Credal Concept Bottleneck Models for Epistemic-Aleatoric Uncertainty Decomposition

Abstract: Concept Bottleneck Models (CBMs) predict through human-interpretable concepts, but they typically output point concept probabilities that conflate epistemic uncertainty (reducible model underspecification) with aleatoric uncertainty (irreducible input ambiguity). This makes concept-level uncertainty hard to interpret and, more importantly, hard to act upon. We introduce CREDENCE (Credal Ensemble Concept Estimation), a CBM framework that decomposes concept uncertainty by construction. CREDENCE represents each concept as a credal prediction (a probability interval), derives epistemic uncertainty from disagreement across diverse concept heads, and estimates aleatoric uncertainty via a dedicated ambiguity output trained to match annotator disagreement when available. The resulting signals support prescriptive decisions: automate low-uncertainty cases, prioritize data collection for high-epistemic cases, route high-aleatoric cases to human review, and abstain when both are high. Across several tasks, we show that epistemic uncertainty is positively associated with prediction errors, whereas aleatoric uncertainty closely tracks annotator disagreement, providing guidance beyond error correlation. Our implementation is available at the following link: https://github.com/Tankiit/Credal_Sets/tree/ensemble-credal-cbm

• The paper introduces CREDENCE, a framework that decomposes uncertainty in CBMs by using credal set representations, clearly distinguishing between epistemic and aleatoric uncertainty.
• It employs an ensemble of diverse concept heads alongside a dedicated aleatoric head to track prediction errors and annotator disagreement, supporting targeted intervention strategies.
• Empirical evaluations across multiple datasets demonstrate improved task accuracy and actionable uncertainty signals that enhance human-AI decision-making in high-stakes NLP tasks.

Credal Concept Bottleneck Models for Epistemic-Aleatoric Uncertainty Decomposition

Motivation and Problem Statement

Concept Bottleneck Models (CBMs) have established a principled approach for achieving interpretable intermediate representations in NLP systems by routing predictions through human-interpretable concepts. However, a fundamental limitation of standard CBMs lies in their representation of concept probabilities as point estimates. This practice conflates epistemic uncertainty—stemming from model underspecification and reducible by acquiring more evidence—with aleatoric uncertainty, which reflects inherent ambiguity or noise in the input and is irreducible. The inability to distinguish these uncertainty types at the concept layer impedes actionable interventions: all uncertain cases are treated uniformly regardless of whether uncertainty arises from fixable model ignorance or irreducible data ambiguity.

High-stakes applications, especially those involving subjective linguistic phenomena (sentiment, toxicity, emotion), require fine-grained uncertainty signals to answer not just “how uncertain,” but “why uncertain.” The dichotomy has practical consequences: high epistemic uncertainty warrants targeted data collection or model improvement, while high aleatoric uncertainty indicates the need for human review, ambiguity-preserving communication, or abstention.

CREDENCE Architecture and Methodology

The CREDENCE framework introduces structural separation of uncertainty within CBMs via credal sets, representing concept predictions as probability intervals rather than single values. Epistemic uncertainty is operationalized as ensemble disagreement across diverse concept heads, while aleatoric uncertainty is predicted by a dedicated output head trained to match annotator disagreement.

Figure 1: CREDENCE architecture. Epistemic uncertainty emerges from ensemble disagreement (top branch); aleatoric uncertainty is predicted by a dedicated head supervised by annotator variance (bottom branch).

The architecture proceeds as follows:

• Input Encoding: A frozen pre-trained model produces representations which are fed into ensemble concept heads and an independent aleatoric head.
• Ensemble of Concept Heads: Multiple lightweight heads (implemented via LoRA adapters with varying ranks and dropout rates) predict concept probabilities, providing functional diversity.
• Credal Aggregation: For each concept, the minimum and maximum value among ensemble predictions defines the credal interval, reflecting the uncertainty.
• Epistemic and Aleatoric Uncertainty Signals: Variance across ensemble heads quantifies epistemic uncertainty; a dedicated head—trained with annotator disagreement labels when available—quantifies aleatoric uncertainty.
• Credal Classification: Interval arithmetic yields exact bounds for label logits, supporting principled decision rules (e.g., $\Gamma$-Maximin, Maximality) under imprecise probability theory.
• Training Procedure: All heads and classifier are trained jointly, with the encoder frozen, using a multi-objective loss comprising task, concept, and aleatoric terms.

Empirical Evaluation and Numerical Results

CREDENCE was evaluated across diverse datasets: CEBaB (concept-level sentiment annotations and explicit “unknown” labels), SST-2 (sentiment; LLM-generated annotations), GoEmotions (emotion), and HateXplain (toxicity). The framework demonstrated robust separation between epistemic and aleatoric uncertainty:

• Epistemic Uncertainty Tracks Prediction Errors: On CEBA, CREDENCE achieves task accuracy of 73.4% and Spearman correlation $\rho_{\text{epi}} = 0.302$ between epistemic uncertainty and prediction errors, outperforming CBM baselines and general uncertainty quantification methods.
• Aleatoric Uncertainty Aligns with Annotator Disagreement: On CEBaB, $\rho_{\text{ale}} = 0.785$ for CREDENCE, a $2.1\times$ improvement over best baseline. Correlation strengthens with concept ambiguity, demonstrating that the aleatoric output correctly captures irreducible annotator disagreement.
• Intervention Analysis: Targeting high-aleatoric concepts for correction yields mean accuracy gains of $+18.9\%$, substantially outpacing epistemic-targeted interventions ($+4.3\%$), affirming that ambiguous concepts drive prediction errors more than confusing ones.
• Quadrant-Based Routing: Samples stratified by epistemic and aleatoric uncertainty support prescriptive decision-making: low-low quadrants suitable for automation, high-epistemic/low-aleatoric for active learning, low-epistemic/high-aleatoric for human review, high-high for abstention.

Ablation and Robustness Studies

Extensive ablations underscored the architectural validity:

• Ensemble Size and Diversity: Increasing $H$ (number of heads) enhances epistemic correlation, while aleatoric correlation is unaffected—highlighting structural independence. Combining dropout and LoRA diversity is essential; without genuine diversity these signals collapse.
• Aleatoric Supervision: Removing the dedicated aleatoric head or training it without explicit annotator labels severely impairs correlation with annotator disagreement. Heteroscedastic regression loss partially recovers utility when labels are unavailable, but fails to match supervised performance.
• Loss Weight Sensitivity: Tuning loss weights for concept and aleatoric objectives provides expected tradeoffs: higher aleatoric weight improves $\rho_{\text{ale}}$; higher concept weight improves task accuracy.

Practical, Theoretical, and Prospective Implications

The formal decomposition of uncertainty at the concept layer enables:

• Actionability: Distinct intervention strategies based on uncertainty source—model retraining versus human oversight—are supported and empirically validated.
• Human-AI Collaboration: Aleatoric uncertainty surfaces ambiguous cases to humans without conflating them with model confusion, aligning triage with practical needs in subjective tasks.
• Deployment Safety: Quadrant-based routing provides defensible abstention and escalation criteria, reducing risk in real-world AI systems.
• Theoretical Advancement: CREDENCE operationalizes credal sets for interpretable systems, instantiating imprecise probability theory within NLP pipelines and strengthening foundations for prescriptive uncertainty quantification.

Future directions include unsupervised aleatoric estimation and expansion to generative tasks, as well as refined ensemble aggregation mechanisms beyond simple averaging.

Conclusion

CREDENCE establishes a CBM framework that structurally separates epistemic and aleatoric uncertainty at the concept level using credal representations and ensemble diversity. With strong empirical evidence that epistemic uncertainty tracks prediction errors and aleatoric uncertainty closely aligns with annotator disagreement, CREDENCE enables actionable, trustworthy interventions and routing in NLP pipelines. The framework’s robustness and architectural separation support its application in human-centric AI systems where uncertainty decomposition is mission-critical (2604.24170).