# Calibrating Bayesian Learning via Regularization, Confidence Minimization, and Selective Inference

arXiv: https://arxiv.org/abs/2404.11350 · HTML: https://mlsanity.com/paper/2404.11350/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 46 of its 66 references that are in the map.
- First posted on arXiv 17 Apr 2024.

## Builds on (most cited first, 30 of 46)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [Energy-based Out-of-distribution Detection](https://mlsanity.com/paper/2010.03759/) (2020)
- [Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift](https://mlsanity.com/paper/1906.02530/) (2019)
- [Deep Anomaly Detection with Outlier Exposure](https://mlsanity.com/paper/1812.04606/) (2018)
- [Selective Classification for Deep Neural Networks](https://mlsanity.com/paper/1705.08500/) (2017)
- [Scaling Out-of-Distribution Detection for Real-World Settings](https://mlsanity.com/paper/1911.11132/) (2019)
- [Likelihood Ratios for Out-of-Distribution Detection](https://mlsanity.com/paper/1906.02845/) (2019)
- [Calibrating Deep Neural Networks using Focal Loss](https://mlsanity.com/paper/2002.09437/) (2020)
- [SelectiveNet: A Deep Neural Network with an Integrated Reject Option](https://mlsanity.com/paper/1901.09192/) (2019)
- [Recent Advances in Open Set Recognition: A Survey](https://mlsanity.com/paper/1811.08581/) (2018)
- [Verified Uncertainty Calibration](https://mlsanity.com/paper/1909.10155/) (2019)
- [Robots That Ask For Help: Uncertainty Alignment for Large Language Model Planners](https://mlsanity.com/paper/2307.01928/) (2023)
- [Monte Carlo Gradient Estimation in Machine Learning](https://mlsanity.com/paper/1906.10652/) (2019)
- [Conformal Language Modeling](https://mlsanity.com/paper/2306.10193/) (2023)
- [Conformal Prediction with Large Language Models for Multi-Choice Question Answering](https://mlsanity.com/paper/2305.18404/) (2023)
- [On Calibration and Out-of-domain Generalization](https://mlsanity.com/paper/2102.10395/) (2021)
- [Self-Adaptive Training: beyond Empirical Risk Minimization](https://mlsanity.com/paper/2002.10319/) (2020)
- [Improving model calibration with accuracy versus uncertainty optimization](https://mlsanity.com/paper/2012.07923/) (2020)
- [Safe Planning in Dynamic Environments using Conformal Prediction](https://mlsanity.com/paper/2210.10254/) (2022)
- [Plex: Towards Reliability using Pretrained Large Model Extensions](https://mlsanity.com/paper/2207.07411/) (2022)
- [Soft Calibration Objectives for Neural Networks](https://mlsanity.com/paper/2108.00106/) (2021)
- [Calibration in Deep Learning: A Survey of the State-of-the-Art](https://mlsanity.com/paper/2308.01222/) (2023)
- [Generalized Variational Inference: Three arguments for deriving new Posteriors](https://mlsanity.com/paper/1904.02063/) (2019)

## Built on by (most cited first, 7 of 7)

- [Distilling Calibration via Conformalized Credal Inference](https://mlsanity.com/paper/2501.06066/) (2025)
- [Uncertainty Quantification and Data Efficiency in AI: An Information-Theoretic Perspective](https://mlsanity.com/paper/2512.05267/) (2025)
- [Optimized Certainty Equivalent Risk-Controlling Prediction Sets](https://mlsanity.com/paper/2602.13660/) (2026)
- [Reliable Inference in Edge-Cloud Model Cascades via Conformal Alignment](https://mlsanity.com/paper/2510.17543/) (2025)
- [Conformal Changepoint Localization and Root Cause Analysis with Corrupted Observations](https://mlsanity.com/paper/2607.26481/) (2026)
- [Bayes2IMC: In-Memory Computing for Bayesian Binary Neural Networks](https://mlsanity.com/paper/2411.07902/) (2024)
- [Attention-Based Feature Online Conformal Prediction for Time Series](https://mlsanity.com/paper/2511.15838/) (2025)

## Abstract (arXiv)

The application of artificial intelligence (AI) models in fields such as engineering is limited by the known difficulty of quantifying the reliability of an AI's decision. A well-calibrated AI model must correctly report its accuracy on in-distribution (ID) inputs, while also enabling the detection of out-of-distribution (OOD) inputs. A conventional approach to improve calibration is the application of Bayesian ensembling. However, owing to computational limitations and model misspecification, practical ensembling strategies do not necessarily enhance calibration. This paper proposes an extension of variational inference (VI)-based Bayesian learning that integrates calibration regularization for improved ID performance, confidence minimization for OOD detection, and selective calibration to ensure a synergistic use of calibration regularization and confidence minimization. The scheme is constructed successively by first introducing calibration-regularized Bayesian learning (CBNN), then incorporating out-of-distribution confidence minimization (OCM) to yield CBNN-OCM, and finally integrating also selective calibration to produce selective CBNN-OCM (SCBNN-OCM). Selective calibration rejects inputs for which the calibration performance is expected to be insufficient. Numerical results illustrate the trade-offs between ID accuracy, ID calibration, and OOD calibration attained by both frequentist and Bayesian learning methods. Among the main conclusions, SCBNN-OCM is seen to achieve best ID and OOD performance as compared to existing state-of-the-art approaches at the cost of rejecting a sufficiently large number of inputs.