# Beyond Prediction-Set Size: Quantifying Conformal Uncertainty through Credal Geometry

arXiv: https://arxiv.org/abs/2602.01667 · HTML: https://mlsanity.com/paper/2602.01667/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 44 of its 108 references that are in the map.
- First posted on arXiv 2 Feb 2026.

## Builds on (most cited first, 30 of 44)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods](https://mlsanity.com/paper/1910.09457/) (2019)
- [OpenML: networked science in machine learning](https://mlsanity.com/paper/1407.7722/) (2014)
- [Classification with Valid and Adaptive Coverage](https://mlsanity.com/paper/2006.02544/) (2020)
- [Uncertainty Sets for Image Classifiers using Conformal Prediction](https://mlsanity.com/paper/2009.14193/) (2020)
- [Predict Responsibly: Improving Fairness and Accuracy by Learning to Defer](https://mlsanity.com/paper/1711.06664/) (2017)
- [Credal Bayesian Deep Learning](https://mlsanity.com/paper/2302.09656/) (2023)
- [Is the Volume of a Credal Set a Good Measure for Epistemic Uncertainty?](https://mlsanity.com/paper/2306.09586/) (2023)
- [Conformal Bayesian Computation](https://mlsanity.com/paper/2106.06137/) (2021)
- [Second-Order Uncertainty Quantification: A Distance-Based Approach](https://mlsanity.com/paper/2312.00995/) (2023)
- [ROAD-R: The Autonomous Driving Dataset with Logical Requirements](https://mlsanity.com/paper/2210.01597/) (2022)
- [Conformal prediction under ambiguous ground truth](https://mlsanity.com/paper/2307.09302/) (2023)
- [Credal Learning Theory](https://mlsanity.com/paper/2402.00957/) (2024)
- [CreINNs: Credal-Set Interval Neural Networks for Uncertainty Estimation in Classification Tasks](https://mlsanity.com/paper/2401.05043/) (2024)
- [Conformalized Credal Set Predictors](https://mlsanity.com/paper/2402.10723/) (2024)
- [Explaining the Uncertain: Stochastic Shapley Values for Gaussian Process Models](https://mlsanity.com/paper/2305.15167/) (2023)
- [Conformalized Credal Regions for Classification with Ambiguous Ground Truth](https://mlsanity.com/paper/2411.04852/) (2024)
- [Ensemble-based Uncertainty Quantification: Bayesian versus Credal Inference](https://mlsanity.com/paper/2107.10384/) (2021)
- [Domain Generalisation via Imprecise Learning](https://mlsanity.com/paper/2404.04669/) (2024)
- [Quantifying Deep Learning Model Uncertainty in Conformal Prediction](https://mlsanity.com/paper/2306.00876/) (2023)
- [A Novel Bayes' Theorem for Upper Probabilities](https://mlsanity.com/paper/2307.06831/) (2023)
- [Credal Wrapper of Model Averaging for Uncertainty Estimation in Classification](https://mlsanity.com/paper/2405.15047/) (2024)
- [Distributionally Robust Statistical Verification with Imprecise Neural Networks](https://mlsanity.com/paper/2308.14815/) (2023)
- [Integral Imprecise Probability Metrics](https://mlsanity.com/paper/2505.16156/) (2025)
- [Scoring Rules and Calibration for Imprecise Probabilities](https://mlsanity.com/paper/2410.23001/) (2024)
- [Validity, consonant plausibility measures, and conformal prediction](https://mlsanity.com/paper/2001.09225/) (2020)
- [Approximating Counterfactual Bounds while Fusing Observational, Biased and Randomised Data Sources](https://mlsanity.com/paper/2307.16577/) (2023)
- [Epistemic Uncertainty in Conformal Scores: A Unified Approach](https://mlsanity.com/paper/2502.06995/) (2025)

## Built on by (most cited first, 4 of 4)

- [Verbalizing LLM's Higher-order Uncertainty via Imprecise Probabilities](https://mlsanity.com/paper/2603.10396/) (2026)
- [Quantification of Credal Uncertainty: A Distance-Based Approach](https://mlsanity.com/paper/2603.27270/) (2026)
- [Set-based v.s. Distribution-based Representations of Epistemic Uncertainty: A Comparative Study](https://mlsanity.com/paper/2602.22747/) (2026)
- [CREDO: Epistemic-Aware Conformalized Credal Envelopes for Regression](https://mlsanity.com/paper/2603.06826/) (2026)

## Abstract (arXiv)

Prediction-set size offers a coarse summary of conformal uncertainty. We develop a richer perspective through the geometry of credal sets: families of probability distributions compatible with conformal prediction (CP) regions. We establish this representation for split CP, extending a correspondence recently identified for full CP. Building on this representation, we derive analytical characterisations and exact algorithms for several widely used credal uncertainty measures, reducing potentially exponential computations to linear time after sorting the conformal p-values. We further unify several of these measures with classical conformal summaries by integrating set-size penalties based on Tsallis entropies across error levels. We also prove an impossibility theorem: for common split-conformal regression constructions, uncertainty summaries of the induced credal sets cannot distinguish between inputs. Classification experiments on selective prediction and distribution-shift detection show that these summaries often recover useful ranking information lost by prediction-set size at a fixed error level, enabling finer-grained uncertainty assessment. These results establish credal geometry as a principled framework for quantifying conformal uncertainty and understanding its limitations.