# Being Bayesian about Categorical Probability

arXiv: https://arxiv.org/abs/2002.07965 · HTML: https://mlsanity.com/paper/2002.07965/

## Key facts

- Cited by 35 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Feb 2020.

## Built on by (most cited first, 30 of 35)

- [A Survey of Uncertainty in Deep Neural Networks](https://mlsanity.com/paper/2107.03342/) (2021)
- [Prior and Posterior Networks: A Survey on Evidential Deep Learning Methods For Uncertainty Estimation](https://mlsanity.com/paper/2110.03051/) (2021)
- [Better Uncertainty Calibration via Proper Scores for Classification and Beyond](https://mlsanity.com/paper/2203.07835/) (2022)
- [Sample-dependent Adaptive Temperature Scaling for Improved Calibration](https://mlsanity.com/paper/2207.06211/) (2022)
- [Post-hoc Uncertainty Learning using a Dirichlet Meta-Model](https://mlsanity.com/paper/2212.07359/) (2022)
- [Exploring Predictive Uncertainty and Calibration in NLP: A Study on the Impact of Method & Data Scarcity](https://mlsanity.com/paper/2210.15452/) (2022)
- [Dirichlet-based Uncertainty Calibration for Active Domain Adaptation](https://mlsanity.com/paper/2302.13824/) (2023)
- [Uncertainty Estimation by Density Aware Evidential Deep Learning](https://mlsanity.com/paper/2409.08754/) (2024)
- [Robust Semantic Segmentation with Superpixel-Mix](https://mlsanity.com/paper/2108.00968/) (2021)
- [Are Uncertainty Quantification Capabilities of Evidential Deep Learning a Mirage?](https://mlsanity.com/paper/2402.06160/) (2024)
- [EdVAE: Mitigating Codebook Collapse with Evidential Discrete Variational Autoencoders](https://mlsanity.com/paper/2310.05718/) (2023)
- [Ambiguous Images With Human Judgments for Robust Visual Event Classification](https://mlsanity.com/paper/2210.03102/) (2022)
- [Explainable Artificial Intelligence for Bayesian Neural Networks: Towards trustworthy predictions of ocean dynamics](https://mlsanity.com/paper/2205.00202/) (2022)
- [Overcoming Recency Bias of Normalization Statistics in Continual Learning: Balance and Adaptation](https://mlsanity.com/paper/2310.08855/) (2023)
- [Consistent and Asymptotically Unbiased Estimation of Proper Calibration Errors](https://mlsanity.com/paper/2312.08589/) (2023)
- [Segmenting Known Objects and Unseen Unknowns without Prior Knowledge](https://mlsanity.com/paper/2209.05407/) (2022)
- [Discretization-Induced Dirichlet Posterior for Robust Uncertainty Quantification on Regression](https://mlsanity.com/paper/2308.09065/) (2023)
- [Revisiting Softmax for Uncertainty Approximation in Text Classification](https://mlsanity.com/paper/2210.14037/) (2022)
- [Optimizing Estimators of Squared Calibration Errors in Classification](https://mlsanity.com/paper/2410.07014/) (2024)
- [Fuzzy Classification of Multi-intent Utterances](https://mlsanity.com/paper/2104.10830/) (2021)
- [A Confidence-based Acquisition Model for Self-supervised Active Learning and Label Correction](https://mlsanity.com/paper/2310.08944/) (2023)
- [Improving self-training under distribution shifts via anchored confidence with theoretical guarantees](https://mlsanity.com/paper/2411.00586/) (2024)
- [Enhancing Uncertainty Estimation and Interpretability via Bayesian Non-negative Decision Layer](https://mlsanity.com/paper/2505.22199/) (2025)
- [Evidential Transformation Network: Turning Pretrained Models into Evidential Models for Post-hoc Uncertainty Estimation](https://mlsanity.com/paper/2604.08627/) (2026)
- [Switchable Representation Learning Framework with Self-compatibility](https://mlsanity.com/paper/2206.08289/) (2022)
- [Bayesian Evidential Learning for Few-Shot Classification](https://mlsanity.com/paper/2207.13137/) (2022)
- [IW-GAE: Importance Weighted Group Accuracy Estimation for Improved Calibration and Model Selection in Unsupervised Domain Adaptation](https://mlsanity.com/paper/2310.10611/) (2023)
- [Subjective Logic Encodings](https://mlsanity.com/paper/2502.12225/) (2025)
- [MedBayes-Lite: A Clinical Uncertainty Governance Layer for Risk-Aware Medical Decision Support](https://mlsanity.com/paper/2511.16625/) (2025)
- [Scene Uncertainty and the Wellington Posterior of Deterministic Image Classifiers](https://mlsanity.com/paper/2106.13870/) (2021)

## Abstract (arXiv)

Neural networks utilize the softmax as a building block in classification tasks, which contains an overconfidence problem and lacks an uncertainty representation ability. As a Bayesian alternative to the softmax, we consider a random variable of a categorical probability over class labels. In this framework, the prior distribution explicitly models the presumed noise inherent in the observed label, which provides consistent gains in generalization performance in multiple challenging tasks. The proposed method inherits advantages of Bayesian approaches that achieve better uncertainty estimation and model calibration. Our method can be implemented as a plug-and-play loss function with negligible computational overhead compared to the softmax with the cross-entropy loss function.