# Weighted Bayesian Conformal Prediction

arXiv: https://arxiv.org/abs/2604.06464 · HTML: https://mlsanity.com/paper/2604.06464/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 37 references that are in the map.
- First posted on arXiv 7 Apr 2026.

## Builds on (most cited first, 20 of 20)

- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Conformal Prediction Under Covariate Shift](https://mlsanity.com/paper/1904.06019/) (2019)
- [Conformal prediction beyond exchangeability](https://mlsanity.com/paper/2202.13415/) (2022)
- [Conformal Risk Control](https://mlsanity.com/paper/2208.02814/) (2022)
- [Distribution-Free, Risk-Controlling Prediction Sets](https://mlsanity.com/paper/2101.02703/) (2021)
- [Conformal Inference of Counterfactuals and Individual Treatment Effects](https://mlsanity.com/paper/2006.06138/) (2020)
- [Localized Conformal Prediction: A Generalized Inference Framework for Conformal Prediction](https://mlsanity.com/paper/2106.08460/) (2021)
- [Distributional conformal prediction](https://mlsanity.com/paper/1909.07889/) (2019)
- [Doubly Robust Calibration of Prediction Sets under Covariate Shift](https://mlsanity.com/paper/2203.01761/) (2022)
- [Conformal Bayesian Computation](https://mlsanity.com/paper/2106.06137/) (2021)
- [Prediction Sets Adaptive to Unknown Covariate Shift](https://mlsanity.com/paper/2203.06126/) (2022)
- [Quantile Risk Control: A Flexible Framework for Bounding the Probability of High-Loss Predictions](https://mlsanity.com/paper/2212.13629/) (2022)
- [Selective Conformal Risk Control](https://mlsanity.com/paper/2512.12844/) (2025)
- [Spatial Conformal Inference through Localized Quantile Regression](https://mlsanity.com/paper/2412.01098/) (2024)
- [Conformal Prediction as Bayesian Quadrature](https://mlsanity.com/paper/2502.13228/) (2025)
- [Uncertainty quantification in automated valuation models with spatially weighted conformal prediction](https://mlsanity.com/paper/2312.06531/) (2023)
- [Generalization and Informativeness of Weighted Conformal Risk Control Under Covariate Shift](https://mlsanity.com/paper/2501.11413/) (2025)
- [GeoConformal prediction: a model-agnostic framework of measuring the uncertainty of spatial prediction](https://mlsanity.com/paper/2412.08661/) (2024)

## Built on by (most cited first, 1 of 1)

- [The Exceedance Design Effect: Effective Sample Size for Thresholds under Clustering](https://mlsanity.com/paper/2608.21262/) (2026)

## Abstract (arXiv)

Machine learning predictors are rarely deployed on data that match the data they were calibrated on. Conformal prediction and its risk-control generalization promise distribution-free guarantees at deployment, but only under exchangeability or a covariate shift whose likelihood ratio is known exactly -- and the estimated-ratio case, the one that occurs in practice, is explicitly open, out of reach of the Bayesian construction available under exchangeability. We reach it from a different starting point: pushing a Dirichlet process prior on the calibration distribution through the likelihood ratio yields the exact Bayesian posterior over the deployed risk. That posterior is exact given the weight function, which at deployment is itself estimated, so we further prove finite-sample upper and lower bounds on the risk the selected threshold actually incurs, in terms of the weight-estimation error and the conditional shift. On synthetic and real covariate shifts, in regression and classification, the realized failure rate then stays close to target where shift-blind selection fails, and what deployment receives is a posterior over the risk of every threshold rather than a single number.