Data to 7 Oct 2026

Distribution-Free Predictive Inference For Regression

arXiv 1604.04173 ↗First posted 14 Apr 2016stat.ME math.ST stat.MLcited by 657

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Abstract (arXiv)

We develop a general framework for distribution-free predictive inference in regression, using conformal inference. The proposed methodology allows for the construction of a prediction band for the response variable using any estimator of the regression function. The resulting prediction band preserves the consistency properties of the original estimator under standard assumptions, while guaranteeing finite-sample marginal coverage even when these assumptions do not hold. We analyze and compare, both empirically and theoretically, the two major variants of our conformal framework: full conformal inference and split conformal inference, along with a related jackknife method. These methods offer different tradeoffs between statistical accuracy (length of resulting prediction intervals) and computational efficiency. As extensions, we develop a method for constructing valid in-sample prediction intervals called it rank-one-out conformal inference, which has essentially the same computational efficiency as split conformal inference. We also describe an extension of our procedures for producing prediction bands with locally varying length, in order to adapt to heteroskedascity in the data. Finally, we propose a model-free notion of variable importance, called it leave-one-covariate-out or LOCO inference. Accompanying this paper is an R package tt conformalInference that implements all of the proposals we have introduced. In the spirit of reproducibility, all of our empirical results can also be easily (re)generated using this package.

Key facts. Cited by 657 papers in the map (data through 7 Oct 2026). First posted on arXiv 14 Apr 2016.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 42; 2022: 70; 2023: 79; 2024: 110; 2025: 149; 2026: 207.

657 papers.

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2021A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantificationcited by 777
2021Adaptive Conformal Inference Under Distribution Shiftcited by 360
2022Conformal Risk Controlcited by 290
2023Conformal Language Modelingcited by 163
2022Adaptive Conformal Predictions for Time Seriescited by 155
2021Human-Centered Explainable AI (XAI): From Algorithms to User Experiencescited by 123
2023Class-Conditional Conformal Prediction with Many Classescited by 109
2021Distribution-free uncertainty quantification for classification under label shiftcited by 99
2024C-TPT: Calibrated Test-Time Prompt Tuning for Vision-Language Models via Text Feature Dispersioncited by 82
2021Conformal Prediction using Conditional Histogramscited by 77
2022Batch Multivalid Conformal Predictioncited by 66
2022Selection by Prediction with Conformal p-valuescited by 66

38 more

2022Practical Adversarial Multivalid Conformal Predictioncited by 65
2022Training Uncertainty-Aware Classifiers with Conformalized Deep Learningcited by 62
2021Few-shot Conformal Prediction with Auxiliary Taskscited by 53
2021Conformalized Survival Analysiscited by 53
2022Conformal Prediction Under Feedback Covariate Shift for Biomolecular Designcited by 53
2024Conformal Prediction for Natural Language Processing: A Surveycited by 52
2024Conformal Alignment: Knowing When to Trust Foundation Models with Guaranteescited by 50
2021Conformal Uncertainty Sets for Robust Optimizationcited by 49
2021Online Multivalid Learning: Means, Moments, and Prediction Intervalscited by 48
2022Probabilistic Conformal Prediction Using Conditional Random Samplescited by 47
2023Federated Conformal Predictors for Distributed Uncertainty Quantificationcited by 46
2024Length Optimization in Conformal Predictioncited by 39
2022Achieving Risk Control in Online Learning Settingscited by 38
2025Decision Theoretic Foundations for Conformal Prediction: Optimal Uncertainty Quantification for Risk-Averse Agentscited by 37
2023Explaining Predictive Uncertainty with Information Theoretic Shapley Valuescited by 36
2022On the Utility of Prediction Sets in Human-AI Teamscited by 34
2022Predictive Inference with Feature Conformal Predictioncited by 33
2023Object Pose Estimation with Statistical Guarantees: Conformal Keypoint Detection and Geometric Uncertainty Propagationcited by 33
2023The Rashomon Importance Distribution: Getting RID of Unstable, Single Model-based Variable Importancecited by 29
2022Conformal Prediction Sets with Limited False Positivescited by 28
2022Distribution Free Prediction Sets for Node Classificationcited by 28
2022Copula Conformal Prediction for Multi-step Time Series Forecastingcited by 28
2023Principal Uncertainty Quantification with Spatial Correlation for Image Restoration Problemscited by 28
2021Set-valued classification -- overview via a unified frameworkcited by 27
2023One-Shot Federated Conformal Predictioncited by 26
2022Efficient and Differentiable Conformal Prediction with General Function Classescited by 25
2022Conformal Prediction with Temporal Quantile Adjustmentscited by 25
2022Explainable Intrusion Detection Systems (X-IDS): A Survey of Current Methods, Challenges, and Opportunitiescited by 25
2023Probabilistically robust conformal predictioncited by 25
2024Boosted Conformal Prediction Intervalscited by 25
2024Conformal Prediction: A Data Perspectivecited by 25
2025Minimum Volume Conformal Sets for Multivariate Regressioncited by 25
2021Locally Valid and Discriminative Prediction Intervals for Deep Learning Modelscited by 24
2023Conformal Prediction with Missing Valuescited by 24
2023Adaptive conformal classification with noisy labelscited by 24
2023Feature Importance: A Closer Look at Shapley Values and LOCOcited by 23
2023Conformal Meta-learners for Predictive Inference of Individual Treatment Effectscited by 23
2024Adaptive Bounding Box Uncertainties via Two-Step Conformal Predictioncited by 23

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