CREDO: Epistemic-Aware Conformalized Credal Envelopes for Regression

Luben M. C. Cabezas; Sabina J. Sloman; Bruno M. Resende; Fanyi Wu; Michele Caprio; Rafael Izbicki

stat.MLMar 6, 2026

CREDO: Epistemic-Aware Conformalized Credal Envelopes for Regression

Authors: Luben M. C. Cabezas, Sabina J. Sloman, Bruno M. Resende, Fanyi Wu, Michele Caprio, Rafael Izbicki

Organizations: Department of Statistics, Federal University of S˜ao Carlos, S˜ao Carlos, Brazil · Institute of Mathematics and Computer Science , University of S˜ao Paulo, S˜ao Carlos, Brazil · Universit´e Grenoble Alpes, Inria, CNRS, Grenoble INP, LJK, France · The University of Manchester, UK, Department of Computer Science

Abstract

Conformal prediction delivers prediction intervals with distribution-free coverage, but its intervals can look overconfident in regions where the model is extrapolating, because standard conformal scores do not explicitly represent epistemic uncertainty. Credal methods, by contrast, make epistemic effects visible by working with sets of plausible predictive distributions, but they are typically model-based and lack calibration guarantees. We introduce CREDO, a simple "credal-then-conformalize" recipe that combines both strengths. CREDO first builds an interpretable credal envelope that widens when local evidence is weak, then applies split conformal calibration on top of this envelope to guarantee marginal coverage without further assumptions. This separation of roles yields prediction intervals that are interpretable: their width can be decomposed into aleatoric noise, epistemic inflation, and a distribution-free calibration slack. We provide a fast implementation based on trimming extreme posterior predictive endpoints, prove validity, and show on benchmark regressions that CREDO maintains target coverage while improving sparsity adaptivity at competitive efficiency.

Figures & tables

Figure 1: Motivation and decomposition. Comparison of split-conformal prediction intervals. Top-left: CREDO yields intervals that widen adaptively in regions of high epistemic uncertainty—near the transition and toward the covariate extremes. Top-right: CQR (which does not take epistemic uncertainty into account) produces comparatively uniform intervals that can look overconfident where local support is weak (few nearby training points), despite marginal validity. Bottom-left: CREDO enables an uncertainty decomposition into aleatoric (green) and epistemic (orange) components; epistemic uncertainty peaks around $x=0$ and at the edges, aligning with where CREDO inflates the envelope.

Figure 2: CREDO scheme. From a model for the aleatoric uncertainty, we form a trimmed credal quantile envelope $[\ell(x),u(x)]$ (at nominal level $1-\alpha_{0}$ ), then split-conformalize using the distance-to-envelope score to output $C(x)=[\ell(x)-\hat{\tau},\;u(x)+\hat{\tau}]$ with marginal coverage $1-\alpha$ .

Figure 3: Data-support–aware trimming via

\gamma(x)

. Top: Prediction intervals under a constant trimming level

\gamma

versus the adaptive rule

\gamma(x)

driven by a kNN-based scarcity score. Adaptive trimming decreases

\gamma(x)

in data-sparse/extrapolative regions (less endpoint trimming, wider credal envelopes) and increases

\gamma(x)

in data-dense regions (more trimming, tighter envelopes). Bottom: The resulting

\gamma(x)

profile as a function of the covariate

x

Appendix figures & tables3 assets

Supplementary material from the paper’s appendix.

Appendix

Dataset	n	p	Scientific Domain	Data Source
Concrete	1,030	8	Civil Engineering	UCI Repository
Airfoil	1,503	5	Aeroacoustics	UCI Repository
Wine White	1,599	11	Enology	UCI Repository
Star	2,161	48	Pedagogy	Harvard Dataverse
Wine Red	4,898	11	Enology	UCI Repository
Cycle	9,568	4	Thermodynamics	UCI Repository

Appendix

Table 3: Benchmark Datasets Overview. We summarize the sample size (

n

), feature count (

p

), and the original scientific domain of each benchmark.

Figure 4: Percentage of Epistemic Uncertainty for outliers and inliers across real-world datasets using the QNN-based implementation of CREDO . The uncertainty decomposition successfully attributes a higher proportion of epistemic uncertainty to outliers compared to inliers, a distinction that is particularly pronounced in small-data domains (top row).

Panel of Figure 5 — Figure 5: Normalized Uncertainty Decomposition for Scenarios 2 and 3. This figure illustrates the ability of CREDO to disentangle aleatoric and epistemic components under complex data-generating processes. In Scenario 2 (left), the decomposition successfully isolates the high epistemic inflation in the scarce region ( $x\in[0,0.4]$ ) from the underlying oscillating heteroscedastic noise. Similarly, in Scenario 3 (right), the epistemic percentage peaks in the gaps between clusters and in the extrapolative tails, despite the presence of multi-modal ”shock” noise components.

Explore similar work

Optimal Conformal Prediction under Epistemic Uncertainty
May 25, 2025Alireza Javanmardi, Soroush H. Zargarbashi, Santo M. A. R. Thies +3Conformal Prediction Conformal Risk Control
1LMU Munich · 2MCML · 3CISPA +3
Co-optimization for Adaptive Conformal Prediction
Mar 2, 2026Xiaoyi Su, Zhixin Zhou, Rui LuoConformal Prediction Regression Prediction Intervals
Department of Systems Engineering, City University of Hong Kong, Hong Kong SAR, China · Alpha Benito Research, Los Angeles, USA
SPACR: Single-Pass Adaptive Training of Uncertainty-Aware Conformal Regressors
Jun 9, 2026Soundouss Messoudi, Sylvain Rousseau, Sébastien DesterckeConformal Prediction Adaptive Conformal Inference
Heudiasyc - UMR CNRS 7253, Université de Technologie de Compiègne

May 25, 2025J/K move · Enter open · S save

Optimal Conformal Prediction under Epistemic Uncertainty

Alireza Javanmardi, Soroush H. Zargarbashi, Santo M. A. R. Thies, Willem Waegeman+2

1LMU Munich · 2MCML · 3CISPA+3

Conformal Prediction Conformal Risk Control Epistemic Uncertainty

Open paper AskPDF arXiv

Conformal prediction (CP) is a widely used frequentist framework to quantify uncertainty by constructing prediction sets with user-specified marginal coverage guarantees. In practice, CP is typically applied on top of probabilistic classifiers, which are able to express aleatoric but not epistemic uncertainty. In this paper, we consider the question of how to optimally employ CP on top of a more expressive formalism, namely credal sets, which can express both aleatoric and epistemic uncertainty. More specifically, we propose probabilistic Bernoulli prediction sets (BPS) and derive a variant that achieves conditional coverage for valid credal sets while remaining minimal in expected size. We then address the more realistic scenario in which the validity of the credal sets is not guaranteed. Assuming access to calibration data with ground-truth distributions over labels, we apply conformal risk control to BPS and derive a PAC-style guarantee: with high probability over the data, the achieved conditional coverage is at least the desired level. We validate our theoretical findings empirically over various datasets.

Abstract

Explore similar work

Optimal Conformal Prediction under Epistemic Uncertainty

Co-optimization for Adaptive Conformal Prediction

SPACR: Single-Pass Adaptive Training of Uncertainty-Aware Conformal Regressors