# Not Just How Much, But Where: Decomposing Epistemic Uncertainty into Per-Class Contributions

arXiv: https://arxiv.org/abs/2602.21160 · HTML: https://mlsanity.com/paper/2602.21160/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 40 references that are in the map.
- First posted on arXiv 24 Feb 2026.

## Builds on (most cited first, 27 of 27)

- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Selective Classification for Deep Neural Networks](https://mlsanity.com/paper/1705.08500/) (2017)
- [Deep Bayesian Active Learning with Image Data](https://mlsanity.com/paper/1703.02910/) (2017)
- [Evidential Deep Learning to Quantify Classification Uncertainty](https://mlsanity.com/paper/1806.01768/) (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)
- [Weight Uncertainty in Neural Networks](https://mlsanity.com/paper/1505.05424/) (2015)
- [Deep Learning for Classical Japanese Literature](https://mlsanity.com/paper/1812.01718/) (2018)
- [Laplace Redux -- Effortless Bayesian Deep Learning](https://mlsanity.com/paper/2106.14806/) (2021)
- [Evaluating Scalable Bayesian Deep Learning Methods for Robust Computer Vision](https://mlsanity.com/paper/1906.01620/) (2019)
- [Understanding Measures of Uncertainty for Adversarial Example Detection](https://mlsanity.com/paper/1803.08533/) (2018)
- [Quantifying Aleatoric and Epistemic Uncertainty in Machine Learning: Are Conditional Entropy and Mutual Information Appropriate Measures?](https://mlsanity.com/paper/2209.03302/) (2022)
- [Striking the Right Balance with Uncertainty](https://mlsanity.com/paper/1901.07590/) (2019)
- [Benchmarking Uncertainty Disentanglement: Specialized Uncertainties for Specialized Tasks](https://mlsanity.com/paper/2402.19460/) (2024)
- [Know Your Limits: Uncertainty Estimation with ReLU Classifiers Fails at Reliable OOD Detection](https://mlsanity.com/paper/2012.05329/) (2020)
- [Label-wise Aleatoric and Epistemic Uncertainty Quantification](https://mlsanity.com/paper/2406.02354/) (2024)
- [Evidential Uncertainty Quantification: A Variance-Based Perspective](https://mlsanity.com/paper/2311.11367/) (2023)
- [A Quantitative Comparison of Epistemic Uncertainty Maps Applied to Multi-Class Segmentation](https://mlsanity.com/paper/2109.10702/) (2021)
- [Class Uncertainty: A Measure to Mitigate Class Imbalance](https://mlsanity.com/paper/2311.14090/) (2023)
- [Measuring Orthogonality as the Blind-Spot of Uncertainty Disentanglement](https://mlsanity.com/paper/2408.12175/) (2024)
- [Singular Bayesian Neural Networks](https://mlsanity.com/paper/2602.00387/) (2026)

## Built on by (most cited first, 2 of 2)

- [Reliable Automated Triage in Spanish Clinical Notes: A Hybrid Framework for Risk-Aware HIV Suspicion Identification](https://mlsanity.com/paper/2605.21256/) (2026)
- [Not All Confusion Is Equal: A Source-Aware Uncertainty Diagnosis for Fine-Grained Aircraft Detection](https://mlsanity.com/paper/2609.29959/) (2026)

## Abstract (arXiv)

In safety-critical classification, the cost of failure is often asymmetric, yet Bayesian deep learning summarises epistemic uncertainty with a single scalar, mutual information (MI), that cannot distinguish whether a model's ignorance involves a benign or safety-critical class. We decompose MI into a per-class vector Ck(x)=σk2/(2μk), with μk=mathbbE[pk] and σk2=Var[pk] across posterior samples. The decomposition follows from a second-order Taylor expansion of the entropy; the 1/μk weighting corrects boundary suppression and makes Ck comparable across rare and common classes. By construction sumk Ck ≈ MI, and a companion skewness diagnostic flags inputs where the approximation degrades. After characterising the axiomatic properties of Ck, we validate it on three tasks: (i) selective prediction for diabetic retinopathy, where critical-class Ck reduces selective risk by 34.7% over MI and 56.2% over variance baselines; (ii) out-of-distribution detection on clinical and image benchmarks, where sumk Ck achieves the highest AUROC and the per-class view exposes asymmetric shifts invisible to MI; and (iii) a controlled label-noise study in which sumk Ck shows less sensitivity to injected aleatoric noise than MI under end-to-end Bayesian training, while both metrics degrade under transfer learning. Across all tasks, the quality of the posterior approximation shapes uncertainty at least as strongly as the choice of metric, suggesting that how uncertainty is propagated through the network matters as much as how it is measured.