Theory

Methods & theory

The careful methodology and the foundational results, by topic. For papers that put conformal prediction to work, see the applications page.

Curated with one filter, in keeping with the rest of the guide: keep the careful methodology and the foundational theory, and skip material that oversells, where conformal prediction is pitched as improving a forecast or delivering “reliable uncertainty” with the marginal-coverage caveat left out. For the exhaustive list (promotional entries and all), see Valeriy Manokhin’s Awesome Conformal Prediction (CC BY-NC-ND 4.0), from which much of this is drawn; the patterns study describes how the wheat was sorted from the chaff.

Start here: surveys and foundations

• Angelopoulos & Bates (2023). Conformal prediction: a gentle introduction. FnT in ML. arXiv:2107.07511, the friendliest entry point.
• Shafer & Vovk (2008). A tutorial on conformal prediction. JMLR. jmlr.org
• Vovk, Gammerman & Shafer (2022). Algorithmic Learning in a Random World (2nd ed.). Springer. link
• Angelopoulos, Barber & Bates (2024). Theoretical foundations of conformal prediction. arXiv:2411.11824

Validity, exchangeability, and the limits

• Lei & Wasserman (2014). Distribution-free prediction bands for non-parametric regression. JRSS-B.
• Foygel Barber, Candès, Ramdas & Tibshirani (2021). The limits of distribution-free conditional predictive inference. Information and Inference. arXiv:1903.04684
• Lei, G’Sell, Rinaldo, Tibshirani & Wasserman (2018). Distribution-free predictive inference for regression. JASA.
• Kuchibhotla (2020). Exchangeability, conformal prediction, and rank tests. arXiv:2005.06095
• Gneiting, Balabdaoui & Raftery (2007). Probabilistic forecasts, calibration and sharpness. JRSS-B, the calibration/sharpness frame.

Conditional coverage: diagnostics and approximations

• Braun, Holzmüller, Jordan & Bach (2025). Conditional coverage diagnostics for conformal prediction (ERT). arXiv:2512.11779
• Laplante (2026). A post-processing conformal approach for conditional coverage via pivotal scores. arXiv:2605.25852
• Gibbs, Cherian & Candès (2023). Conformal prediction with conditional guarantees. arXiv:2305.12616

Regression and quantile methods

• Romano, Patterson & Candès (2019). Conformalized quantile regression. NeurIPS. arXiv:1905.03222
• Foygel Barber, Candès, Ramdas & Tibshirani (2021). Predictive inference with the jackknife+. Annals of Statistics. arXiv:1905.02928
• Gupta, Kuchibhotla & Ramdas (2022). Nested conformal prediction and quantile out-of-bag ensembles. arXiv:1910.10562
• Toccaceli (2026). CRPS-optimal binning for univariate conformal regression. arXiv:2603.22000

Classification, calibration, and training

• Angelopoulos, Bates, Jordan & Malik (2021). Uncertainty sets for image classifiers using conformal prediction (RAPS). ICLR. arXiv:2009.14193
• Stutz, Dvijotham, Cemgil & Doucet (2022). Learning optimal conformal classifiers (conformal training). ICLR. arXiv:2110.09192
• Vovk & Petej (2014). Venn–Abers predictors. arXiv:1211.0025
• Angelopoulos, Bates, Fisch, Lei & Schuster (2024). Conformal risk control. ICLR.
• Einbinder, Bates, Angelopoulos, Gendler & Romano (2022). Conformal prediction is robust to label noise. arXiv:2209.14295

Time series and distribution shift

• Tibshirani, Foygel Barber, Candès & Ramdas (2019). Conformal prediction under covariate shift. NeurIPS. arXiv:1904.06019
• Gibbs & Candès (2021). Adaptive conformal inference under distribution shift (ACI). NeurIPS. arXiv:2106.00170
• Xu & Xie (2021). Conformal prediction interval for dynamic time-series (EnbPI). ICML. PMLR
• Xu & Xie (2023). Sequential predictive conformal inference for time series (SPCI). arXiv:2212.03463
• Zaffran, Féron, Goude, Josse & Dieuleveut (2022). Adaptive conformal predictions for time series (AgACI). ICML.
• Auer, Gauch, Klotz & Hochreiter (2023). Conformal prediction for time series with modern Hopfield networks (HopCPT). NeurIPS. arXiv:2303.12783
• Barber, Candès, Ramdas & Tibshirani (2023). Conformal prediction beyond exchangeability. Annals of Statistics. arXiv:2202.13415

Conformal predictive distributions and systems

• Vovk, Shen, Manokhin & Xie (2019). Nonparametric predictive distributions based on conformal prediction. Machine Learning. link
• Vovk, Nouretdinov, Manokhin & Gammerman (2018). Cross-conformal predictive distributions. PMLR. PMLR
• Boström, Johansson & Löfström (2021). Mondrian conformal predictive distributions. COPA.
• Correia, Massoli, Louizos & Behboodi (2024). An information theoretic perspective on conformal prediction. NeurIPS. arXiv:2405.02140

Software

• Python: MAPIE, crepes, TorchCP, PUNCC, nonconformist (legacy).
• R: conformalInference, tidymodels, AdaptiveConformal. Julia: ConformalPrediction.jl.

Talks

• Candès. Conformal prediction in 2022 (NeurIPS keynote). slideslive
• Jordan, Vovk & Wasserman, moderated by Ramdas. Panel (ICML 2021). slideslive

Applications

Papers that use conformal prediction where coverage or containment is genuinely the objective, selective prediction, anomaly detection, retrieval, language models, robotics and control, risk control, scientific discovery, causal inference, survival analysis, and medical imaging, are listed and discussed, by domain, on the applications page.