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Conformal Bayes under Continuous Label Shift: Sensitivity Analysis and the Limits of Exact Validity

arXiv 2609.27976 ↗First posted 24 Aug 2026stat.ML cs.LGcited by 0

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Abstract (arXiv)

Conformal Bayes combines Bayesian posterior predictive scores with conformal calibration, but under continuous label shift both the score and calibration weight depend on the unknown response-marginal density ratio. Existing methods typically estimate one shift parameter from pseudo-labels or predictive samples and plug it into calibration. We instead propose Joint Tilt-Sensitivity Conformal Bayes (JTS-CB), which performs sensitivity analysis over a prespecified set of plausible tilts; its split-conformal realization is JTS-SCB. Each tilt jointly determines the Bayesian conformal score and conformal importance weight. JTS-SCB forms a bounded sensitivity envelope over candidate tilts, but its calibration-only construction does not inherit the exact finite-sample weighted-conformal guarantee. We therefore study a separate candidate-weighted exact counterpart and show that its usefulness depends sharply on tail behavior. For scalar linear exponential tilts, any nonzero candidate tilt makes the exact set unbounded. More generally, tail-growing density ratios produce the same pathology, whereas quadratic tilts with a negative coefficient on (y2) have vanishing tail weights and admit bounded exact inference on the original target. Ratio clipping provides a complementary bounded exact construction for a surrogate target when tails grow. Experiments show that strong plug-in predictive sampling can match the oracle when the shift is well identified, while sensitivity analysis is most useful for richer, weakly identified, or systematically biased shift models, at the cost of wider prediction sets.

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References · 18

  1. 2016Distribution-Free Predictive Inference For Regressioncited by 668
  2. 2019Conformal Prediction Under Covariate Shiftcited by 519
  3. 2018Detecting and Correcting for Label Shift with Black Box Predictorscited by 366
  4. 2022Conformal prediction beyond exchangeabilitycited by 355
  5. 2023Conformal Prediction With Conditional Guaranteescited by 152
  6. 2020A Unified View of Label Shift Estimationcited by 119
  7. 2021Distribution-free uncertainty quantification for classification under label shiftcited by 101
  8. 2020Robust Validation: Confident Predictions Even When Distributions Shiftcited by 82
  9. 2021Sensitivity Analysis of Individual Treatment Effects: A Robust Conformal Inference Approachcited by 62
  10. 2021Conformal Sensitivity Analysis for Individual Treatment Effectscited by 40
  11. 2021Conformal Bayesian Computationcited by 39
  12. 2017Sensitivity analysis for inverse probability weighting estimators via the percentile bootstrapcited by 33
6 more
  1. 2024Conformal Prediction for Causal Effects of Continuous Treatmentscited by 19
  2. 2024Not all distributional shifts are equal: Fine-grained robust conformal inferencecited by 16
  3. 2025Wasserstein-regularized Conformal Prediction under General Distribution Shiftcited by 15
  4. 2025Conformal Prediction under Levy-Prokhorov Distribution Shifts: Robustness to Local and Global Perturbationscited by 12
  5. 2026Conformal Bayes under Label Shift: Post-Hoc Calibration vs. In-Training Adaptationcited by 5
  6. 2026Conformal Bayes for Two-Sided Censored Gaussian Regression under Label Shiftcited by 2

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