# Robust Bayes-Assisted Conformal Prediction

arXiv: https://arxiv.org/abs/2607.04236 · HTML: https://mlsanity.com/paper/2607.04236/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 28 of its 50 references that are in the map.
- First posted on arXiv 5 Jul 2026.

## Builds on (most cited first, 28 of 28)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Conformal Prediction Under Covariate Shift](https://mlsanity.com/paper/1904.06019/) (2019)
- [Age Progression/Regression by Conditional Adversarial Autoencoder](https://mlsanity.com/paper/1702.08423/) (2017)
- [Classification with Valid and Adaptive Coverage](https://mlsanity.com/paper/2006.02544/) (2020)
- [Adaptive Conformal Inference Under Distribution Shift](https://mlsanity.com/paper/2106.00170/) (2021)
- [Least Ambiguous Set-Valued Classifiers with Bounded Error Levels](https://mlsanity.com/paper/1609.00451/) (2016)
- [Bayesian Neural Network Priors Revisited](https://mlsanity.com/paper/2102.06571/) (2021)
- [Localized Conformal Prediction: A Generalized Inference Framework for Conformal Prediction](https://mlsanity.com/paper/2106.08460/) (2021)
- [Priors in Bayesian Deep Learning: A Review](https://mlsanity.com/paper/2105.06868/) (2021)
- [Conformal Prediction using Conditional Histograms](https://mlsanity.com/paper/2105.08747/) (2021)
- [Conformal Bayesian Computation](https://mlsanity.com/paper/2106.06137/) (2021)
- [Length Optimization in Conformal Prediction](https://mlsanity.com/paper/2406.18814/) (2024)
- [Boosted Conformal Prediction Intervals](https://mlsanity.com/paper/2406.07449/) (2024)
- [Conformal Prediction with Missing Values](https://mlsanity.com/paper/2306.02732/) (2023)
- [Probabilistic Conformal Prediction with Approximate Conditional Validity](https://mlsanity.com/paper/2407.01794/) (2024)
- [Bayes-optimal prediction with frequentist coverage control](https://mlsanity.com/paper/2105.14045/) (2021)
- [Improving Adaptive Conformal Prediction Using Self-Supervised Learning](https://mlsanity.com/paper/2302.12238/) (2023)
- [How Reliable is Your Regression Model's Uncertainty Under Real-World Distribution Shifts?](https://mlsanity.com/paper/2302.03679/) (2023)
- [Efficiency of conformalized ridge regression](https://mlsanity.com/paper/1404.2083/) (2014)
- [On the Expected Size of Conformal Prediction Sets](https://mlsanity.com/paper/2306.07254/) (2023)
- [A Conformal Prediction Score that is Robust to Label Noise](https://mlsanity.com/paper/2405.02648/) (2024)
- [On the Hyperprior Choice for the Global Shrinkage Parameter in the Horseshoe Prior](https://mlsanity.com/paper/1610.05559/) (2016)
- [Optimal Conformal Prediction for Small Areas](https://mlsanity.com/paper/2204.08122/) (2022)
- [Bayes-assisted Confidence Regions: Focal Point Estimator and Bounded-influence Priors](https://mlsanity.com/paper/2410.20169/) (2024)
- [The Interplay between Bayesian Inference and Conformal Prediction](https://mlsanity.com/paper/2510.26930/) (2025)
- [Frequentist Prediction Sets for Species Abundance using Indirect Information](https://mlsanity.com/paper/2311.15860/) (2023)

## Abstract (arXiv)

Bayes-assisted conformal prediction combines the strengths of Bayesian modelling with exact, distribution-free frequentist coverage guarantees. Although conformal validity is preserved even when the Bayesian working model (BWM) is misspecified, the size of the resulting prediction sets can degrade substantially when the prior is poorly aligned with the observed data. We address this limitation by introducing RoBAS (Robust Bayes-Assisted Shrinkage): a Bayes-assisted framework for constructing robust nonconformity scores, with two instantiations: one induced by a heavy-tailed BWM, and a closed-form empirical Bayes shrinkage score. The resulting scores adapt to the quality of the working information encoded in the prior: when this information is reliable, they exploit it to produce efficient prediction sets; when it is weak or inaccurate, they revert to the Distance-To-Average (DTA) score, a robust non-informative baseline. We evaluate the proposed scores on tabular and image regression tasks where the training distribution may differ from the calibration and test distributions, while the calibration and test data themselves remain exchangeable. We find that they are competitive with widely used scores in the absence of such shift, while substantially reducing interval widths in shifted settings.