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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…

Statistics Theory · Mathematics 2026-03-09 Anastasios N. Angelopoulos , Rina Foygel Barber , Stephen Bates

Conformal Prediction methods have finite-sample distribution-free marginal coverage guarantees. However, they generally do not offer conditional coverage guarantees, which can be important for high-stakes decisions. In this paper, we…

Machine Learning · Statistics 2024-09-27 Ruijiang Gao , Mingzhang Yin , James McInerney , Nathan Kallus

Science and technology have a growing need for effective mechanisms that ensure reliable, controlled performance from black-box machine learning algorithms. These performance guarantees should ideally hold conditionally on the input-that is…

Machine Learning · Computer Science 2025-03-28 Vincent Blot , Anastasios N Angelopoulos , Michael I Jordan , Nicolas J-B Brunel

We consider the problem of constructing distribution-free prediction sets with finite-sample conditional guarantees. Prior work has shown that it is impossible to provide exact conditional coverage universally in finite samples. Thus, most…

Methodology · Statistics 2024-09-18 Isaac Gibbs , John J. Cherian , Emmanuel J. Candès

Conformal prediction is an assumption-lean approach to generating distribution-free prediction intervals or sets, for nearly arbitrary predictive models, with guaranteed finite-sample coverage. Conformal methods are an active research topic…

Methodology · Statistics 2024-01-19 Jerzy Wieczorek

While the predictions produced by conformal prediction are set-valued, the data used for training and calibration is supposed to be precise. In the setting of superset learning or learning from partial labels, a variant of weakly supervised…

Machine Learning · Computer Science 2023-06-05 Alireza Javanmardi , Yusuf Sale , Paul Hofman , Eyke Hüllermeier

Conformal Prediction (CP) is a popular method for uncertainty quantification with machine learning models. While conformal prediction provides probabilistic guarantees regarding the coverage of the true label, these guarantees are agnostic…

Machine Learning · Computer Science 2025-10-21 Aditya T. Vadlamani , Anutam Srinivasan , Pranav Maneriker , Ali Payani , Srinivasan Parthasarathy

We give a simple, generic conformal prediction method for sequential prediction that achieves target empirical coverage guarantees against adversarially chosen data. It is computationally lightweight -- comparable to split conformal…

Machine Learning · Computer Science 2022-06-03 Osbert Bastani , Varun Gupta , Christopher Jung , Georgy Noarov , Ramya Ramalingam , Aaron Roth

We introduce Conformal Decision Theory, a framework for producing safe autonomous decisions despite imperfect machine learning predictions. Examples of such decisions are ubiquitous, from robot planning algorithms that rely on pedestrian…

Credal sets are sets of probability distributions that are considered as candidates for an imprecisely known ground-truth distribution. In machine learning, they have recently attracted attention as an appealing formalism for uncertainty…

Machine Learning · Statistics 2024-02-19 Alireza Javanmardi , David Stutz , Eyke Hüllermeier

Conformal prediction has emerged as an effective strategy for uncertainty quantification by modifying a model to output sets of labels instead of a single label. These prediction sets come with the guarantee that they contain the true label…

Machine Learning · Computer Science 2025-05-28 Haosen Ge , Hamsa Bastani , Osbert Bastani

Conformal predictive systems allow forecasters to issue predictive distributions for real-valued future outcomes that have out-of-sample calibration guarantees. On a more abstract level, conformal prediction makes use of in-sample…

Methodology · Statistics 2025-03-07 Sam Allen , Georgios Gavrilopoulos , Alexander Henzi , Gian-Reto Kleger , Johanna Ziegel

This paper develops a conformal method to compute prediction intervals for non-parametric regression that can automatically adapt to skewed data. Leveraging black-box machine learning algorithms to estimate the conditional distribution of…

Methodology · Statistics 2021-10-26 Matteo Sesia , Yaniv Romano

We investigate generically applicable and intuitively appealing prediction intervals based on $k$-fold cross validation. We focus on the conditional coverage probability of the proposed intervals, given the observations in the training…

Statistics Theory · Mathematics 2022-05-13 Lukas Steinberger , Hannes Leeb

Most existing examples of full conformal predictive systems, split-conformal predictive systems, and cross-conformal predictive systems impose severe restrictions on the adaptation of predictive distributions to the test object at hand. In…

Machine Learning · Computer Science 2019-02-19 Vladimir Vovk , Ivan Petej , Paolo Toccaceli , Alex Gammerman

We consider the problem of distribution-free conformal prediction and the criterion of group conditional validity. This criterion is motivated by many practical scenarios including hidden stratification and group fairness. Existing methods…

Machine Learning · Computer Science 2023-03-21 Samuel Deng , Navid Ardeshir , Daniel Hsu

We develop a new approach to multi-label conformal prediction in which we aim to output a precise set of promising prediction candidates with a bounded number of incorrect answers. Standard conformal prediction provides the ability to adapt…

Machine Learning · Computer Science 2022-02-16 Adam Fisch , Tal Schuster , Tommi Jaakkola , Regina Barzilay

Conformal prediction is a distribution-free technique for establishing valid prediction intervals. Although conventionally people conduct conformal prediction in the output space, this is not the only possibility. In this paper, we propose…

Machine Learning · Computer Science 2023-04-11 Jiaye Teng , Chuan Wen , Dinghuai Zhang , Yoshua Bengio , Yang Gao , Yang Yuan

Conformal prediction has emerged as a widely used framework for constructing valid prediction sets in classification and regression tasks. In this work, we extend the split conformal prediction framework to hierarchical classification,…

Machine Learning · Statistics 2026-04-13 Thomas Mortier , Alireza Javanmardi , Yusuf Sale , Eyke Hüllermeier , Willem Waegeman

In this paper, we focus on the problem of conformal prediction with conditional guarantees. Prior work has shown that it is impossible to construct nontrivial prediction sets with full conditional coverage guarantees. A wealth of research…

Machine Learning · Computer Science 2024-04-29 Shayan Kiyani , George Pappas , Hamed Hassani