# On Uncertainty, Tempering, and Data Augmentation in Bayesian Classification

arXiv: https://arxiv.org/abs/2203.16481 · HTML: https://mlsanity.com/paper/2203.16481/

## Key facts

- Cited by 46 papers in the map (data through 14 Oct 2026).
- Builds on 38 of its 61 references that are in the map.
- First posted on arXiv 30 Mar 2022.

## Builds on (most cited first, 30 of 38)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (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)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Identity Mappings in Deep Residual Networks](https://mlsanity.com/paper/1603.05027/) (2016)
- [AugMix: A Simple Data Processing Method to Improve Robustness and Uncertainty](https://mlsanity.com/paper/1912.02781/) (2019)
- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [Loss Surfaces, Mode Connectivity, and Fast Ensembling of DNNs](https://mlsanity.com/paper/1802.10026/) (2018)
- [A Simple Baseline for Bayesian Uncertainty in Deep Learning](https://mlsanity.com/paper/1902.02476/) (2019)
- [Predictive Uncertainty Estimation via Prior Networks](https://mlsanity.com/paper/1802.10501/) (2018)
- [Bayesian Deep Learning and a Probabilistic Perspective of Generalization](https://mlsanity.com/paper/2002.08791/) (2020)
- [Deep Kernel Learning](https://mlsanity.com/paper/1511.02222/) (2015)
- [Laplace Redux -- Effortless Bayesian Deep Learning](https://mlsanity.com/paper/2106.14806/) (2021)
- [Stochastic Gradient Hamiltonian Monte Carlo](https://mlsanity.com/paper/1402.4102/) (2014)
- [Are we done with ImageNet?](https://mlsanity.com/paper/2006.07159/) (2020)
- [What Are Bayesian Neural Network Posteriors Really Like?](https://mlsanity.com/paper/2104.14421/) (2021)
- [Identifying Mislabeled Data using the Area Under the Margin Ranking](https://mlsanity.com/paper/2001.10528/) (2020)
- [Cyclical Stochastic Gradient MCMC for Bayesian Deep Learning](https://mlsanity.com/paper/1902.03932/) (2019)
- [Efficient and Scalable Bayesian Neural Nets with Rank-1 Factors](https://mlsanity.com/paper/2005.07186/) (2020)
- [Practical Deep Learning with Bayesian Principles](https://mlsanity.com/paper/1906.02506/) (2019)
- [Modeling the Dynamics of PDE Systems with Physics-Constrained Deep Auto-Regressive Networks](https://mlsanity.com/paper/1906.05747/) (2019)
- [Bayesian Neural Network Priors Revisited](https://mlsanity.com/paper/2102.06571/) (2021)
- [Scalable Marginal Likelihood Estimation for Model Selection in Deep Learning](https://mlsanity.com/paper/2104.04975/) (2021)
- [Inconsistency of Bayesian Inference for Misspecified Linear Models, and a Proposal for Repairing It](https://mlsanity.com/paper/1412.3730/) (2014)
- [A Systematic Comparison of Bayesian Deep Learning Robustness in Diabetic Retinopathy Tasks](https://mlsanity.com/paper/1912.10481/) (2019)
- [Understanding Generalization through Visualizations](https://mlsanity.com/paper/1906.03291/) (2019)
- [A statistical theory of cold posteriors in deep neural networks](https://mlsanity.com/paper/2008.05912/) (2020)
- [Dirichlet-based Gaussian Processes for Large-scale Calibrated Classification](https://mlsanity.com/paper/1805.10915/) (2018)
- [Rethinking Parameter Counting in Deep Models: Effective Dimensionality Revisited](https://mlsanity.com/paper/2003.02139/) (2020)

## Built on by (most cited first, 30 of 46)

- [Variational Bayesian Last Layers](https://mlsanity.com/paper/2404.11599/) (2024)
- [Position: Bayesian Deep Learning is Needed in the Age of Large-Scale AI](https://mlsanity.com/paper/2402.00809/) (2024)
- [How to Build the Virtual Cell with Artificial Intelligence: Priorities and Opportunities](https://mlsanity.com/paper/2409.11654/) (2024)
- [Credal Bayesian Deep Learning](https://mlsanity.com/paper/2302.09656/) (2023)
- [Rethinking Aleatoric and Epistemic Uncertainty](https://mlsanity.com/paper/2412.20892/) (2024)
- [How Much Data Are Augmentations Worth? An Investigation into Scaling Laws, Invariance, and Implicit Regularization](https://mlsanity.com/paper/2210.06441/) (2022)
- [Is the Volume of a Credal Set a Good Measure for Epistemic Uncertainty?](https://mlsanity.com/paper/2306.09586/) (2023)
- [Second-Order Uncertainty Quantification: A Distance-Based Approach](https://mlsanity.com/paper/2312.00995/) (2023)
- [From Risk to Uncertainty: Generating Predictive Uncertainty Measures via Bayesian Estimation](https://mlsanity.com/paper/2402.10727/) (2024)
- [A Primer on Bayesian Neural Networks: Review and Debates](https://mlsanity.com/paper/2309.16314/) (2023)
- [Quantifying Aleatoric and Epistemic Uncertainty with Proper Scoring Rules](https://mlsanity.com/paper/2404.12215/) (2024)
- [A Novel Bayes' Theorem for Upper Probabilities](https://mlsanity.com/paper/2307.06831/) (2023)
- [Understanding the Detrimental Class-level Effects of Data Augmentation](https://mlsanity.com/paper/2401.01764/) (2023)
- [A Structured Review of Literature on Uncertainty in Machine Learning & Deep Learning](https://mlsanity.com/paper/2406.00332/) (2024)
- [Scalable Stochastic Gradient Riemannian Langevin Dynamics in Non-Diagonal Metrics](https://mlsanity.com/paper/2303.05101/) (2023)
- [Dirichlet-based Uncertainty Quantification for Personalized Federated Learning with Improved Posterior Networks](https://mlsanity.com/paper/2312.11230/) (2023)
- [Textual Bayes: Quantifying Prompt Uncertainty in LLM-Based Systems](https://mlsanity.com/paper/2506.10060/) (2025)
- [Training, Architecture, and Prior for Deterministic Uncertainty Methods](https://mlsanity.com/paper/2303.05796/) (2023)
- [Can a Confident Prior Replace a Cold Posterior?](https://mlsanity.com/paper/2403.01272/) (2024)
- [Stochasticity in Motion: An Information-Theoretic Approach to Trajectory Prediction](https://mlsanity.com/paper/2410.01628/) (2024)
- [Cooperative learning of Pl@ntNet's Artificial Intelligence algorithm: how does it work and how can we improve it?](https://mlsanity.com/paper/2406.03356/) (2024)
- [Learning to Explore for Stochastic Gradient MCMC](https://mlsanity.com/paper/2408.09140/) (2024)
- [Uncertainty Calibration in Bayesian Neural Networks via Distance-Aware Priors](https://mlsanity.com/paper/2207.08200/) (2022)
- [The fine print on tempered posteriors](https://mlsanity.com/paper/2309.05292/) (2023)
- [On Uncertainty Quantification for Near-Bayes Optimal Algorithms](https://mlsanity.com/paper/2403.19381/) (2024)
- [BayesAdapter: enhanced uncertainty estimation in CLIP few-shot adaptation](https://mlsanity.com/paper/2412.09718/) (2024)
- [If there is no underfitting, there is no Cold Posterior Effect](https://mlsanity.com/paper/2310.01189/) (2023)
- [Robust Classification by Coupling Data Mollification with Label Smoothing](https://mlsanity.com/paper/2406.01494/) (2024)
- [Learning Hyperparameters via a Data-Emphasized Variational Objective](https://mlsanity.com/paper/2502.01861/) (2025)
- [Rethinking Approximate Gaussian Inference in Classification](https://mlsanity.com/paper/2502.03366/) (2025)

## Abstract (arXiv)

Aleatoric uncertainty captures the inherent randomness of the data, such as measurement noise. In Bayesian regression, we often use a Gaussian observation model, where we control the level of aleatoric uncertainty with a noise variance parameter. By contrast, for Bayesian classification we use a categorical distribution with no mechanism to represent our beliefs about aleatoric uncertainty. Our work shows that explicitly accounting for aleatoric uncertainty significantly improves the performance of Bayesian neural networks. We note that many standard benchmarks, such as CIFAR, have essentially no aleatoric uncertainty. Moreover, we show data augmentation in approximate inference has the effect of softening the likelihood, leading to underconfidence and profoundly misrepresenting our honest beliefs about aleatoric uncertainty. Accordingly, we find that a cold posterior, tempered by a power greater than one, often more honestly reflects our beliefs about aleatoric uncertainty than no tempering -- providing an explicit link between data augmentation and cold posteriors. We show that we can match or exceed the performance of posterior tempering by using a Dirichlet observation model, where we explicitly control the level of aleatoric uncertainty, without any need for tempering.