# Validity, consonant plausibility measures, and conformal prediction

arXiv: https://arxiv.org/abs/2001.09225 · HTML: https://mlsanity.com/paper/2001.09225/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Jan 2020.

## Built on by (most cited first, 9 of 9)

- [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)
- [Conformal Credal Self-Supervised Learning](https://mlsanity.com/paper/2205.15239/) (2022)
- [Guaranteed prediction sets for functional surrogate models](https://mlsanity.com/paper/2501.18426/) (2025)
- [Conformal Prediction Regions are Imprecise Highest Density Regions](https://mlsanity.com/paper/2502.06331/) (2025)
- [Beyond Prediction-Set Size: Quantifying Conformal Uncertainty through Credal Geometry](https://mlsanity.com/paper/2602.01667/) (2026)
- [Distilling Calibration via Conformalized Credal Inference](https://mlsanity.com/paper/2501.06066/) (2025)
- [Model-free generalized fiducial inference](https://mlsanity.com/paper/2307.12472/) (2023)
- [CREDO: Epistemic-Aware Conformalized Credal Envelopes for Regression](https://mlsanity.com/paper/2603.06826/) (2026)

## Abstract (arXiv)

Prediction of future observations is an important and challenging problem. The two mainstream approaches for quantifying prediction uncertainty use prediction regions and predictive distributions, respectively, with the latter believed to be more informative because it can perform other prediction-related tasks. The standard notion of validity, what we refer to here as Type-1 validity, focuses on coverage probability of prediction regions, while a notion of validity relevant to the other prediction-related tasks performed by predictive distributions is lacking. Here we present a new notion, called Type-2 validity, relevant to these other prediction tasks. We establish connections between Type-2 validity and coherence properties, and show that imprecise probability considerations are required in order to achieve it. We go on to show that both types of prediction validity can be achieved by interpreting the conformal prediction output as the contour function of a consonant plausibility measure. We also offer an alternative characterization of conformal prediction, based on a new nonparametric inferential model construction, wherein the appearance of consonance is natural, and prove its validity.