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arxiv: 2604.24170 · v1 · submitted 2026-04-27 · 💻 cs.AI

Credal Concept Bottleneck Models for Epistemic-Aleatoric Uncertainty Decomposition

Tanmoy Mukherjee , Thomas Bailleux , Pierre Marquis , Zied Bouraoui This is my paper

Pith reviewed 2026-05-08 03:44 UTC · model grok-4.3

classification 💻 cs.AI
keywords concept bottleneck modelsepistemic uncertaintyaleatoric uncertaintycredal setsensemble methodsuncertainty decompositioninterpretable machine learning
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The pith

CREDENCE represents concepts as probability intervals and uses ensemble disagreement to isolate epistemic uncertainty from aleatoric uncertainty in concept bottleneck models.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Concept bottleneck models predict through human-interpretable concepts but typically output single probabilities that blend reducible model uncertainty with irreducible input ambiguity. This paper introduces CREDENCE, which instead represents each concept as a credal set in the form of a probability interval. Epistemic uncertainty is then read off from disagreement among a diverse collection of concept heads, while aleatoric uncertainty comes from a separate ambiguity head trained to reproduce annotator disagreement where labels exist. The resulting signals directly support actions such as automation, data collection, human review, or abstention. Experiments across tasks show epistemic uncertainty rising with model errors and aleatoric uncertainty aligning with human label variation.

Core claim

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.

What carries the argument

The credal prediction, a probability interval per concept that enables separate extraction of epistemic uncertainty via ensemble head disagreement and aleatoric uncertainty via an ambiguity output.

If this is right

  • Epistemic uncertainty correlates positively with prediction errors.
  • Aleatoric uncertainty tracks levels of annotator disagreement.
  • Low combined uncertainty supports automated decisions.
  • High epistemic uncertainty flags cases for additional data collection.
  • High aleatoric uncertainty flags cases for human review or abstention.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same credal-plus-ensemble construction could be applied to other concept-based or prototype-based architectures beyond the original CBM formulation.
  • In deployment pipelines the two uncertainty streams could be combined into a single routing score that decides between model-only, human-in-the-loop, and data-acquisition actions.
  • If the decomposition generalizes, it would allow quantitative comparison of how much uncertainty in a given domain is reducible versus inherent.

Load-bearing premise

Disagreement among the ensemble heads measures reducible epistemic uncertainty and annotator disagreement serves as a faithful proxy for irreducible aleatoric uncertainty.

What would settle it

A held-out test set in which cases with high epistemic uncertainty do not show elevated prediction error rates or in which the ambiguity output scores fail to correlate with measured annotator disagreement.

Figures

Figures reproduced from arXiv: 2604.24170 by Pierre Marquis, Tanmoy Mukherjee, Thomas Bailleux, Zied Bouraoui.

Figure 1
Figure 1. Figure 1: CREDENCE architecture. Epistemic uncertainty emerges from ensemble disagreement (top branch); view at source ↗
Figure 2
Figure 2. Figure 2: Compact quadrant-based decision support. view at source ↗
read the original 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

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper proposes CREDENCE, an extension to Concept Bottleneck Models (CBMs) that represents each concept via a credal prediction (probability interval). Epistemic uncertainty is derived from disagreement across an ensemble of diverse concept heads, while aleatoric uncertainty is estimated by a dedicated ambiguity output trained to match annotator disagreement when labels are available. The framework enables prescriptive actions (automate low-uncertainty cases, collect data for high-epistemic, route high-aleatoric to humans, abstain when both high). Experiments across tasks show positive association between epistemic scores and prediction errors, and close tracking of annotator disagreement by the aleatoric head.

Significance. If the decomposition is shown to be robust, the work offers a practical advance for interpretable models by turning uncertainty into actionable signals rather than a single conflated score. The open-source implementation at the provided GitHub link is a clear strength that supports reproducibility.

major comments (2)
  1. [Experiments] Experiments section: the claim that epistemic uncertainty captures reducible model underspecification rests on positive correlation with errors, but no interventional validation (e.g., scaling training data or ensemble diversity and checking whether epistemic scores decrease while aleatoric remains stable) is reported. Without this, ensemble disagreement could reflect optimization noise rather than true epistemic uncertainty, weakening the central decomposition guarantee.
  2. [Method] Method (credal ensemble construction): aleatoric uncertainty is obtained by supervised training of an ambiguity head to match annotator disagreement. This makes the reported tracking tautological rather than an independent estimate; the paper should explicitly separate the fitted component from any derived separation and discuss the implications for domains without annotator labels.
minor comments (2)
  1. [Method] The definition of the credal set (probability interval) and how the ensemble heads are diversified should be stated with a precise equation or algorithm box for reproducibility.
  2. [Experiments] Figure captions and axis labels in the uncertainty correlation plots could be expanded to include exact metrics (e.g., Spearman rho values) rather than qualitative descriptions.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback and for recognizing the practical utility of CREDENCE for turning uncertainty into actionable signals in Concept Bottleneck Models. We address each major comment below, indicating the revisions we will make to strengthen the manuscript.

read point-by-point responses

  1. Referee: [Experiments] Experiments section: the claim that epistemic uncertainty captures reducible model underspecification rests on positive correlation with errors, but no interventional validation (e.g., scaling training data or ensemble diversity and checking whether epistemic scores decrease while aleatoric remains stable) is reported. Without this, ensemble disagreement could reflect optimization noise rather than true epistemic uncertainty, weakening the central decomposition guarantee.

    Authors: We agree that interventional validation would provide stronger causal evidence that the ensemble-derived epistemic scores reflect reducible underspecification rather than optimization artifacts. The current manuscript reports only the positive association with prediction errors (a standard proxy in ensemble-based epistemic uncertainty work) and notes that aleatoric tracks annotator disagreement independently. To address the concern, we will revise the Experiments and Discussion sections to explicitly acknowledge this correlational limitation, clarify that the decomposition is by construction (epistemic from head diversity, aleatoric from supervised ambiguity), and outline how future interventional studies (varying ensemble size or data volume) could be performed. We will not add new experiments in this revision but will strengthen the interpretive caveats. revision: partial

  2. Referee: [Method] Method (credal ensemble construction): aleatoric uncertainty is obtained by supervised training of an ambiguity head to match annotator disagreement. This makes the reported tracking tautological rather than an independent estimate; the paper should explicitly separate the fitted component from any derived separation and discuss the implications for domains without annotator labels.

    Authors: We appreciate this clarification. The aleatoric component is indeed obtained via direct supervision on multi-annotator disagreement where such labels exist, so the reported tracking is a validation of the training objective rather than an independent discovery. The epistemic component, by contrast, arises from disagreement across the diverse concept heads without direct supervision on uncertainty. We will revise the Method section to explicitly separate these two sources, describe the credal interval construction as the union of the two, and add a dedicated paragraph on implications for label-scarce domains: in such settings the framework can still deliver epistemic uncertainty via the ensemble while aleatoric uncertainty would be unavailable or require proxy supervision. This makes the design choices and their scope transparent. revision: yes

Circularity Check

1 steps flagged

Uncertainty decomposition is imposed by construction via ensemble disagreement and supervised training on annotator disagreement

specific steps
  1. self definitional [Abstract]
    "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 decomposition is explicitly 'by construction': epistemic uncertainty is set equal to (derived from) head disagreement, while aleatoric uncertainty is the output of a head trained to match the annotator-disagreement proxy. The claimed separation of reducible vs. irreducible uncertainty therefore reduces to these definitional choices and the supervised fitting objective rather than emerging from an independent derivation chain.

full rationale

The paper's core contribution is framed as a decomposition 'by construction' that defines epistemic uncertainty directly as disagreement across concept heads and trains the aleatoric component explicitly to match annotator disagreement. This makes the separation of epistemic (reducible) and aleatoric (irreducible) labels equivalent to the chosen architectural proxies and training targets rather than an independent derivation. Experiments then report associations and tracking that follow directly from these definitions. The central claim therefore reduces to the model design without additional first-principles justification or interventional validation that the proxies isolate the intended uncertainty types.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Only the abstract is available, so the ledger is necessarily incomplete. The framework assumes standard properties of credal sets and ensemble disagreement as proxies for the two uncertainty types.

axioms (2)
  • domain assumption Ensemble disagreement across diverse concept heads measures epistemic uncertainty
    Invoked to derive the epistemic component from multiple heads.
  • domain assumption Annotator disagreement is a suitable training target for aleatoric uncertainty
    Used to supervise the dedicated ambiguity output.

pith-pipeline@v0.9.0 · 5523 in / 1267 out tokens · 43492 ms · 2026-05-08T03:44:35.877505+00:00 · methodology

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Reference graph

Works this paper leans on

4 extracted references · 2 canonical work pages · 1 internal anchor

  1. [1]

    LoRA: Low-Rank Adaptation of Large Language Models

    PMLR. Jianfeng He, Xuchao Zhang, Shuo Lei, Zhiqian Chen, Fanglan Chen, Abdulaziz Alhamadani, Bei Xiao, and ChangTien Lu. 2020. Towards more accurate uncer- tainty estimation in text classification. InProceed- ings of the 2020 Conference on Empirical Methods in Natural Language Processing (EMNLP), pages 8362–8372, Online. Association for Computational Ling...

    work page internal anchor Pith review arXiv 2020

  2. [2]

    Is the volume of a credal set a good mea- sure for epistemic uncertainty? InProceedings of the Thirty-Ninth Conference on Uncertainty in Artificial Intelligence, volume 216 ofProceedings of Machine Learning Research, pages 1795–1804. PMLR. Murat Sensoy, Lance Kaplan, and Melih Kandemir

  3. [3]

    InAdvances in Neural Information Processing Systems, volume 31

    Evidential deep learning to quantify classifica- tion uncertainty. InAdvances in Neural Information Processing Systems, volume 31. Curran Associates, Inc. Mohammad Hossein Shaker and Eyke Hüllermeier

  4. [4]

    non-dominated

    Aleatoric and epistemic uncertainty with ran- dom forests.Preprint, arXiv:2001.00893. Chung-En Sun, Tuomas Oikarinen, Berk Ustun, and Tsui-Wei Weng. 2025. Concept bottleneck large lan- guage models.Preprint, arXiv:2412.07992. Mukund Sundararajan, Ankur Taly, and Qiqi Yan. 2017. Axiomatic attribution for deep networks.Preprint, arXiv:1703.01365. Dennis Ulm...

    work page arXiv 2001