Distribution-free predictive inference for individual treatment effects is impossible: any valid set must have infinite expected length under standard assumptions with continuous covariates.
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Theoretical Foundations of Conformal Prediction
36 Pith papers cite this work. Polarity classification is still indexing.
36
Pith papers citing it
abstract
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 quantification guarantees for machine learning systems. Much of the current interest in conformal prediction is due to its ability to integrate into complex machine learning workflows, solving the problem of forming prediction sets without any assumptions on the form of the data generating distribution. Since contemporary machine learning algorithms have generally proven difficult to analyze directly, conformal prediction's main appeal is its ability to provide formal, finite-sample guarantees when paired with such methods. The goal of this book is to teach the reader about the fundamental technical arguments that arise when researching conformal prediction and related questions in distribution-free inference. Many of these proof strategies, especially the more recent ones, are scattered among research papers, making it difficult for researchers to understand where to look, which results are important, and how exactly the proofs work. We hope to bridge this gap by curating what we believe to be some of the most important results in the literature and presenting their proofs in a unified language, with illustrations, and with an eye towards pedagogy.
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representative citing papers
A noise-based orthogonalization framework for valid hypothesis testing that extends to post-selection inference under mild assumptions.
The relaxation to permutation invariance in distribution is shown to be insufficient for full conformal prediction validity under stochastic non-conformity measures, and Conditional Independence & Permutation Invariance in Distribution is provided as the correct sufficient condition.
Develops a weighted conformal clustering method that corrects for synthetic labels via conditional distribution shift to achieve finite-sample marginal coverage with explicit bounds for estimated weights.
The leave-a-window-out jackknife achieves valid predictive coverage in time series under mild model stability by introducing coefficients that quantify departure from cyclic exchangeability.
Two novel online conformal prediction algorithms enforce nested prediction sets across coverage levels using online optimization with regret bounds for quantile error control.
Non-asymptotic decomposition of conditional miscoverage in conformal prediction into score-estimation error, finite-sample calibration error, and intrinsic conditional-mismatch error, with guidance for model selection and extensions to covariate shift and structured data.
Trade-off functions between two distributions are finitely testable if and only if their Neyman-Pearson rejection regions are attainable by a VC-class of sets.
Risk-controlled post-processing yields a threshold-structured policy that follows the baseline except where an oracle fallback sharply reduces conditional violation risk, achieving O(log n/n) expected excess risk in i.i.d. settings and exact risk control under exchangeability.
Split conformal clustering with stochastic labels provides finite-sample marginal coverage guarantees for cluster label confidence sets, controlled by soft-label consistency and replace-one stability of the clustering algorithm.
Conformal risk control for bounded non-monotone losses over a grid of size m achieves excess risk of order sqrt(log m / n) with n calibration samples, which is minimax optimal.
ST-BCP tightens the coverage bound in Backward Conformal Prediction by applying a computable data-dependent transformation to nonconformity scores, reducing the average gap from 4.20% to 1.12% on benchmarks while proving superiority over the identity baseline.
PAC-Bayesian bounds are derived for quadratic closed-loop control via SLS parameterization, yielding Chernoff certificates for posteriors over responses, a mean-response deployment result, and a data-driven learning algorithm.
Machine learning models recover most warm-rain and ice microphysical process rates from standard ICON model outputs for accumulation intervals of 10 minutes or less using a two-step classification-regression approach with calibrated uncertainty.
MDCP constructs conformal prediction intervals for Markov processes with non-asymptotic unconditional coverage bounds under beta-mixing and asymptotic conditional validity using kernel estimators and PIT to iid-ify the data.
C-SymmPI reformulates conditional coverage as miscoverage error over a user-specified function class to deliver near-conditional guarantees under group symmetries and distributional invariance.
A conformal procedure for CoT replaces majority voting with weighted aggregation and calibrates abstention to guarantee low confident-error rates, achieving 90.1% selective accuracy on GSM8K by abstaining on under 5% of cases.
OCULAR applies conformal prediction to semantic perception data for local calibration of dynamics model uncertainty, yielding guaranteed prediction regions without environment-specific calibration data.
PASC converts multi-stage joint coverage into a single scalar conformal problem on the joint max nonconformity score, delivering finite-sample distribution-free guarantees and higher empirical coverage than Bonferroni or independent calibration.
A quantized model exchange framework for decentralized conformal novelty detection preserves conditional exchangeability and delivers finite-sample global FDR control.
A PIT-calibrated percentile interval method delivers finite-sample marginal coverage, asymptotic conditional coverage, and shorter intervals than prior conformal approaches.
An approximate inequality for the probability involving order statistics under near-i.i.d. conditions is established and applied to justify resampling-based statistical procedures.
Conformal inference produces robust prediction intervals for treatment effects under experimental attrition, outperforming complete-case, imputation, and weighting approaches in simulations.
The paper proposes AQCP, an algorithm that provides asymptotic average coverage guarantees for quantum conformal prediction under arbitrary hardware noise by repeated recalibration.
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Local Conformal Calibration of Dynamics Uncertainty from Semantic Images
OCULAR applies conformal prediction to semantic perception data for local calibration of dynamics model uncertainty, yielding guaranteed prediction regions without environment-specific calibration data.