CREDO: Epistemic-Aware Conformalized Credal Envelopes for Regression

TL;DR

This work introduces CREDO, a simple credal-then-conformalizerecipe that combines both strengths, and provides 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.

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 (5)

• 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 $x$.
• 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).
• 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.

Theorems & Definitions (11)

• Remark 2.1
• Theorem 3.1
• Theorem 3.2
• Theorem 3.3
• Theorem 3.4
• Lemma D.1: Quantile sandwich
• proof
• proof : Proof of Theorem \ref{['thm:credal-coverage-envelope']}
• proof : Proof of Theorem \ref{['theorem:posterior-predictive-trimmed']}
• proof : Proof of Theorem \ref{['thm:split-conformal']}