Literature
Literature
A working bibliography of conformal prediction, by topic. For papers that put it to work where coverage is genuinely the objective, see the applications page. For where it all sits relative to the information gap, see the map and the connections.
Curated with one filter, in keeping with the rest of the site: keep the careful methodology and the foundational theory, and the work that states the guarantee precisely; skip material that pitches conformal prediction as improving a forecast or delivering “reliable uncertainty” with the marginal-coverage caveat left out. Descriptions are our own one-line readings, not the papers’ abstracts. Corrections welcome.
Start here: surveys, books, foundations
- Angelopoulos & Bates (2023). A gentle introduction to conformal prediction and distribution-free uncertainty quantification. FnT in ML. arXiv:2107.07511 — the friendliest entry point, with code.
- Shafer & Vovk (2008). A tutorial on conformal prediction. JMLR. jmlr.org — self-contained, by a co-inventor.
- Vovk, Gammerman & Shafer (2005; 2nd ed. 2022). Algorithmic Learning in a Random World. Springer. link — the founding monograph.
- Angelopoulos, Barber & Bates (2024). Theoretical foundations of conformal prediction. arXiv:2411.11824 — the exchangeability/permutation machinery in full.
- Fontana, Zeni & Vantini (2023). Conformal prediction: a unified review of theory and new challenges. Bernoulli. arXiv:2005.07972
- Campos, Farinhas, Zerva, Figueiredo & Martins (2024). Conformal prediction for natural language processing: a survey. TACL. arXiv:2405.01976
- Manokhin (2023). Practical Guide to Applied Conformal Prediction in Python. Packt (book).
The alrw.net working papers
Vovk and collaborators keep the working-paper series behind Algorithmic Learning in a Random World at alrw.net — the field’s primary source, often ahead of the journal versions. Several entries appear elsewhere on this page in their published forms; the complete series is folded here.
The complete series (48 working papers)
- #1. On-line predictive linear regression. Vovk, Nouretdinov & Gammerman. Annals of Statistics 37:1566–1590 (2009). pdf
- #2. Hedging predictions in machine learning. Gammerman & Vovk. Computer Journal 50:151–177 (2007). pdf
- #3. A tutorial on conformal prediction. Shafer & Vovk. JMLR 9:371–421 (2008). pdf
- #4. Plug-in martingales for testing exchangeability on-line. Fedorova, Gammerman, Nouretdinov & Vovk. ICML 2012. pdf
- #5. Conditional validity of inductive conformal predictors. Vovk. Machine Learning 92:349–376 (2013). pdf
- #6. Cross-conformal predictors. Vovk. Ann. Math. Artif. Intell.. pdf
- #7. Venn–Abers predictors. Vovk & Petej. UAI 2014. pdf
- #8. Transductive conformal predictors. Vovk. IJAIT 24(6) (2015). pdf
- #9. Conformal prediction under hypergraphical models. Fedorova, Gammerman, Nouretdinov & Vovk. IJAIT 24(6) (2015). pdf
- #10. Efficiency of conformalized ridge regression. Burnaev & Vovk. COLT 2014. pdf
- #11. Criteria of efficiency for conformal prediction. Vovk, Fedorova, Nouretdinov & Gammerman. Ann. Math. Artif. Intell. (COPA 2016). pdf
- #12. From conformal to probabilistic prediction. Vovk, Petej & Fedorova. COPA 2014. pdf
- #13. Large-scale probabilistic prediction with and without validity guarantees. Vovk, Petej & Fedorova. NIPS 2015. pdf
- #14. Universal probability-free prediction. Vovk & Pavlovic. Ann. Math. Artif. Intell. (COPA 2016). pdf
- #15. On the concept of Bernoulliness. Vovk. pdf
- #16. Test statistics and p-values. Gurevich & Vovk. COPA 2019. pdf
- #17. Nonparametric predictive distributions based on conformal prediction. Vovk, Shen, Manokhin & Xie. Machine Learning (2019). pdf
- #18. Universally consistent conformal predictive distributions. Vovk. Pattern Recognition 126 (2022). pdf
- #19. Conformal predictive decision making. Vovk & Bendtsen. COPA 2018. pdf
- #20. Conformal predictive distributions with kernels. Vovk, Nouretdinov, Manokhin & Gammerman. Braverman Readings. pdf
- #21. Combining p-values via averaging. Vovk & Wang. Biometrika 107:791–808 (2020). pdf
- #22. Computationally efficient versions of conformal predictive distributions. Vovk, Nouretdinov, Manokhin & Gammerman. Neurocomputing 397 (2020). pdf
- #23. Conformal calibrators. Vovk, Petej, Toccaceli & Gammerman. COPA 2020. pdf
- #24. Testing randomness online. Vovk. Statistical Science 36:595–611 (2021). pdf
- #25. Non-algorithmic theory of randomness. Vovk. Gurevich Festschrift (2020). pdf
- #26. Conformal e-prediction. Vovk. Pattern Recognition 166 (2025). pdf
- #27. Confidence and discoveries with e-values. Vovk & Wang. Statistical Science 38:329–354 (2023). pdf
- #28. Training conformal predictors. Colombo & Vovk. COPA 2020. pdf
- #29. Conformal e-testing. Vovk, Nouretdinov & Gammerman. Pattern Recognition 168 (2025). pdf
- #30. Conformal predictive distributions: an approach to nonparametric fiducial prediction. Vovk. Handbook of Bayesian, Fiducial, and Frequentist Inference. pdf
- #31. Testing for concept shift online. Vovk. pdf
- #32. Retrain or not retrain: conformal test martingales for change-point detection. Vovk, Petej, Nouretdinov, Ahlberg, Carlsson & Gammerman. COPA 2021. pdf
- #33. Conformal testing in a binary model situation. Vovk. COPA 2021. pdf
- #34. Protected probabilistic regression. Vovk. pdf
- #35. Protected probabilistic classification. Vovk, Petej & Gammerman. pdf
- #36. Conformal testing: binary case with Markov alternatives. Vovk, Nouretdinov & Gammerman. COPA 2022. pdf
- #37. The power of forgetting in statistical hypothesis testing. Vovk. COPA 2023. pdf
- #38. Testing exchangeability in the batch mode with e-values and Markov alternatives. Vovk. Machine Learning 114 (2025). pdf
- #39. An optimality property of the Bayes–Kelly algorithm. Vovk. pdf
- #40. Conditionality principle under unconstrained randomness. Vovk. Statistical Science 41:218–221 (2026). pdf
- #41. Validity and efficiency of the conformal CUSUM procedure. Vovk, Nouretdinov & Gammerman. COPA 2025. pdf
- #42. Randomness, exchangeability, and conformal prediction. Vovk. Gammerman Festschrift. pdf
- #43. Universality of conformal prediction under the assumption of randomness. Vovk. ALT 2026. pdf
- #44. Inductive randomness predictors: beyond conformal. Vovk. COPA 2025. pdf
- #45. Exchangeability and randomness for infinite and finite sequences. Vovk. pdf
- #46. Conformal e-prediction in the presence of confounding. Vovk & Wang. pdf
- #47. Inductive Venn–Abers and related regressors. Petej & Vovk. COPA 2026, to appear. pdf
- #48. Aggregation in conformal e-classification. Vovk. COPA 2026, to appear. pdf
Origins and the core method
- Vovk, Gammerman & Saunders (1999). Machine-learning applications of algorithmic randomness. ICML — the precursor: confidence from algorithmic randomness.
- Saunders, Gammerman & Vovk (1999). Transduction with confidence and credibility. IJCAI — transductive (full) conformal in embryo.
- Papadopoulos, Proedrou, Vovk & Gammerman (2002). Inductive confidence machines for regression. ECML — the split conformal predictor, the cheap variant now standard.
- Vovk (2015). Cross-conformal predictors. Ann. Math. Artif. Intell. — a CV/inductive hybrid.
- Dümbgen, Igl & Munk (2008). P-values for classification. EJS. arXiv:0801.2934 — an independent near-discovery of conformal p-values, from the nonparametrics literature.
- Lei, G’Sell, Rinaldo, Tibshirani & Wasserman (2018). Distribution-free predictive inference for regression. JASA. arXiv:1604.04173 — the canonical full/split/locally-weighted regression treatment.
Validity, exchangeability, and the limits
- Lei & Wasserman (2014). Distribution-free prediction bands for non-parametric regression. JRSS-B. doi — the first no-go: finite-length conditional coverage is impossible distribution-free.
- Foygel Barber, Candès, Ramdas & Tibshirani (2021). The limits of distribution-free conditional predictive inference. Information and Inference. arXiv:1903.04684 — even approximate subgroup coverage is essentially unattainable.
- Vovk (2012). Conditional validity of inductive conformal predictors. ACML. arXiv:1209.2673 — object/label-conditional validity, the calibration-conditional Beta law, and the germ of the conditional-validity no-go.
- Shah & Peters (2020). The hardness of conditional independence testing and the generalised covariance measure. Annals of Statistics. arXiv:1804.07203 — no finite-sample valid conditional-independence test has nontrivial power; why conditional coverage can be detected but never certified.
- Barber (2020). Is distribution-free inference possible for binary regression? EJS. arXiv:2004.09477 — an explicit lower bound on the length of any distribution-free interval for a conditional probability.
- Gupta, Podkopaev & Ramdas (2020). Distribution-free binary classification: prediction sets, confidence intervals and calibration. NeurIPS. arXiv:2006.10564 — distribution-free calibration with continuous features is possible only through binning; the tripod connecting sets, intervals, and calibration.
- Medarametla & Candès (2021). Distribution-free conditional median inference. arXiv:2102.07967 — sharp limits on distribution-free confidence intervals for the conditional median.
- Bian & Barber (2023). Training-conditional coverage for distribution-free predictive inference. EJS. arXiv:2205.03647 — split has it; full and jackknife+ do not, without assumptions.
- Liang & Barber (2025). Algorithmic stability implies training-conditional coverage. Annals of Statistics. arXiv:2311.04295
- Kuchibhotla (2020). Exchangeability, conformal prediction, and rank tests. arXiv:2005.06095 — conformal as a classical rank test.
- Marques F. (2025). Universal distribution of the empirical coverage in split conformal prediction. Stat. & Prob. Letters. arXiv:2303.02770 — the exact Beta law of calibration-conditional coverage.
- Barber & Tibshirani (2025). Unifying different theories of conformal prediction. arXiv:2504.02292 — one frame for the many robustness-to-non-exchangeability results, each as an explicit deviation from exchangeability.
Game-theoretic foundations, e-values, exchangeability testing
- Shafer & Vovk (2019). Game-Theoretic Foundations for Probability and Finance. Wiley — the martingale-betting backdrop for conformal testing.
- Vovk, Nouretdinov & Gammerman (2003). Testing exchangeability on-line. ICML — conformal test martingales for monitoring the assumption.
- Fedorova, Gammerman, Nouretdinov & Vovk (2012). Plug-in martingales for testing exchangeability on-line. ICML. arXiv:1204.3251
- Vovk & Wang (2021). E-values: calibration, combination, and applications. Annals of Statistics. arXiv:1912.06116
- Vovk (2025). Randomness, exchangeability, and conformal prediction. arXiv:2501.11689
Regression and interval methods
- Lei, Robins & Wasserman (2013). Distribution-free prediction sets. JASA. arXiv:1111.1418 — the efficiency benchmark: conformal regions that asymptotically match the optimal density level set.
- Romano, Patterson & Candès (2019). Conformalized quantile regression. NeurIPS. arXiv:1905.03222 — conformalize a quantile model for heteroscedastic-adaptive intervals.
- Foygel Barber, Candès, Ramdas & Tibshirani (2021). Predictive inference with the jackknife+. Annals of Statistics. arXiv:1905.02928 — jackknife+ and CV+, leave-one-out with provable coverage.
- Gupta, Kuchibhotla & Ramdas (2022). Nested conformal prediction and quantile out-of-bag ensembles. Pattern Recognition. arXiv:1910.10562 — conformal as calibrating nested sets.
- Papadopoulos, Gammerman & Vovk (2008). Normalized nonconformity measures for regression conformal prediction. IASTED AIA — locally-weighted, variable-width intervals.
- Sesia & Candès (2020). A comparison of some conformal quantile regression methods. Stat. arXiv:1909.05433
- Kivaranovic, Johnson & Leeb (2020). Adaptive, distribution-free prediction intervals for deep networks. AISTATS. PMLR
- Sesia & Romano (2021). Conformal prediction using conditional histograms. NeurIPS. arXiv:2105.08747 — shortest intervals from a conditional histogram.
- Lei, Rinaldo & Wasserman (2015). A conformal prediction approach to explore functional data. Ann. Math. Artif. Intell. arXiv:1302.6452 — bands for curves rather than scalars.
Conditional coverage: methods and guarantees
- Romano, Barber, Sabatti & Candès (2020). With malice toward none: assessing uncertainty via equalized coverage. HDSR. arXiv:1908.05428 — equal coverage across protected groups.
- Guan (2023). Localized conformal prediction. Biometrika. doi — reweight calibration toward a local neighbourhood.
- Hore & Barber (2025). Conformal prediction with local weights: randomization enables local guarantees. JRSS-B. arXiv:2310.07850 — randomized local weights buy a genuine local guarantee.
- Jung, Noarov, Ramalingam & Roth (2023). Batch multivalid conformal prediction. ICLR. arXiv:2209.15145 — the multicalibration bridge.
- Cauchois, Gupta & Duchi (2021). Knowing what you know: valid and validated confidence sets. JMLR. arXiv:2004.10181 — the worst-slab coverage diagnostic.
- Gibbs, Cherian & Candès (2025). Conformal prediction with conditional guarantees. JRSS-B. arXiv:2305.12616 — exact coverage over a finite-dimensional class of shifts.
Conditional coverage: diagnostics and calibration tests
- Diebold, Gunther & Tay (1998). Evaluating density forecasts. Int. Economic Review — the PIT: a calibrated forecast gives i.i.d. uniform PIT values.
- Gneiting, Balabdaoui & Raftery (2007). Probabilistic forecasts, calibration and sharpness. JRSS-B — the maximize-sharpness-subject-to-calibration frame.
- Widmann, Lindsten & Zachariah (2019). Calibration tests in multi-class classification. NeurIPS. arXiv:1910.11385 — kernel calibration error with a hypothesis test.
- Widmann, Lindsten & Zachariah (2021). Calibration tests beyond classification. ICLR. arXiv:2210.13355
- Feldman, Bates & Romano (2021). Improving conditional coverage via orthogonal quantile regression. NeurIPS. arXiv:2106.00394 — HSIC between the miscoverage indicator and interval length.
- Braun, Holzmüller, Jordan & Bach (2025). Conditional coverage diagnostics for conformal prediction (ERT). arXiv:2512.11779 — classify the coverage indicator on the features.
- Cotton (2026). A Feynman–Wigner diagnostic for conformal prediction. this site — distance covariance between the conformal rank and the features, the runnable, level-free check.
Classification
- Sadinle, Lei & Wasserman (2019). Least ambiguous set-valued classifiers with bounded error levels. JASA. arXiv:1609.00451 — smallest sets at a fixed error level, marginal or per-class.
- Romano, Sesia & Candès (2020). Classification with valid and adaptive coverage (APS). NeurIPS. arXiv:2006.02544
- Angelopoulos, Bates, Jordan & Malik (2021). Uncertainty sets for image classifiers using conformal prediction (RAPS). ICLR. arXiv:2009.14193
- Ding, Angelopoulos, Bates, Jordan & Tibshirani (2023). Class-conditional conformal prediction with many classes (clustered). NeurIPS. arXiv:2306.09335
- Vovk & Petej (2014). Venn–Abers predictors. UAI. arXiv:1211.0025 — calibrated probability intervals via isotonic regression.
- Vovk, Lindsay, Nouretdinov & Gammerman (2003). Mondrian confidence machine. RHUL tech report — per-category (label-conditional) validity.
Risk control and beyond coverage
- Bates, Angelopoulos, Lei, Malik & Jordan (2021). Distribution-free, risk-controlling prediction sets (RCPS). JACM. arXiv:2101.02703 — control any bounded loss with high probability.
- Angelopoulos, Bates, Fisch, Lei & Schuster (2024). Conformal risk control. ICLR. arXiv:2208.02814 — control the expectation of any monotone loss; coverage is the 0–1 case.
- Angelopoulos, Bates, Candès, Jordan & Lei (2021). Learn then test: calibrating predictive algorithms to achieve risk control. arXiv:2110.01052 — risk control as multiple testing over configurations.
- Laufer-Goldshtein, Fisch, Barzilay & Jaakkola (2023). Efficiently controlling multiple risks with Pareto testing. ICLR. arXiv:2210.07913
Selection, outliers, and novelty
- Bates, Candès, Lei, Romano & Sesia (2023). Testing for outliers with conformal p-values. Annals of Statistics. arXiv:2104.08279 — conformal prediction’s most natural home: a distribution-free test.
- Marandon, Lei, Mary & Roquain (2024). Adaptive novelty detection with false discovery rate guarantee (AdaDetect). Annals of Statistics. arXiv:2208.06685
- Guan & Tibshirani (2022). Prediction and outlier detection in classification problems (BCOPS). JRSS-B. arXiv:1905.04396
- Jin & Candès (2023). Selection by prediction with conformal p-values. JMLR. arXiv:2210.01408 — shortlist with FDR control.
- Fisch, Schuster, Jaakkola & Barzilay (2022). Conformal prediction sets with limited false positives. ICML. arXiv:2202.07650 — cap the expected number of wrong labels in the set, not just the miss rate.
- Laxhammar & Falkman (2015). Inductive conformal anomaly detection for sequential detection of anomalous sub-trajectories. Ann. Math. Artif. Intell. — calibrated alarm rates online.
Conformal training and efficiency
- Stutz, Dvijotham, Cemgil & Doucet (2022). Learning optimal conformal classifiers (ConfTr). ICLR. arXiv:2110.09192 — differentiate through conformalization to train for small sets.
- Einbinder, Romano, Sesia & Zhou (2022). Training uncertainty-aware classifiers with conformalized deep learning. NeurIPS. arXiv:2205.05878
- Yang & Kuchibhotla (2025). Selection and aggregation of conformal prediction sets. JASA. arXiv:2104.13871 — pick the score that gives the smallest valid set.
- Kiyani, Pappas & Hassani (2024). Length optimization in conformal prediction. NeurIPS. arXiv:2406.18814
- Einbinder, Feldman, Bates, Angelopoulos, Gendler & Romano (2022). Label noise robustness of conformal prediction. arXiv:2209.14295
- Gendler, Weng, Daniel & Romano (2022). Adversarially robust conformal prediction (RSCP). ICLR. openreview
Distribution shift and weighted conformal
- Tibshirani, Foygel Barber, Candès & Ramdas (2019). Conformal prediction under covariate shift. NeurIPS. arXiv:1904.06019 — weighted exchangeability when the likelihood ratio is known.
- Podkopaev & Ramdas (2021). Distribution-free uncertainty quantification for classification under label shift. UAI. arXiv:2103.03323
- Park, Dobriban, Lee & Bastani (2022). PAC prediction sets under covariate shift. ICLR. arXiv:2106.09848
- Prinster, Liu & Saria (2022). JAWS: auditing predictive uncertainty under covariate shift. NeurIPS. arXiv:2207.10716 — weighted jackknife+.
- Fannjiang, Bates, Angelopoulos, Listgarten & Jordan (2022). Conformal prediction under feedback covariate shift for biomolecular design. PNAS. arXiv:2202.03613 — exact coverage when the model chooses its own next inputs.
- Prinster, Stanton, Liu & Saria (2024). Conformal validity guarantees exist for any data distribution (and how to find them). ICML. arXiv:2405.06627 — weighted conformal extends in principle to any joint distribution; the catch is that you must know the weights, which a time series rarely tells you.
Time series and non-exchangeability
A guided tour of this section, which game each result plays and what remains open, is on the time-series pages: the coverage games and conditional coverage and sharpness.
Two threads run through this literature. One modifies the method to survive dependence — blocks, ensembles, weights, fitted residual quantiles. The other leaves split conformal untouched and prices the damage: how much coverage does temporal dependence actually cost? That accounting is now essentially settled, and the answer is remarkably benign: the loss is (dependence range) / (calibration size), linear and tight, with a matching bound against over-coverage. First the accounting:
- Barber, Candès, Ramdas & Tibshirani (2023). Conformal prediction beyond exchangeability. Annals of Statistics. arXiv:2202.13415 — the general-purpose robustness result: the coverage gap bounded by a total-variation term per calibration point. But swapping single points is the wrong deformation for a time series (under short-range dependence the TV term stays large), which is what the two entries below repair.
- Oliveira, Orenstein, Ramos & Romano (2024). Split conformal prediction and non-exchangeable data. JMLR. arXiv:2203.15885 — blocking plus empirical-process concentration: unmodified split conformal on a β-mixing series loses at most on the order of √(tmix/n) of its coverage. The first general no-modification guarantee, at the classical square-root rate.
- Barber & Pananjady (2026). Predictive inference for time series: why is split conformal effective despite temporal dependence? ALT. arXiv:2510.02471 — the sharp accounting. A “switch coefficient” (the total variation between the score sequence and a copy with a block of τ entries deleted and one point rotated to the end) bounds the coverage loss by minτ {τ/n + 2β(τ)} — linear in τ/n where blocking arguments gave the square root, tight over stationary β-mixing processes, and paired with a matching upper bound so the set cannot silently over-cover either. Handles predictors with memory L (an extra L/n) and calibration-trained scores (a second buffer τ∗ after the training block). The trick is quantile stability under insertion and deletion rather than concentration. The best explanation yet of why vanilla split conformal works on time series.
- Chernozhukov, Wüthrich & Zhu (2018). Exact and robust conformal inference for dependent data. COLT. arXiv:1802.06300 — permute blocks rather than points: approximately valid under ergodicity, exact under block-exchangeability.
- Chernozhukov, Wüthrich & Zhu (2021). Distributional conformal prediction. PNAS. arXiv:1909.07889 — probability-integral-transform scores with permuted estimated ranks; built for dependent-data uses such as k-step forecasts, synthetic controls, and counterfactuals.
- Nettasinghe, Chatterjee, Tipireddy & Halappanavar (2023). Extending conformal prediction to hidden Markov models with exact validity via de Finetti’s theorem for Markov chains. arXiv:2210.02271 — block exchangeability inside a Markov chain restores exact validity; the de Finetti thread in a temporal setting.
- Zheng & Proutiere (2024). Conformal predictions under Markovian data. arXiv:2407.15277 — the coverage gap under Markov sampling, analyzed directly.
Background for the bounds above, from the mixing literature:
- Doukhan (1994). Mixing: properties and examples. Springer — the standard reference for β-mixing coefficients.
- Yu (1994). Rates of convergence for empirical processes of stationary mixing sequences. Annals of Probability — the blocking technique behind most square-root-rate analyses under mixing.
- Mohri & Rostamizadeh (2010). Stability bounds for stationary φ-mixing and β-mixing processes. JMLR. jmlr.org — generalization under dependence, same toolbox.
And the modified methods:
- Stankevičiūtė, Alaa & van der Schaar (2021). Conformal time-series forecasting. NeurIPS. proceedings — Bonferroni across horizons for RNN forecasts; the guarantee runs across independent series, not along a single path.
- Xu & Xie (2021; TPAMI 2023). Conformal prediction interval for dynamic time-series (EnbPI). ICML. arXiv:2010.09107 — out-of-bag ensemble residuals along a single series; approximate coverage under strongly-mixing errors and a consistent predictor — the second assumption is the one a black box may not honour.
- Xu & Xie (2023). Sequential predictive conformal inference for time series (SPCI). ICML. arXiv:2212.03463 — replaces the empirical residual quantile with a fitted conditional quantile of recent residuals.
- Lin, Trivedi & Sun (2022). Conformal prediction with temporal quantile adjustments (TQA). NeurIPS. arXiv:2205.09940 — adjusts the quantile level per time step from recent errors.
- Sun & Yu (2024). Copula conformal prediction for multi-step time series (CopulaCPTS). ICLR. arXiv:2212.03281 — a copula across horizons for joint multi-step coverage.
- Auer, Gauch, Klotz & Hochreiter (2023). Conformal prediction for time series with modern Hopfield networks (HopCPT). NeurIPS. arXiv:2303.12783 — attention over similar past regimes to reweight residuals.
Online and adaptive
- Gibbs & Candès (2021). Adaptive conformal inference under distribution shift (ACI). NeurIPS. arXiv:2106.00170 — long-run time-average coverage, no distributional assumptions.
- Gibbs & Candès (2024). Conformal inference for online prediction with arbitrary distribution shifts. JMLR. arXiv:2208.08401
- Zaffran, Féron, Goude, Josse & Dieuleveut (2022). Adaptive conformal predictions for time series (AgACI). ICML. arXiv:2202.07282
- Bhatnagar, Wang, Xiong & Bai (2023). Improved online conformal prediction via strongly adaptive online learning. ICML. arXiv:2302.07869
- Angelopoulos, Candès & Tibshirani (2023). Conformal PID control for time series prediction. NeurIPS. arXiv:2307.16895
- Podkopaev, Xu & Lee (2024). Adaptive conformal inference by betting. arXiv:2412.19318 — the ACI step size replaced by a betting scheme; parameter-free adaptation, in the game-theoretic spirit.
- Yang, Candès & Lei (2024). Bellman conformal inference: calibrating prediction intervals for time series. arXiv:2402.05203 — the rare entry that makes width the objective: minimize average interval length subject to long-run coverage, by dynamic programming over multi-step forecasts. It optimizes width; the guarantee remains long-run coverage, and no distribution-free width theorem exists in this thread.
Network and relational data
- Lunde, Levina & Zhu (2023). Conformal prediction for network-assisted regression. arXiv:2302.10095 — regression with network covariates, with exchangeability supplied by the sampling design.
- Lunde (2023). On the validity of conformal prediction for network data under non-uniform sampling. arXiv:2306.07252 — which subgraph-sampling schemes leave the scores exchangeable, and which quietly do not.
Conformal predictive distributions and systems
- Vovk, Shen, Manokhin & Xie (2019). Nonparametric predictive distributions based on conformal prediction. Machine Learning. link — a full predictive distribution with finite-sample validity.
- Vovk, Nouretdinov, Manokhin & Gammerman (2018). Cross-conformal predictive distributions. COPA. PMLR
- Vovk, Petej, Nouretdinov, Manokhin & Gammerman (2019). Computationally efficient versions of conformal predictive distributions. Neurocomputing. arXiv:1911.00941
- Boström, Johansson & Löfström (2021). Mondrian conformal predictive distributions. COPA. PMLR — shape and location vary per region.
- Boström (2022). crepes: a Python package for conformal regressors and predictive systems. COPA. PMLR
Connections: information theory, proper scores, Bayes, fiducial
- Correia, Massoli, Louizos & Behboodi (2024). An information theoretic perspective on conformal prediction. NeurIPS. arXiv:2405.02140 — set size bounds the conditional entropy.
- Hoff (2023). Bayes-optimal prediction with frequentist coverage control. Bernoulli. arXiv:2105.14045
- Fong & Holmes (2021). Conformal Bayesian computation. NeurIPS. arXiv:2106.06137
- Fong, Holmes & Walker (2023). Martingale posteriors. JRSS-B (with discussion) — Bayesian uncertainty as uncertainty over future data.
- Cella & Martin (2022). Validity, consonant plausibility measures, and conformal prediction. Int. J. Approx. Reasoning. arXiv:2001.09225 — the fiducial / imprecise-probability reading.
- Gneiting & Raftery (2007). Strictly proper scoring rules, prediction, and estimation. JASA — the log score and CRPS as the right graders.
- Cotton. Marginally Useful, the Feynman–Wigner note, Betting Against a Conformal Predictor, The Width of the Conformal Fan, A Contragredient View of Conformal Placement and Steinitz Balancing, and The Two Prices of Dependence. this site — the coverage–sharpness gap as the mutual information I(R;X), the sign of the de Finetti measure, the gap as the parimutuel rent an X-informed bettor extracts, the sign of dependence as the width of the realized-coverage fan, conformal placement as a Steinitz balancing problem, and dependence priced twice — a coverage tax that vanishes with n and a sharpness rent (the entropy-rate gap) that does not.
- Snell & Griffiths (2025). Conformal prediction as Bayesian quadrature. ICML. arXiv:2502.13228 — Dirichlet quantile spacings give a distribution-free posterior over realized risk: conformal risk control is its mean, and their HPD rule reports the quantile instead. A data-conditional guarantee, conditional on the calibration draw — it crosses the fan, not the information gap.
Causal inference, treatment effects, and survival
- Lei & Candès (2021). Conformal inference of counterfactuals and individual treatment effects. JRSS-B. arXiv:2006.06138
- Chernozhukov, Wüthrich & Zhu (2021). An exact and robust conformal inference method for counterfactual and synthetic controls. JASA. arXiv:1712.09089 — permutation-based inference for synthetic-control counterfactuals.
- Candès, Lei & Ren (2023). Conformalized survival analysis. JRSS-B. arXiv:2103.09763 — calibrated lower bounds on survival time under censoring.
- Gui, Hore, Ren & Barber (2024). Conformalized survival analysis with adaptive cut-offs. Biometrika. arXiv:2211.01227
- Jin, Ren & Candès (2023). Sensitivity analysis of individual treatment effects: a robust conformal inference approach. PNAS. arXiv:2111.12161
- Yin, Shi, Wang & Blei (2024). Conformal sensitivity analysis for individual treatment effects. JASA. arXiv:2112.03493
Language models and generation
- Quach, Fisch, Schuster, Yala, Sohn, Jaakkola & Barzilay (2024). Conformal language modeling. ICLR. arXiv:2306.10193 — a calibrated stopping rule so a generated set contains an acceptable answer.
- Mohri & Hashimoto (2024). Language models with conformal factuality guarantees. ICML. arXiv:2402.10978 — back off to less specific claims until factuality holds.
- Kumar, Lu, Gupta, et al. (2023). Conformal prediction with large language models for multi-choice question answering. arXiv:2305.18404
- Su, Luo, Wang & Cheng (2024). API is enough: conformal prediction for LLMs without logit-access. EMNLP Findings. arXiv:2403.01216
- Ren et al. (2023). Robots that ask for help: uncertainty alignment for LLM planners (KnowNo). CoRL. arXiv:2307.01928
Software
- Python: MAPIE, crepes, TorchCP, PUNCC, Fortuna, conformal-prediction (examples), nonconformist (legacy).
- R: conformalInference, probably (tidymodels), AdaptiveConformal. Julia: ConformalPrediction.jl.
Talks
- Candès. Conformal prediction in 2022 (NeurIPS keynote). neurips.cc
- 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.
Using conformal prediction in your own project? Tell Claude: “Read https://conformalprediction.net/SKILL.md and create a project skill from it.” It adds a check for whether your coverage is conditionally trustworthy.