# Conformal prediction beyond exchangeability

arXiv: https://arxiv.org/abs/2202.13415 · HTML: https://mlsanity.com/paper/2202.13415/

## Key facts

- Cited by 355 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Feb 2022.

## Built on by (most cited first, 30 of 355)

- [Conformal Risk Control](https://mlsanity.com/paper/2208.02814/) (2022)
- [Language Models with Conformal Factuality Guarantees](https://mlsanity.com/paper/2402.10978/) (2024)
- [Conformal Inference for Online Prediction with Arbitrary Distribution Shifts](https://mlsanity.com/paper/2208.08401/) (2022)
- [Uncertainty Quantification over Graph with Conformalized Graph Neural Networks](https://mlsanity.com/paper/2305.14535/) (2023)
- [Improved Online Conformal Prediction via Strongly Adaptive Online Learning](https://mlsanity.com/paper/2302.07869/) (2023)
- [Sequential Predictive Conformal Inference for Time Series](https://mlsanity.com/paper/2212.03463/) (2022)
- [Training Uncertainty-Aware Classifiers with Conformalized Deep Learning](https://mlsanity.com/paper/2205.05878/) (2022)
- [Trustworthy clinical AI solutions: a unified review of uncertainty quantification in deep learning models for medical image analysis](https://mlsanity.com/paper/2210.03736/) (2022)
- [Online conformal prediction with decaying step sizes](https://mlsanity.com/paper/2402.01139/) (2024)
- [Conformal Prediction for Natural Language Processing: A Survey](https://mlsanity.com/paper/2405.01976/) (2024)
- [How to Trust Your Diffusion Model: A Convex Optimization Approach to Conformal Risk Control](https://mlsanity.com/paper/2302.03791/) (2023)
- [Credal Bayesian Deep Learning](https://mlsanity.com/paper/2302.09656/) (2023)
- [Conformal Prediction for Time Series with Modern Hopfield Networks](https://mlsanity.com/paper/2303.12783/) (2023)
- [LLM-as-a-Prophet: Understanding Predictive Intelligence with Prophet Arena](https://mlsanity.com/paper/2510.17638/) (2025)
- [Conformal prediction for multi-dimensional time series by ellipsoidal sets](https://mlsanity.com/paper/2403.03850/) (2024)
- [Predictive Inference with Feature Conformal Prediction](https://mlsanity.com/paper/2210.00173/) (2022)
- [Conformal Prediction for Federated Uncertainty Quantification Under Label Shift](https://mlsanity.com/paper/2306.05131/) (2023)
- [Non-Exchangeable Conformal Risk Control](https://mlsanity.com/paper/2310.01262/) (2023)
- [Distribution Free Prediction Sets for Node Classification](https://mlsanity.com/paper/2211.14555/) (2022)
- [Conformal Validity Guarantees Exist for Any Data Distribution (and How to Find Them)](https://mlsanity.com/paper/2405.06627/) (2024)
- [Conformal Prediction with Missing Values](https://mlsanity.com/paper/2306.02732/) (2023)
- [Adaptive conformal classification with noisy labels](https://mlsanity.com/paper/2309.05092/) (2023)
- [Conformal Prediction: A Data Perspective](https://mlsanity.com/paper/2410.06494/) (2024)
- [Conformal Meta-learners for Predictive Inference of Individual Treatment Effects](https://mlsanity.com/paper/2308.14895/) (2023)
- [Uncertainty in Graph Neural Networks: A Survey](https://mlsanity.com/paper/2403.07185/) (2024)
- [Multivariate Conformal Prediction using Optimal Transport](https://mlsanity.com/paper/2502.03609/) (2025)
- [Reliable Text-to-SQL with Adaptive Abstention](https://mlsanity.com/paper/2501.10858/) (2025)
- [Integrative conformal p-values for powerful out-of-distribution testing with labeled outliers](https://mlsanity.com/paper/2208.11111/) (2022)
- [Conformal Prediction for Class-wise Coverage via Augmented Label Rank Calibration](https://mlsanity.com/paper/2406.06818/) (2024)
- [Conformal Prediction for Causal Effects of Continuous Treatments](https://mlsanity.com/paper/2407.03094/) (2024)

## Abstract (arXiv)

Conformal prediction is a popular, modern technique for providing valid predictive inference for arbitrary machine learning models. Its validity relies on the assumptions of exchangeability of the data, and symmetry of the given model fitting algorithm as a function of the data. However, exchangeability is often violated when predictive models are deployed in practice. For example, if the data distribution drifts over time, then the data points are no longer exchangeable; moreover, in such settings, we might want to use a nonsymmetric algorithm that treats recent observations as more relevant. This paper generalizes conformal prediction to deal with both aspects: we employ weighted quantiles to introduce robustness against distribution drift, and design a new randomization technique to allow for algorithms that do not treat data points symmetrically. Our new methods are provably robust, with substantially less loss of coverage when exchangeability is violated due to distribution drift or other challenging features of real data, while also achieving the same coverage guarantees as existing conformal prediction methods if the data points are in fact exchangeable. We demonstrate the practical utility of these new tools with simulations and real-data experiments on electricity and election forecasting.