# On the Out-of-Distribution Coverage of Combining Split Conformal Prediction and Bayesian Deep Learning

arXiv: https://arxiv.org/abs/2311.12688 · HTML: https://mlsanity.com/paper/2311.12688/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 30 of its 49 references that are in the map.
- First posted on arXiv 21 Nov 2023.

## Builds on (most cited first, 30 of 30)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Benchmarking Neural Network Robustness to Common Corruptions and Perturbations](https://mlsanity.com/paper/1903.12261/) (2019)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift](https://mlsanity.com/paper/1906.02530/) (2019)
- [MedMNIST v2 -- A large-scale lightweight benchmark for 2D and 3D biomedical image classification](https://mlsanity.com/paper/2110.14795/) (2021)
- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Conformal Prediction Under Covariate Shift](https://mlsanity.com/paper/1904.06019/) (2019)
- [The Liver Tumor Segmentation Benchmark (LiTS)](https://mlsanity.com/paper/1901.04056/) (2019)
- [Bayesian Deep Learning and a Probabilistic Perspective of Generalization](https://mlsanity.com/paper/2002.08791/) (2020)
- [Classification with Valid and Adaptive Coverage](https://mlsanity.com/paper/2006.02544/) (2020)
- [Uncertainty Sets for Image Classifiers using Conformal Prediction](https://mlsanity.com/paper/2009.14193/) (2020)
- [Laplace Redux -- Effortless Bayesian Deep Learning](https://mlsanity.com/paper/2106.14806/) (2021)
- [Conformal prediction beyond exchangeability](https://mlsanity.com/paper/2202.13415/) (2022)
- [Stochastic Gradient Hamiltonian Monte Carlo](https://mlsanity.com/paper/1402.4102/) (2014)
- [What Are Bayesian Neural Network Posteriors Really Like?](https://mlsanity.com/paper/2104.14421/) (2021)
- [Conformal Risk Control](https://mlsanity.com/paper/2208.02814/) (2022)
- [Least Ambiguous Set-Valued Classifiers with Bounded Error Levels](https://mlsanity.com/paper/1609.00451/) (2016)
- [Learn then Test: Calibrating Predictive Algorithms to Achieve Risk Control](https://mlsanity.com/paper/2110.01052/) (2021)
- [Learning Optimal Conformal Classifiers](https://mlsanity.com/paper/2110.09192/) (2021)
- [The Case for Bayesian Deep Learning](https://mlsanity.com/paper/2001.10995/) (2020)
- [Conformal Prediction Under Feedback Covariate Shift for Biomolecular Design](https://mlsanity.com/paper/2202.03613/) (2022)
- [On Uncertainty, Tempering, and Data Augmentation in Bayesian Classification](https://mlsanity.com/paper/2203.16481/) (2022)
- [Conformal Bayesian Computation](https://mlsanity.com/paper/2106.06137/) (2021)
- [Valid prediction intervals for regression problems](https://mlsanity.com/paper/2107.00363/) (2021)
- [Bayesian Optimization with Conformal Prediction Sets](https://mlsanity.com/paper/2210.12496/) (2022)
- [Bayes-optimal prediction with frequentist coverage control](https://mlsanity.com/paper/2105.14045/) (2021)
- [Empirical Frequentist Coverage of Deep Learning Uncertainty Quantification Procedures](https://mlsanity.com/paper/2010.03039/) (2020)
- [Calibration of Neural Networks](https://mlsanity.com/paper/2303.10761/) (2023)

## Abstract (arXiv)

Bayesian deep learning and conformal prediction are two methods that have been used to convey uncertainty and increase safety in machine learning systems. We focus on combining Bayesian deep learning with split conformal prediction and how this combination effects out-of-distribution coverage; particularly in the case of multiclass image classification. We suggest that if the model is generally underconfident on the calibration set, then the resultant conformal sets may exhibit worse out-of-distribution coverage compared to simple predictive credible sets. Conversely, if the model is overconfident on the calibration set, the use of conformal prediction may improve out-of-distribution coverage. We evaluate prediction sets as a result of combining split conformal methods and neural networks trained with (i) stochastic gradient descent, (ii) deep ensembles, and (iii) mean-field variational inference. Our results suggest that combining Bayesian deep learning models with split conformal prediction can, in some cases, cause unintended consequences such as reducing out-of-distribution coverage.