# Conformal Prediction Regions are Imprecise Highest Density Regions

arXiv: https://arxiv.org/abs/2502.06331 · HTML: https://mlsanity.com/paper/2502.06331/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 69 references that are in the map.
- First posted on arXiv 10 Feb 2025.

## Builds on (most cited first, 23 of 23)

- [Conformal prediction beyond exchangeability](https://mlsanity.com/paper/2202.13415/) (2022)
- [Conformal Prediction With Conditional Guarantees](https://mlsanity.com/paper/2305.12616/) (2023)
- [Quantifying Aleatoric and Epistemic Uncertainty in Machine Learning: Are Conditional Entropy and Mutual Information Appropriate Measures?](https://mlsanity.com/paper/2209.03302/) (2022)
- [Theoretical Foundations of Conformal Prediction](https://mlsanity.com/paper/2411.11824/) (2024)
- [Is the Volume of a Credal Set a Good Measure for Epistemic Uncertainty?](https://mlsanity.com/paper/2306.09586/) (2023)
- [Optimal Testing for Properties of Distributions](https://mlsanity.com/paper/1507.05952/) (2015)
- [Second-Order Uncertainty Quantification: A Distance-Based Approach](https://mlsanity.com/paper/2312.00995/) (2023)
- [Credal Learning Theory](https://mlsanity.com/paper/2402.00957/) (2024)
- [Robust Hypothesis Testing Using Wasserstein Uncertainty Sets](https://mlsanity.com/paper/1805.10611/) (2018)
- [Conformalized Credal Set Predictors](https://mlsanity.com/paper/2402.10723/) (2024)
- [Conformalized Credal Regions for Classification with Ambiguous Ground Truth](https://mlsanity.com/paper/2411.04852/) (2024)
- [A Novel Bayes' Theorem for Upper Probabilities](https://mlsanity.com/paper/2307.06831/) (2023)
- [Distributionally Robust Statistical Verification with Imprecise Neural Networks](https://mlsanity.com/paper/2308.14815/) (2023)
- [Validity, consonant plausibility measures, and conformal prediction](https://mlsanity.com/paper/2001.09225/) (2020)
- [Judicious Judgment Meets Unsettling Updating: Dilation, Sure Loss, and Simpson's Paradox](https://mlsanity.com/paper/1712.08946/) (2017)
- [On the Calibration of Probabilistic Classifier Sets](https://mlsanity.com/paper/2205.10082/) (2022)
- [Conformal Credal Self-Supervised Learning](https://mlsanity.com/paper/2205.15239/) (2022)
- [Valid inferential models for prediction in supervised learning problems](https://mlsanity.com/paper/2112.10234/) (2021)
- [On the Robustness of Kernel Goodness-of-Fit Tests](https://mlsanity.com/paper/2408.05854/) (2024)
- [Conformal Prediction with Partially Labeled Data](https://mlsanity.com/paper/2306.01191/) (2023)
- [Imprecise Markov Semigroups and their Ergodicity](https://mlsanity.com/paper/2405.00081/) (2024)
- [Valid and efficient imprecise-probabilistic inference with partial priors, II. General framework](https://mlsanity.com/paper/2211.14567/) (2022)
- [Possibility-theoretic statistical inference offers performance and probativeness assurances](https://mlsanity.com/paper/2304.05740/) (2023)

## Built on by (most cited first, 7 of 7)

- [Integral Imprecise Probability Metrics](https://mlsanity.com/paper/2505.16156/) (2025)
- [Beyond Prediction-Set Size: Quantifying Conformal Uncertainty through Credal Geometry](https://mlsanity.com/paper/2602.01667/) (2026)
- [Quantification of Credal Uncertainty: A Distance-Based Approach](https://mlsanity.com/paper/2603.27270/) (2026)
- [When Do Credal Sets Stabilize? Fixed-Point Theorems for Credal Set Updates](https://mlsanity.com/paper/2510.04769/) (2025)
- [Adaptive Conformal Prediction for Quantum Machine Learning](https://mlsanity.com/paper/2511.18225/) (2025)
- [CREDO: Epistemic-Aware Conformalized Credal Envelopes for Regression](https://mlsanity.com/paper/2603.06826/) (2026)
- [On the QUEST for Uncertainty Quantification via Highest Density Regions](https://mlsanity.com/paper/2606.19569/) (2026)

## Abstract (arXiv)

Recently, Cella and Martin proved how, under an assumption called consonance, a credal set (i.e. a closed and convex set of probabilities) can be derived from the conformal transducer associated with transductive conformal prediction. We show that the Imprecise Highest Density Region (IHDR) associated with such a credal set corresponds to the classical Conformal Prediction Region. In proving this result, we establish a new relationship between Conformal Prediction and Imprecise Probability (IP) theories, via the IP concept of a cloud. A byproduct of our presentation is the discovery that consonant plausibility functions are monoid homomorphisms, a new algebraic property of an IP tool.