Elements of Conformal Prediction
stat.ME, stat.ML
Submitted: 2026-03-25
Updated: 2026-08-28
Comments: Accepted for publication at Annual Review of Statistics and Its Application
License: http://creativecommons.org/licenses/by-nc-nd/4.0/
The gist: Predictive inference is a fundamental task in statistics, traditionally addressed using parametric assumptions about the data distribution and detailed analyses of how models learn from data.
Terminology
Abstract
Predictive inference is a fundamental task in statistics, traditionally addressed using parametric assumptions about the data distribution and detailed analyses of how models learn from data. In recent years, conformal prediction has emerged as an alternative framework that is well suited to modern applications involving high-dimensional data and complex machine learning models. Its appeal stems from being both distribution-free---relying mainly on symmetry assumptions such as exchangeability---and model-agnostic, treating the learning algorithm as a black box. Even under such limited assumptions, conformal prediction provides exact finite-sample guarantees, although these are typically marginal and require careful interpretation. This paper explains the core ideas of conformal prediction and reviews selected methods. Rather than offering an exhaustive survey, it aims to provide a clear conceptual entry point and a pedagogical overview of the field.
Sources
- Theoretical Foundations of Conformal Prediction
- Gradient Equilibrium in Online Learning: Theory and Applications
- Unifying Different Theories of Conformal Prediction
- Optimized conformal classification using gradient descent approximation
- Noise-Adaptive Conformal Classification with Marginal Coverage
- Minimum Volume Conformal Sets for Multivariate Regression
- Efficient Conformal Prediction for Regression Models under Label Noise
- Joint Coverage Regions: Simultaneous Confidence and Prediction Sets
- Interpretable Multivariate Conformal Prediction with Fast Transductive Standardization
- Doubly Robust and Efficient Calibration of Prediction Sets for Right-Censored Time-to-Event Outcomes
- E-Values Expand the Scope of Conformal Prediction
- Powerful batch conformal prediction for classification
- Conformal Inference under High-Dimensional Covariate Shifts via Likelihood-Ratio Regularization
- Exchangeability, Conformal Prediction, and Rank Tests
- Conformal Prediction with Large Language Models for Multi-Choice Question Answering
- Full-conformal novelty detection
- Batch Predictive Inference
- Conditional Predictive Inference for Missing Outcomes
- Conformal prediction after data-dependent model selection
- Structured Conformal Inference for Matrix Completion with Applications to Group Recommender Systems
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