Distribution-free predictive inference for individual treatment effects is impossible: any valid set must have infinite expected length under standard assumptions with continuous covariates.
hub
Theoretical Foundations of Conformal Prediction
27 Pith papers cite this work. Polarity classification is still indexing.
27
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.
hub tools
citation-role summary
background 2
baseline 1
citation-polarity summary
representative citing papers
OCULAR calibrates dynamics uncertainty using perception from similar environments to give guaranteed prediction regions for unseen test conditions.
Two novel online conformal prediction algorithms enforce nested prediction sets across coverage levels using online optimization with regret bounds for quantile error control.
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.
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.
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.
GAIF dynamically adjusts testing thresholds with feedback for finite-sample FDR control in sequential settings and extends to conformal selection via feedback-driven model selection.
Develops non-asymptotic estimators for set cardinality via cascading exclusion that bridge classic extremes and apply to convex volumes and unseen species.
A cross-validated prediction-powered calibration technique that fine-tunes predictors and estimates synthetic label bias to produce prediction sets with coverage guarantees for wireless indoor localization using scarce calibration data.
Tube Loss is a novel loss function enabling simultaneous prediction interval bound estimation with asymptotic coverage guarantees, tunable positioning for skewed distributions, and trade-offs between coverage and width via single optimization.
A self-supervised conformal prediction method with equivariant bootstrapping enables uncertainty quantification for ill-posed imaging inverse problems such as weak lensing mass mapping without requiring ground truth calibration data.
Venn-Abers predictors are extended to unbounded regression via conformal prediction, producing point regressors that modestly improve efficiency over standard methods for large datasets.
Conformalized super learner builds prediction intervals by weighting conformity scores from base learners via a majority vote, delivering valid coverage for continuous outcomes under exchangeability and heterogeneity.
Formal connections between PAC bounds for three data-driven reachability methods are established, with empirical results showing they are not interchangeable despite similarities.
citing papers explorer
-
Impossibility of Distribution-Free Predictive Inference for Individual Treatment Effects
Distribution-free predictive inference for individual treatment effects is impossible: any valid set must have infinite expected length under standard assumptions with continuous covariates.
-
Local Conformal Calibration of Dynamics Uncertainty from Semantic Images
OCULAR calibrates dynamics uncertainty using perception from similar environments to give guaranteed prediction regions for unseen test conditions.
-
Online Conformal Prediction: Enforcing monotonicity via Online Optimization
Two novel online conformal prediction algorithms enforce nested prediction sets across coverage levels using online optimization with regret bounds for quantile error control.
-
When Are Trade-Off Functions Testable from Finite Samples?
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 of Decision Policies
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.
-
Inference for Clustering: Conformal Sets for Cluster Labels
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 under Non-Monotone Losses: Theory and Finite-Sample Guarantees
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: Tightening Coverage Bound for Backward Conformal Prediction via Non-Conformity Score Transformation
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.
-
Conditional Predictive Inference for General Structured Data with Group Symmetries
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.
-
Pause and Reflect: Conformal Aggregation for Chain-of-Thought Reasoning
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.
-
PASC: Pipeline-Aware Conformal Prediction with Joint Coverage Guarantees for Multi-Stage NLP and LLM Pipelines
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.
-
Decentralized Conformal Novelty Detection via Quantized Model Exchange
A quantized model exchange framework for decentralized conformal novelty detection preserves conditional exchangeability and delivers finite-sample global FDR control.
-
Conformalized Percentile Interval: Finite Sample Validity and Improved Conditional Performance
A PIT-calibrated percentile interval method delivers finite-sample marginal coverage, asymptotic conditional coverage, and shorter intervals than prior conformal approaches.
-
On a Probability Inequality for Order Statistics with Applications to Bootstrap, Conformal Prediction, and more
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 for Experimental Attrition in Social Science Research
Conformal inference produces robust prediction intervals for treatment effects under experimental attrition, outperforming complete-case, imputation, and weighting approaches in simulations.
-
Adaptive Conformal Prediction for Quantum Machine Learning
The paper proposes AQCP, an algorithm that provides asymptotic average coverage guarantees for quantum conformal prediction under arbitrary hardware noise by repeated recalibration.
-
Feedback-Enhanced Online Multiple Testing with Applications to Conformal Selection
GAIF dynamically adjusts testing thresholds with feedback for finite-sample FDR control in sequential settings and extends to conformal selection via feedback-driven model selection.
-
Estimating the size of a set using cascading exclusion
Develops non-asymptotic estimators for set cardinality via cascading exclusion that bridge classic extremes and apply to convex volumes and unseen species.
-
Reliable Wireless Indoor Localization via Cross-Validated Prediction-Powered Calibration
A cross-validated prediction-powered calibration technique that fine-tunes predictors and estimates synthetic label bias to produce prediction sets with coverage guarantees for wireless indoor localization using scarce calibration data.
-
Tube Loss: A Novel Approach for Prediction Interval Estimation
Tube Loss is a novel loss function enabling simultaneous prediction interval bound estimation with asymptotic coverage guarantees, tunable positioning for skewed distributions, and trade-offs between coverage and width via single optimization.
-
Self-Supervised Conformal Prediction with Equivariant Bootstrapping for Image Uncertainty Quantification
A self-supervised conformal prediction method with equivariant bootstrapping enables uncertainty quantification for ill-posed imaging inverse problems such as weak lensing mass mapping without requiring ground truth calibration data.
-
Inductive Venn-Abers and related regressors
Venn-Abers predictors are extended to unbounded regression via conformal prediction, producing point regressors that modestly improve efficiency over standard methods for large datasets.
-
Conformalized Super Learner
Conformalized super learner builds prediction intervals by weighting conformity scores from base learners via a majority vote, delivering valid coverage for continuous outcomes under exchangeability and heterogeneity.
-
Probably Approximately Correct (PAC) Guarantees for Data-Driven Reachability Analysis: A Theoretical and Empirical Comparison
Formal connections between PAC bounds for three data-driven reachability methods are established, with empirical results showing they are not interchangeable despite similarities.
-
Conformal prediction for uncertainties in the neutron star equation of state
Conformalized quantile regression applied post hoc to neutron star posterior samples yields reliable uncertainty bands validated by empirical coverage studies.
-
Aggregation in conformal e-classification
The paper experimentally studies cross-conformal e-prediction and conceptually simpler modifications for aggregating conformal e-predictors while retaining validity.
- A Unified Theory of Conditional Coverage in Conformal Prediction with Applications