Bayesian Conformal Prediction via the Bayesian Bootstrap

TL;DR

This paper presents a Bayesian conformal prediction method using the Bayesian bootstrap that improves uncertainty quantification by providing well-calibrated and sharp prediction intervals across various models and data settings.

Contribution

It introduces a practical Bayesian conformal approach leveraging influence functions and data-driven tuning of the Dirichlet parameter for better calibration and sharpness.

Findings

Improved empirical coverage over standard Bayesian methods.

Enhanced log-score performance across multiple models.

Fast and easy-to-implement calibration procedure.

Abstract

Reliable uncertainty quantification remains a central challenge in predictive modeling. While Bayesian methods are theoretically appealing, their predictive intervals can exhibit poor frequentist calibration, particularly with small sample sizes or model misspecification. We introduce a practical and broadly applicable Bayesian conformal approach based on the influence-function Bayesian bootstrap (BB) with data-driven tuning of the Dirichlet concentration parameter, {\alpha}. By efficiently approximating the Bayesian bootstrap predictive distribution via influence functions and calibrating {\alpha} to optimize empirical coverage or average log-probability, our method constructs prediction intervals and distributions that are both well-calibrated and sharp. Across a range of regression models and data settings, this Bayesian conformal framework consistently yields improved empirical coverage and log-score compared to standard Bayesian posteriors. Our procedure is fast, easy to implement, and offers a flexible approach for distributional calibration in predictive modeling.