the methods consistently across samples, inter-method agreement remains low. This suggests no single metric sufficiently evaluates uncertainty attribution quality. The proposed evaluation framework contributes to the body of knowledge by establishing a foundation for systematic comparison and development of uncertainty attribution methods.

Figures & tables

Figure 1: Uncertainty attribution method by Bley et al. Bley et al. (2025) . Predictive variance is estimated via ensemble-based UQ. Each of

K

predictions is explained, and uncertainty attributions are derived as diagonal elements of the covariance matrix of these explanations. Illustration adapted from Bley et al. Bley et al. (2025) .

Figure 2: Uncertainty and feature attributions using mcd and (a) LRP and (b) Integrated Gradients for test samples from the MNIST dataset. Dark blue pixels indicate low importance and dark red pixels indicate high importance to predictive uncertainty (uncertainty attribution) or the prediction (feature attribution).

Figure 3: Overview of the proposed evaluation framework. We combine a feature attribution method with an uq method (blue panel) to generate uncertainty attributions. We evaluate these uncertainty attributions by adapting and extending properties (orange panel) and metrics (red panel) from feature attribution to the uncertainty setting; novel categories and metrics appear in italics. Metric results are aggregated into an overall score for each uncertainty attribution method.

Co-12 Property	Metrics used in Literature on uncertainty attributions	Metrics selected for our Evaluation Framework
correctness 4.1	feature flipping Bley et al. (2025) , blurring test Perez et al. (2022) ; Wang et al. (2023a) ; Iversen et al. (2025)	feature flipping
consistency 4.2	-	repeatability
continuity 4.3	local Lipschitz continuity Iversen et al. (2025)	relative input stability (RIS)
compactness 4.4	-	complexity
conveyance 4.5	distribution shift detection Brown and Talbert (2022) ; Wang et al. (2023b) ; Watson et al. (2023) ; Pohland and Tomlin (2024) , controlled aleatoric uncertainty Iversen et al. (2025)	relative rank improvement (RRI) , uncertainty conveyance similarity (UCS)

Table 1: Evaluation properties and metrics for uncertainty attributions. We adapt four Co-12 properties Nauta et al. (2023) for evaluating uncertainty attribution methods. For each property, we report metrics from the prior uncertainty-attribution literature and from our framework. Conveyance (highlighted in blue) is our proposed property specific to uncertainty attributions. Bold metrics are novel adaptations from feature attribution research to uncertainty attributions. Bold italics indicate our novel uncertainty similarity conveyance metric.

Figure 4: Experimental setup. Using 5-fold cross-validation, we train a CNN for MNIST and an MLP for Wine Quality. We compute uncertainty attributions for 100 test samples per fold using combinations of UQ and feature attribution methods (blue panel), rate them using our evaluation framework, and assess metrics via sanity checks.

Figure 5: Metric scores for the Wine Quality dataset with 95% confidence interval. Arrows indicate whether lower (

\downarrow

) or higher (

\uparrow

) values are better. Gradient-based methods (IxG, IG) and LRP outperform perturbation-based methods on most metrics for mcd and mcdc . mcdc shows better repeatability, feature flipping, and higher UCS than MCD.

Figure 6: Metric scores for the MNIST dataset with 95% confidence interval. Arrows indicate whether lower (

\downarrow

) or higher (

\uparrow

) values are better. mcdc outperforms mcd in UCS but achieves higher feature flipping scores. All methods exhibit near-perfect repeatability and RIS.

	Metric	UQ Method	LRP	IG	IxG	SHAP	LIME
Wine Quality	complexity $\downarrow$	mcd	1.722	1.704	1.695	2.378	2.356
		mcdc	1.689	1.624	1.567	2.375	2.357
	repeatability (cosine) $\uparrow$	mcd	0.976	0.979	0.979	0.964	0.947
		mcdc	0.976	0.988	0.987	0.961	0.948
	repeatability (Spearman) $\uparrow$	mcd	0.961	0.967	0.966	0.005	0.128
		mcdc	0.965	0.975	0.974	0.014	0.115

Table 2: Metric scores averaged over all 5 folds for Wine Quality and MNIST datasets. Arrows indicate whether lower (

\downarrow

) or higher (

\uparrow

) values are better. Best metric values across all uncertainty attribution methods are highlighted in blue.

Metric	Dataset	Inter-method reliability $\uparrow$	Ranking consistency $\uparrow$	Average coefficient of variation $\downarrow$
complexity	Wine Quality	0.279	0.766	0.018
complexity	MNIST	0.656	0.553	0.135
repeatability (cosine)	Wine Quality	0.076	0.646	0.019
repeatability (cosine)	MNIST	0.213	0.328	0.014
repeatability (Spearman)	Wine Quality	0.168	0.762	1.227
repeatability (Spearman)	MNIST	0.647	0.527	0.000

Table 3: Sanity checks of all evaluation metrics for Wine Quality and MNIST. Arrows indicate whether lower (

\downarrow

) or higher (

\uparrow

) values are better for each sanity check. Best scores for Wine Quality and MNIST are highlighted in blue and red, respectively.

	Metrics	UQ Method	LRP	IG	IxG	SHAP	LIME
Wine Quality	UCS (Spearman) vs RRI	mcd	0.025	0.045	0.087	-0.015	-0.002
	UCS (Spearman) vs RRI	mcdc	0.032	-0.003	0.034	0.049	-0.001
	UCS (cosine) vs RRI	mcd	-0.100	0.038	-0.106	0.014	-0.002
	UCS (cosine) vs RRI	mcdc	-0.031	0.031	0.011	0.027	-0.004
	Metrics	UQ Method	LRP	IG	IxG	GradientSHAP
MNIST	UCS (Spearman) vs RRI	mcd	0.025	-0.011	-0.024	0.001

Table 4: Spearman’s

\rho

(internal consistency reliability) between pairs of conveyance metrics for each uncertainty attribution method for Wine Quality and MNIST.

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This paper surveys uncertainty-aware explainable artificial intelligence (UAXAI), examining how uncertainty is incorporated into explanatory pipelines and how such methods are evaluated. Across the literature, three recurring approaches to uncertainty quantification emerge (Bayesian, Monte Carlo, and Conformal methods), alongside distinct strategies for integrating uncertainty into explanations: assessing trustworthiness, constraining models or explanations, and explicitly communicating uncertainty. Evaluation practices remain fragmented and largely model centered, with limited attention to users and inconsistent reporting of reliability properties (e.g., calibration, coverage, explanation stability). Recent work leans towards calibration, distribution free techniques and recognizes explainer variability as a central concern. We argue that progress in UAXAI requires unified evaluation principles that link uncertainty propagation, robustness, and human decision-making, and highlight counterfactual and calibration approaches as promising avenues for aligning interpretability with reliability.

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