# Conformal Prediction as Bayesian Quadrature

arXiv: https://arxiv.org/abs/2502.13228 · HTML: https://mlsanity.com/paper/2502.13228/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 34 references that are in the map.
- First posted on arXiv 18 Feb 2025.

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

- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Conformal Risk Control](https://mlsanity.com/paper/2208.02814/) (2022)
- [Distribution-Free, Risk-Controlling Prediction Sets](https://mlsanity.com/paper/2101.02703/) (2021)
- [Conformal Prediction With Conditional Guarantees](https://mlsanity.com/paper/2305.12616/) (2023)
- [Bayesian Probabilistic Numerical Methods](https://mlsanity.com/paper/1702.03673/) (2017)
- [Fast Predictive Uncertainty for Classification with Bayesian Deep Networks](https://mlsanity.com/paper/2003.01227/) (2020)
- [Bayesian Optimization with Conformal Prediction Sets](https://mlsanity.com/paper/2210.12496/) (2022)
- [Conformal Validity Guarantees Exist for Any Data Distribution (and How to Find Them)](https://mlsanity.com/paper/2405.06627/) (2024)
- [Bayes-optimal prediction with frequentist coverage control](https://mlsanity.com/paper/2105.14045/) (2021)
- [Quantile Risk Control: A Flexible Framework for Bounding the Probability of High-Loss Predictions](https://mlsanity.com/paper/2212.13629/) (2022)
- [Quantile Learn-Then-Test: Quantile-Based Risk Control for Hyperparameter Optimization](https://mlsanity.com/paper/2407.17358/) (2024)

## Built on by (most cited first, 6 of 6)

- [TECP: Token-Entropy Conformal Prediction for LLMs](https://mlsanity.com/paper/2509.00461/) (2025)
- [Conformal Policy Control](https://mlsanity.com/paper/2603.02196/) (2026)
- [Multi-Condition Conformal Selection](https://mlsanity.com/paper/2510.08075/) (2025)
- [Bayesian Conformal Prediction as a Decision Risk Problem](https://mlsanity.com/paper/2602.03331/) (2026)
- [Bayesian Quadrature](https://mlsanity.com/paper/2602.16218/) (2026)
- [Weighted Bayesian Conformal Prediction](https://mlsanity.com/paper/2604.06464/) (2026)

## Abstract (arXiv)

As machine learning-based prediction systems are increasingly used in high-stakes situations, it is important to understand how such predictive models will perform upon deployment. Distribution-free uncertainty quantification techniques such as conformal prediction provide guarantees about the loss black-box models will incur even when the details of the models are hidden. However, such methods are based on frequentist probability, which unduly limits their applicability. We revisit the central aspects of conformal prediction from a Bayesian perspective and thereby illuminate the shortcomings of frequentist guarantees. We propose a practical alternative based on Bayesian quadrature that provides interpretable guarantees and offers a richer representation of the likely range of losses to be observed at test time.