# Theoretical Foundations of Conformal Prediction

arXiv: https://arxiv.org/abs/2411.11824 · HTML: https://mlsanity.com/paper/2411.11824/

## Key facts

- Cited by 101 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Nov 2024.

## Built on by (most cited first, 30 of 101)

- [Minimum Volume Conformal Sets for Multivariate Regression](https://mlsanity.com/paper/2503.19068/) (2025)
- [E-Values Expand the Scope of Conformal Prediction](https://mlsanity.com/paper/2503.13050/) (2025)
- [Multivariate Conformal Prediction using Optimal Transport](https://mlsanity.com/paper/2502.03609/) (2025)
- [Rectifying Conformity Scores for Better Conditional Coverage](https://mlsanity.com/paper/2502.16336/) (2025)
- [WATCH: Adaptive Monitoring for AI Deployments via Weighted-Conformal Martingales](https://mlsanity.com/paper/2505.04608/) (2025)
- [Conformal Prediction for Image Segmentation Using Morphological Prediction Sets](https://mlsanity.com/paper/2503.05618/) (2025)
- [Backward Conformal Prediction](https://mlsanity.com/paper/2505.13732/) (2025)
- [Kandinsky Conformal Prediction: Beyond Class- and Covariate-Conditional Coverage](https://mlsanity.com/paper/2502.17264/) (2025)
- [Conformal Prediction under Levy-Prokhorov Distribution Shifts: Robustness to Local and Global Perturbations](https://mlsanity.com/paper/2502.14105/) (2025)
- [Conformal Calibration: Ensuring the Reliability of Black-Box AI in Wireless Systems](https://mlsanity.com/paper/2504.09310/) (2025)
- [Relational Conformal Prediction for Correlated Time Series](https://mlsanity.com/paper/2502.09443/) (2025)
- [Volume Optimality in Conformal Prediction with Structured Prediction Sets](https://mlsanity.com/paper/2502.16658/) (2025)
- [Conformal Prediction Sets for Deep Generative Models via Reduction to Conformal Regression](https://mlsanity.com/paper/2503.10512/) (2025)
- [Predictive inference for time series: why is split conformal effective despite temporal dependence?](https://mlsanity.com/paper/2510.02471/) (2025)
- [Conformal Risk Control for Non-Monotonic Losses](https://mlsanity.com/paper/2602.20151/) (2026)
- [Conformal Prediction Regions are Imprecise Highest Density Regions](https://mlsanity.com/paper/2502.06331/) (2025)
- [PASC: Pipeline-Aware Conformal Prediction with Joint Coverage Guarantees for Multi-Stage NLP and LLM Pipelines](https://mlsanity.com/paper/2605.18812/) (2026)
- [Improving the statistical efficiency of cross-conformal prediction](https://mlsanity.com/paper/2503.01495/) (2025)
- [Conformalized Generative Bayesian Imaging: An Uncertainty Quantification Framework for Computational Imaging](https://mlsanity.com/paper/2504.07696/) (2025)
- [Enforcing tail calibration when training probabilistic forecast models](https://mlsanity.com/paper/2506.13687/) (2025)
- [Valid Selection among Conformal Sets](https://mlsanity.com/paper/2506.20173/) (2025)
- [Conformal Prediction for Time-series Forecasting with Change Points](https://mlsanity.com/paper/2509.02844/) (2025)
- [Adaptive Coverage Policies in Conformal Prediction](https://mlsanity.com/paper/2510.04318/) (2025)
- [Theoretical guarantees for change localization using conformal p-values](https://mlsanity.com/paper/2510.08749/) (2025)
- [Distributed Conformal Prediction via Message Passing](https://mlsanity.com/paper/2501.14544/) (2025)
- [Dynamic Estimation Loss Control in Variational Quantum Sensing via Online Conformal Inference](https://mlsanity.com/paper/2505.23389/) (2025)
- [One Sample is Enough to Make Conformal Prediction Robust](https://mlsanity.com/paper/2506.16553/) (2025)
- [Leave a Window Out: Modifying the Jackknife for Predictive Inference in Time Series](https://mlsanity.com/paper/2605.30292/) (2026)
- [Distilling Calibration via Conformalized Credal Inference](https://mlsanity.com/paper/2501.06066/) (2025)
- [Generalization and Informativeness of Weighted Conformal Risk Control Under Covariate Shift](https://mlsanity.com/paper/2501.11413/) (2025)

## Abstract (arXiv)

This book is about conformal prediction and related inferential techniques that build on permutation tests and exchangeability. These techniques are useful in a diverse array of tasks, including hypothesis testing and providing uncertainty quantification guarantees for machine learning systems. Much of the current interest in conformal prediction is due to its ability to integrate into complex machine learning workflows, solving the problem of forming prediction sets without any assumptions on the form of the data generating distribution. Since contemporary machine learning algorithms have generally proven difficult to analyze directly, conformal prediction's main appeal is its ability to provide formal, finite-sample guarantees when paired with such methods. The goal of this book is to teach the reader about the fundamental technical arguments that arise when researching conformal prediction and related questions in distribution-free inference. Many of these proof strategies, especially the more recent ones, are scattered among research papers, making it difficult for researchers to understand where to look, which results are important, and how exactly the proofs work. We hope to bridge this gap by curating what we believe to be some of the most important results in the literature and presenting their proofs in a unified language, with illustrations, and with an eye towards pedagogy.