# Full Conformal Prediction under Stochastic Non-Conformity Measure

arXiv: https://arxiv.org/abs/2606.28730 · HTML: https://mlsanity.com/paper/2606.28730/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 23 references that are in the map.
- First posted on arXiv 27 Jun 2026.

## Builds on (most cited first, 12 of 12)

- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Conformal prediction beyond exchangeability](https://mlsanity.com/paper/2202.13415/) (2022)
- [Conformal Language Modeling](https://mlsanity.com/paper/2306.10193/) (2023)
- [API Is Enough: Conformal Prediction for Large Language Models Without Logit-Access](https://mlsanity.com/paper/2403.01216/) (2024)
- [Conformal Nucleus Sampling](https://mlsanity.com/paper/2305.02633/) (2023)
- [Distribution-free inference with hierarchical data](https://mlsanity.com/paper/2306.06342/) (2023)
- [Optimized Conformal Selection: Powerful Selective Inference After Conformity Score Optimization](https://mlsanity.com/paper/2411.17983/) (2024)
- [LLMs are Overconfident: Evaluating Confidence Interval Calibration with FermiEval](https://mlsanity.com/paper/2510.26995/) (2025)
- [Leave-One-Out Stable Conformal Prediction](https://mlsanity.com/paper/2504.12189/) (2025)
- [conformalClassification: A Conformal Prediction R Package for Classification](https://mlsanity.com/paper/1804.05494/) (2018)
- [Approximating Full Conformal Prediction for Neural Network Regression with Gauss-Newton Influence](https://mlsanity.com/paper/2507.20272/) (2025)

## Abstract (arXiv)

The theory of full conformal prediction uses deterministic non-conformity measure, but modern usage of full conformal prediction often relies on machine learning training, making stochasticity inevitable. A simple sufficient condition of almost sure permutation invariance of the non-conformity measure can be too restrictive, so many have suggested the relaxation to permutation in distribution as a condition for full conformal prediction validity. We, however, show that this commonly known condition is actually insufficient. We then provide a correct sufficient condition: Conditional Independence & Permutation Invariance in Distribution, which encompasses several stochastic settings that may be used in machine learning.